FINAL CA...XYZ Ltd has issued convertible debentures with interest rate of 12%. Every debenture has an option to convert to 20 equity shares at any time until the date of maturity

CAFCINTER CAFINAL CA

FINAL CAREVISION NOTES

MAY '19

Strategic Financial Management

Bond Management

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J.K.SHAH CLASSES FINAL C.A. – FINANCIAL REPORTING

: 1 : REVISION NOTES – MAY ‘19

Q.1. A is willing to purchase a 5 years Rs. 1000 par value bond having a coupon rate of 9%.

A’s required rate of return is 10%. How much A should pay to purchase the bond if it matures at par.

Q.2. A PSU is proposing to sell a 8 years bond of Rs. 1000 at 10% coupon rate per annum.

The bond amount will be amortised equally over its life. If an investor has a minimum required rate of return of 8%, what is the bond’s present value.

Q.3. A 6 years bond of Rs.1000 has an annual rate of interest of 14%. The interest is paid

half yearly. If the required rate of return is 16% what is the value of the bond. Q.4. XYZ Ltd has issued convertible debentures with interest rate of 12%. Every debenture

has an option to convert to 20 equity shares at any time until the date of maturity. Debentures will be redeemed at Rs. Rs. Rs. Rs. 100 on maturity which is after 5 years. An investor normally requires a rate of return of 8% per annum on a 5 year security. As an investor when will you exercise the purchase option if MV of ES is (a) `̀̀̀ 4, (b) `̀̀̀ 5 or (c) `̀̀̀ 6.

Q.5. There is a 9% 5 year bond issue in the market. The issue price is Rs.Rs.Rs.Rs. 90 and the

redemption price is Rs.Rs.Rs.Rs. 105. For an investor with marginal income tax rate of 30% and capital gains tax rate of 10% (assuming no indexation), what is the post-tax yield to maturity?

Q.6. An investor is considering the purchase of the following bond:

Face value Rs.Rs.Rs.Rs. 100 Coupon rate 11% Maturity 3 years i. If he wants a yield of 13% what is the maximum price he should be ready to pay

for the bond? ii. If the bond is selling for Rs.Rs.Rs.Rs. 97.60 what should be his yield?

Q.7. Given a 2 year 8% annual coupon bond with a face value of ` 1000 and with annual

coupon payments that is fully taxable and selling at par and an identical bond that is tax free, what would the yield and price on the tax free bond have to be for an investor in a 35% tax bracket to be indifferent between the two bonds

Q.8. A bond pays Rs.Rs.Rs.Rs. 90 interest annually into perpetuity.

i. What is its value if the current yield is 10% ii. If the current yield changes to 8% and 12% then what is its value.

Q.9. The bonds of Texas Industries of face value ` 100 with 10% coupon paid semiannually

is presently selling at 5% discount on the face value. These bonds will be redeemed at par by equal instalment at the end of 5th and 6th years. The effective tax rate of Texas is 40%. What is the YTM of the bond.

Q.10. An investor purchased at a par a bond with a face value of ` 1000. The bond had 5

years to maturity and a 10% coupon rate. The bond was called two years later for a price of Rs. 1200 after making its second annual interest payment. He then reinvested the proceeds in a bond selling at its face value of ` 1000 with three years to maturity and a 7% coupon rate. What was his actual YTM over the 5 year period.

BOND OF MANAGEMENT



Q.11. An investor acquired at par a bond for ` 1000 that offered a 15% coupon rate. At the time of purchase, the bond had 4 years to maturity. Assuming annual interest payments, calculate his actual yield to maturity if all the interest payments were reinvested in an investment earning 18% per yer. What would his actual yield to maturity be if all interest payments were spent immediately upon receipt.

Q.12. The following data are available for a bond;

Face value `̀̀̀ 1,000 Coupon rate 16% Years to Maturity 6 Redemption value `̀̀̀1,000 Yield to maturity 17%

What are the current market price, duration and volatility of this bond? Calculate the expected market price, if we witness an increase in required yield by 75 basis points.

Q.13. Find the current market price of a bond having face value of `̀̀̀ 1,00,000 redeemable

after 6 years maturity with YTM at 16% payable annually and duration of 4.3202 years. Given 1.166 = 2.4364

Q.14 .(a) Consider two bonds with 5 years to maturity and other with 20 years to maturity.

Both the bonds have a face value of `̀̀̀ 1,00,000 and coupon rate of 8% (with annual interest payments and both are selling at par. Assume that the yields of both of bonds fall to 6%, whether the price of the bond will increase or decrease? What percentage of this increase / decrease comes from a change in the present value of bond’s principal amount and what percentage of this increase / decrease comes from a change in the present value of bond’s interest payment.

(b) Consider a bond selling at its par value of `̀̀̀1000 with 6 years to maturity and a 7% coupon rate (with annual interest payment), what is the bond’s duration?

(c) If the YTM of the bond in (b) above increase to 10%, how it affects the bond’s duration? And why?

(d) Why should the duration of a coupon carrying bond always be less that the time to maturity?.

Q.15. The investment portfolio of a bank is as follows :

Government Bond Coupon rate Purchase rate (FV `̀̀̀ 100)

Duration (years)

GOI 2006 11.68% 106.50 3.50

GOI 2010 7.55% 105.00 6.50

GOI 2015 7.38% 105.00 7.50

GOI 2022 8.35% 110.00 8.75

GOI 2032 7.95% 101.00 13.00

Face value of total investment in Rs.Rs.Rs.Rs. 5 crores in each government bond. Calculate the actual investment in the portfolio. What is a suitable action to churn out investment portfolio in the following scenario: a. Interest rates are expected to lower by 25 basis points b. Interest rates are expected to rise by 75 basis points

Also calculate the revised duration of investment portfolio in each scenario.



Q.16. M/s Transindia Ltd is contemplating calling `̀̀̀ 3 crores of 30 years Rs.Rs.Rs.Rs. 1000 bonds issued 5 years ago with a coupon interest rate of 14%. The bonds have a call price of `̀̀̀

1140 and had initially collected proceeds of `̀̀̀ 2.91 crores due to a discount of `̀̀̀ 30 per bond. The initial floating cost was `̀̀̀ 3,60,000. The company intends to sell `̀̀̀ 3 crores of 12% coupon rate, 25 years bonds to raise funds for retiring the old bonds. It proposes to sell the new bonds at their par value of `̀̀̀1000. The estimated flotation cost

is `̀̀̀ 4,00,000. The company is paying 40% tax and its after tax cost of debt is 8%. As the new bonds must first be sold and their proceeds then used to retire old bonds, the company expects a two months period of overlapping interest during which interest must be paid on both the old and new bonds. What is the feasibility of refunding bonds?

Q.17. The data given below relates to a convertible bond

Face Value `̀̀̀ 250 Coupon rate 12% No of shares per bond 20 Market price of share `̀̀̀ 12 Straight value of bond `̀̀̀235 Market price of convertible bond `̀̀̀ 265

Calculate: a) The stock value of bond b) The percentage of downside risk c) The conversion premium d) The conversion parity price of bond

Q.18. Duration & IMMUNISATION OF PORTFOLIO

A company has to pay Rs. 10 million after 6 years from today. The company wants to fund this obligation today only. The current interest rate in the market is 8%. Two zero coupon bonds are traded in the market on the basis of 8% YTM – one with a 5 year maturity and the other with a 7 year maturity. Suggest the interest rate immunized investment plan. Calculate the total amount to be received from the investments in following three cases :

a. market interest rates remain unchanged throughout the period of 6 years .

b. Market interest rates declines to 6%.

c. Market interest rate rises to 10%.

J.K.SHAH CLASSES FINAL C.A. – STRATEGIC FINANCIAL MANAGEMENT


Q.1. A company is proposing to set-up a project worth ` 7.5 lacs. The following additional

information is available : (a) The project will result in production of product X as below :

i) First year 10,000 units ii) Second year 20,000 units iii) Third year onwards till the end of eighth year 50,000 units annually.

(b) The company can market the entire production thinking of pricing it at ` 10.50 in the first year and ` 11 in subsequent years.

(c) The estimated relevant cost per unit is ` 8.50 in the first year and ` 8 from the second year onwards.

(d) Life of the machine is estimated to be eight years at the end of which the company expects to sell the equipment for ` 2.5 lacs.

(e) The depreciation is to be calculated as per Income Tax provision at 25%. (f) This project will reduce the cost of certain existing operations at ` 5,000 per

annum uniformly. Discounting rate is 10%. Is the investment worthwhile? Assume tax rate of 52.5%.

Q.2. A large profit making company is considering the installation of a machine to process

the waste produced by one of its existing manufacturing process to be converted into a marketable product. At present, the waste is removed by a contractor for disposal on payment by the company of ` 50 lacs per annum for the next four years. The contract can be terminated upon installation of the aforesaid machine on payment of a compensation of ` 30 lacs before the processing operation starts. This compensation is not allowed as deduction for tax purposes.

The machine required for carrying out the processing will cost ` 200 lacs to be financed by a loan repayable in 4 equal installments commencing from the end of year 1. The interest rate is 16% per annum. At the end of the 4th year, the machine can be sold for `

20 lacs and the cost of dismantling and removal will be `15 lacs. Sales and direct costs of the product emerging from waste processing for 4 years are

estimated as under :

Year 1 2 3 4

Sales Material consumption Wages Other expenses Factory overheads Depreciation (as per income - tax rules)

322 30 75 40 55 50

322 40 75 45 60 38

418 85 85 54

110 28

413 85

100 70

145 21

Initial stock of materials required before commencement of the processing operations is ` 20 lacs at the start of year 1. The stock levels of materials to be maintained at the end of year 1, 2 and 3 will be ` 55 lacs and the stocks at the end of year 4 will be nil. The storage of materials will utilise space which would otherwise have been rented out for ` 10 lacs per annum. Labour costs include wages of 40 workers, whose transfer to this process will reduce idle time payments of ` 15 lacs, in year 1 and ` 10 lacs in year 2 Factory overheads include apportionment of general factory overheads except to the extent of insurance charges of ` 30 lacs per annum payable on this venture. The company's tax rate is 50%.

CAPITAL BUDGETING



Present value factors for four years are as under :

Year 1 2 3 4

Present value factors 0.870 0.756 0.658 0.572

Advise the management on the desirability of installing the machine for processing the waste. All calculations should form part of the answer.

Q.3. An automobiles ancillary unit is proposing to set up a manufacturing establishment

whose project cost is ` 320 lacs. The cost of land and buildings included in the project

cost is ` 40 lacs, the breakup of which is as follows :

(`̀̀̀)

Land (4,400 sq. yards) Building (area 25,000 sq. feet)

15 lacs 25 lacs

It is anticipated that in the first 4 years, the profitability will be low due to the time required for cultivating the market. To meet the situation, management is planning to hire factory premises of the same size at Re. 0.80 per square foot per month for the first four years, instead of own buildings. Repairs and maintenance, taxes, etc. will be borne by the landlord.

In the present project, the provision has been made for depreciation at 7% p.a. on original cost of buildings. Provision has also been made for repairs, maintenance, taxes etc., on buildings at ` 1,20,000 p.a.

The annual sales and profit figures as projected in the project report are as follows (`̀̀̀ in lacs)

Year Sales Net profit (NPADIT) Capacity Utilization

I II III IV

200 275 350 450

(-5) 5 10 20

60% 75% 90% 100%

After 4 years, the profit is expected to be steady at ` 40 lacs per annum. Institutional

finance is available upto ` 200 lacs under both the alternatives. (a) You are required to work out the average rate of return for the first four years on

shareholders initial investment, under both the alternatives. (b) If the lease is available for 4 years only, would you recommend leasing the

premises, if it is anticipated that the cost of land will increase by 40% and the cost of construction by 20% at the end of the four year period? For this purpose, opportunity cost of finance may be taken at 10% p.a.

Q.4. Delhi Bridge Construction Company plans to build a bridge over a crossing. The

construction work is expected to last 5 years and will be undertaken by a private sector firm to which ` 100 lacs will be payable at the end of year 1 and ` 50 lacs each at the end of next 4 years.

The annual maintenance cost of the bridge is expected to be ` 10,00,000 at current prices. This cost is expected to increase at 7% p.a. At the end of 15 years after completion, the bridge will require a major repair work requiring materials of `100 lacs and expenses of `100 lacs, both in current prices. The prices of materials are expected to rise at the rate of general inflation for 16 years and constant thereafter but expense cost is expected to rise 6% over the general interest for the first three years and then will increase in line with general inflation rate.

The required rate of return may be taken as 17% p.a. and the life of the bridge may be taken as infinite. Numbers of vehicles using the bridge per day is 20,000 and the toll tax is expected to increase in line with general inflation. Find out the minimum toll tax chargeable per vehicle in the first year of operation so that the investment in bridge may breakeven over its life. (Assumption : All annual cash flows arise on the last day of the year).



Q.5. A and Co. is contemplating whether to replace an existing machine or to spend money on overhauling it. A and Co. currently pays no taxes. The replacement machine costs ` 90,000 now and requires maintenance of ` 10,000 at the end of each year for eight

years. At the end of eight years, it would have a salvage value of ` 20,000 and would be sold. The existing machines require increasing amounts to maintenance each year and its salvage value falls each year as follows :

Year Maintenance (`̀̀̀) Salvage (`̀̀̀)

Present 1 2 3 4

0 10,000 20,000 30,000 40,000

40,000 25,000 15,000 10,000

0

COC is 15%. When should the machine be replaced? (Annuity for 8 years 4.4873 and at the end of the 8th year 0.3269).

Q.6. A delivery van must be replaced every four years and related cash flow are as under : (Figures in ‘ `̀̀̀ 000)

Age for Van in Years

Year 0 Year 1 Year 2 Year 3 Year 4

Cost of Van Maintenance Cost Repairs Scrap Value

1,500 ---- ---- ----

---- 400 ---- 800

---- 450 100 600

---- 500 200 400

---- 500 400 200

The firm is faced with the decision : Should the van be kept for four years and then scrapped away for ` 2,00,000? Or should it be replaced earlier?

Q.7. Catix Corporation is a divisionalised company and each division has the authority to

make capital expenditure upto ` 2,00,000 without the approval of the corporate headquarters. The corporate controller has determined that the cost of capital for Catix Corporation is 12%. This rate does not include an allowance for inflation, which is expected to occur at an average rate of 8% over the next five years. Catix pays income tax at the rate of 40%. The Electronics Division of Catix is considering the purchase of an automated assembly machine. The divisional controller estimates that if the machine is purchased, two positions will be eliminated yielding a cost saving for wages and employees benefits. However, the machine would require additional supplies and more power would be required to operate the machine. The cost savings and additional cost in current 19x0 prices are as follows : Wages and employee benefit of the two Positions eliminated (` 25,000 each) `̀̀̀ 50,000

Cost of additional supplies `̀̀̀ 3,000 Cost of additional power `̀̀̀ 10,000

The new machine would be purchased and installed at the end of 19x0 at a net cost of ` 80,000. If purchased, the machine would be depreciated @ 25% as per Income Tax Laws. The machine will become technologically obsolete in four years and will have no scrap value at that time.

The Electronics Division compensates for inflation in capital expenditure analysis by adjusting the expected cash flows by an estimated price level index.

The adjusted after tax cash flows are then discounted using the appropriate discount rate.



The estimated year end index values for each of the next five years are presented below :

Year Year – End Price Index

19x0 19x1 19x2 19x3 19x4 19x5

1.00 1.08 1.17 1.26 1.36 1.47

All operating revenues and expenses occur at the end of the year. You are required to prepare an analysis of the automated assembly machine for the

Electronics Division. Q.8. XYZ Ltd. an infrastructure company is evaluating a proposal to build, operate and

transfer a section of 35 kms. of road at a project cost of ` 200 crores to be financed as follows :

Equity Share Capital of ` 50 crores, loans at the rate of interest of 15% p.a. from financial institutions ` 150 crores. The Project after completion will be opened to traffic and a toll will be collected for a period of 15 years from the vehicles using the road the company is also required to maintain the road during the above 15 years and after the completion of that period, it will be handed over to the Highway authorities at zero value. It is estimated that the toll revenue will be ` 50 crores per annum and the annual toll collection expenses including maintenance of the roads will amount to 5% of the project cost. The company considers to write off the total cost of the project in 15 years on a straight line basis. For Corporate Income - tax purposes the company is allowed to take depreciation @ 10% on WDV basis. The financial institutions are agreeable for the repayment of the loan in 15 equal annual instalments - consisting of principal and interest.

Calculate Project IRR and Equity IRR. Ignore Corporate taxation. Explain the difference in Project IRR and Equity IRR.

CAFCINTER CAFINAL CA

FINAL CAREVISION NOTES

MAY '19

Strategic Financial Management

Mergers & Acquisitions

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Including Corporate Valuation



Q.1. A Ltd. is keen or reporting an earning per share of ` 6 after acquiring T Ltd. The

following financial data are given : A Ltd. T Ltd.

EPS Market price per share No. of shares

` 5

` 60

10,00,000

` 5

` 50

8,00,000

There is an exected synergy gain of 5%. What exchange ratio will result in post - merger EPS of ` 6 for A Ltd.?

Q.2. You have been provided the following financial data of two companies :

T Ltd. A Ltd.

Earnings after taxes Equity shares outstanding Earnings per share Price - earnings (P / E) ratio Market price per share

` 7,00,000

2,00,000 3.50

10 times ` 35

` 10,00,000

4,00,000 2.50 14 times

` 35

Company A is acquiring the Company T, exchanging its shares on a one to one basis for Company T's shares. The exchange ratio is based on the market prices of the shares of the two companies. (i) What will be the EPS subsequent to merger ? (ii) What is the change in EPS for the shareholders of companies A and T ? (iii) Determine the market value of the post - merger firm. P.E. Ratio is likely to remain

same. (iv) Ascertain the profits accruing to shareholders of both the firms. (v) T Ltd. wants to be sure that it's shareholders' earnings will not be dimished by the

merger. What should be the exchange ratio in that case? (vi) Determine gain (loss) for shareholders of the two companies after acquisition.

Q.3. T Ltd. and E Ltd. are in the same industry. The former is in negotiation for acquisition of

the latter. Important information about the two companies as per their latest financial statements is given below:

T Ltd. E Ltd.

` 10 Equity shares outstanding Debt: 10% Debentures (` Lakhs) 12.5% Institutional Loan (` Lakhs) Earnings before interest, depreciation and tax (EBIDAT) (` Lakhs) Market Price/share (`)

12 Lakhs

580 --

400.86 220.00

6 Lakhs --

240

115.71 110.00

T Ltd. plans to offer a price for E Ltd., business as a whole which will be 7 times EBIDAT reduced by outstanding debt, to be discharged by own shares at market price.

E Ltd. is planning to seek one share in T Ltd. for every 2 shares in E Ltd. based on the market price. Tax rate for the two companies may be assumed as 30%.

Calculate and show the following under both alternatives - T Ltd.'s offer and E Ltd.'s plan: (i) Net consideration payable. (ii) No. of shares to be issued by T Ltd. (iii) EPS of T Ltd. after acquisition. (iv) Expected market price per share of T Ltd. after acquisition. (v) State briefly the advantages to T Ltd. from the acquisition.

Calculations (except EPS) may be rounded off to 2 decimals in lakhs.

MERGERS & ACQUISITIONS INCLUDING CORPORATE VALUATION



Q.4. The shares of Nisha Ltd., are currently being traded for ` 24 per share. The top management together with their families control 40% of the 10 lakh shares outstanding. Sangeeta Ltd. wishes to acquire Nisha Ltd. because of likely synergies. The estimated present value of these synergies is ` 80 lakh. Moreover, Sangeeta feels that the management of Nisha is overpaid. It feels with better management motivation, lower salaries and fewer perks for the top management, approximately ` 4 lakh of expenses per annum can be saved. This would add ` 30 lakh in value to the acquisition. The following additional information is available regarding Sangeeta : Earnings per share ` 4.00 Number of shares outstanding 15 lakh Market price of shares ` 40.00 (a) What is the maximum price per share which Sangeeta can offer to pay for Nisha? (b) What is the minimum price per share at which the management of Nisha will be

willing to give up their controlling interest? Q.5. Following are the financial statements for A Ltd. and B Ltd. for the current financial year.

Both firms operate in the same industry. Balance Sheet

A Ltd. B Ltd.

Total current assets Total fixed assets (net) Total Assets Equity capital (of ` 10 each)

Retained earnings 14% Long term debt Total current liabilities

` 14,00,000 10,00,000

` 10,00,000 5,00,000

24,00,000 15,00,000

10,00,000 2,00,000 5,00,000 7,00,000

8,00,000 ----

3,00,000 4,00,000

24,00,000 15,00,000

Income Statements A Ltd. B Ltd.

Net sales Cost of goods sold Gross profit Operating expenses Interest Earnings before taxes Taxes (50%) Earnings after taxes (EAT) Additional Information : Number of equity shares Dividend payment ratio Market price per share (MPS)

` 34,50,000 27,60,000

` 17,00,000 13,60,000

6,90,000 2,00,000 70,0000

3,40,000 1,00,000 42,000

4,20,000 2,10,000

1,98,000 99,000

2,10,000 99,000

1,00,000

40% ` 40

88,000 60% ` 15

Assume that the two firms are in the process of negotiating a merger through an exchange of equity shares. You have been asked to assist in establishing equitable exchange terms, and are required to : (i) Decompose the share prices of both the firms into EPS and PE components, and

also segregate their EPS figures into return on equity (ROE) and book value / intrinsic value per share (BVPS) components.

(ii) Estimate future EPS growth rates for each firm. (iii) Calculate the post - merger EPS based on an exchange ratio of 0.4 : 1 being

offered by A Ltd. Indicate the immediate EPS accretion or dilution, if any, that will occur for each group of shareholders.

(iv) Based on a 0.4 : 1 exchange ratio, and assuming that A's pre - merger PE ratio will continue after the merger, estimate the post - merger market price. Show the resulting accretion or dilution in pre - merger market prices.



Q.6. The following information is provided relating to the acquiring company. Efficient Ltd., and the target Company Healthy Ltd.

Efficient Ltd. Healthy Ltd.

No. of shares (F.V. ` 10 each) Market Capitalisation P / E ratio (times) Reserves and Surplus Promoter's Holding (No. of shares)

10.00 lakhs 500.00 lakhs

10.00 300.00 lakhs 4.75 lakhs

7.5 lakhs 750.00 lakhs

5.00 165.00 lakhs 5.00 lakhs

Board of Directors of both the Companies have decided to give a fair deal to the shareholders and accordingly for swap ratio the weights are decided as 40%, 25% and 35% respectively for Earning. Book Value and Market Price of share of each company : (i) Calculate the swap ratio and also calculate Promoter's holding % after acquisition. (ii) What is the EPS of Efficient Ltd., after acquisition of Healthy Ltd.? (iii) What is the expected market price per share and market capitalization of Efficient

Ltd. after acquisition, assuming P/E ratio of Firm Efficient Ltd., remains unchanged.

(iv) Calculate free float market capitalization of the merged firm. Q.7. The following information is relating to Fortune India Ltd., having two division, viz.

Pharma Division and Fast Moving Consumer Goods Division (FMCG Division). Paid up share capital of Fortune India Ltd., is consisting of 3,000 Lakhs equity shares of Re. 1 each. Fortune India Ltd., decided to de - merge Pharma Division as Fortune Pharma Ltd., w.e.f. 1.4.2005. Details of Fortune India Ltd., as on 31.3.2005 and of Fortune Pharma Ltd., as on 1.4.2005 are given below :

Particulars Fortune Pharma Ltd. Fortune India Ltd.

`̀̀̀ `̀̀̀

Outside Liabilities Secured Loans Unsecured Loans Current Liabilities & Provisions Assets Fixed Assets Investments Current Assets Loans & Advances Deferred tax / Miscellaneous Expenses

400 lakh

2,400 lakh 1,300 lakh

7,740 lakh 7,600 lakh 8,800 lakh 900 lakh 60 lakh

3,000 lakh 800 lakh

21,200 lakh

20,400 lakh 12,300 lakh 30,200 lakh 7,300 lakh (200) lakh

Board of Directors of the Company have decided to issue necessary equity shares of Fortune Pharma Ltd., of Re. 1 each, without any consideration to the shareholders of Fortune India Ltd. For that purpose following points are to be considered : 1. Transfer of Liabilities & Assets at Book value. 2. Estimated Profit for the year 2005-06 is ` 11,400 Lakh for Fortune India Ltd. &

` 1,470 lakhs for Fortune Pharma Ltd. 3. Estimated Market Price of Fortune Pharma Ltd. is ` 24.50 per share. 4. Average P/E Ratio of FMCG sector is 42 & Pharma sector is 25, which is to be

expected for both the companies. Calculate :

1. The Ratio in which shares of Fortune Pharma are to be issued to the shareholders of Fortune India Ltd.

2. Expected Market price of Fortune India Ltd. 3. Book Value per share of both the Companies immediately after Demerger.



Q.8. A Ltd. Wants to value T Ltd. in accordance with Chop Shop method. T Ltd. is carrying out 3 streams of business namely telecom, real estate, toys. The market capitalization of equity shares of T Ltd. is ` 15,200 crores. The other financial details of T Ltd. are as follows :

Particulars Telecom Real Estate Toys Total

Turnover 5000 cr. 4000 cr. 1000 cr. 10000 cr.

Assets 1250 cr. 2000 cr. 1000 cr. 4250 cr.

Net operating profits after tax 1000 cr. 500 cr. 400 cr. 1900 cr.

Industry Statistics

Market Capitalization to Sales 1.65 1.40 0.7

Market Capitalization to Assets 3 4 2

Market Capitalization NOPAT 12 9 11

Q.9. The total value (equity + debt) of two companies, A Ltd. and B Ltd. are expected to

fluctuate according to the state of the economy.

State of the economy Probability Value of A Ltd. ` ` ` ` in lakh

Value of B Ltd. `̀̀̀ in lakh

Rapid growth 0.30 720 1150

Slow growth 0.50 520 750

Recession 0.20 380 600

A Ltd. and B Ltd. currently have a debt of ` 420 lakhs and ` 80 lakhs, respectively. The two companies are deciding for merger. Assuming that no operational synergy is

expected as a result of the merger, you are required to calculate the expected value of debt and equity of the merged company.

Also explain the reasons for any difference that exists from the expected values of debt and equity, if they do not change.

Q.10. Timby Ltd. is in the business of making sports equipment. The company operates from

Thailand. To globalize its operations, Timby has identified Find Toys Ltd. an Indian Company, as a potential takeover candidate. After due diligence of Find Toys Ltd. the following information is available. (a)

(b) The net worth of Find Toys Ltd. (`in lakhs) after considering certain adjustments suggested by the due diligence team reads as under:

Tangible Inventories Receivables Less:Creditors Bank Loans

160 250

750 145 75

971

(415)

Represented by equity shares of `1,000 each 555

Talks for takeover have crystallized on the following: 1. Timby Ltd. will not be able to use Machinery worth ` 75 lakhs which will be

disposed of by them subsequent to take over. The expected realization will be ` 50 lakhs.

2. The inventories and receivables are agreed for takeover of values of `100 and `50 lakhs respectively which is price they will realize on disposal.

Cash Flow Forecasts (`̀̀̀ in crore):

Year 10 9 8 7 6 5 4 3 2 1

Find Toys Ltd. 24 21 15 16 15 12 10 8 6 3

Timby Ltd. 108 70 55 60 52 44 32 30 20 16



3. The liabilities of Fine Toys Ltd. will be discharged in full on take over along with an employee settlement of `90 lakhs for the employees who are not interested in continuing under the new management.

4. Timby Ltd. will invest a sum of `150 lakhs for upgrading the Plant of Find Toys Ltd.

on takeover. A further sum of `50 lakhs will also be incurred in the second year to revamp the machine shop floor of Find Toys Ltd.

5. The Anticipated Cash Flows (in `crore) post takeover are as follows: Year 1 2 3 4 5 6 7 8 9 10 18 24 36 44 60 80 96 100 140 200

You are required to advice the management the maximum price which they can pay per share of Find Toys Ltd. if a discount factor of 20 per cent is considered appropriate.

Q.11. AB Ltd., is planning to acquire and absorb the running business of XY Ltd. The

valuation is to be based on the recommendation of merchant bankers and the consideration is to be discharged in the form of equity shares to be issued by AB Ltd. As on 31.3.2006, the paid up capital of AB Ltd. consists of 80 lakhs shares of ` 10 each.

The highest and the lowest market quotation during the last 6 months were ` 570 and ` 430. For the purpose of the exchange, the price per share is to be reckoned as the average of the highest and lowest market price during the last 6 months ended on 31.3.2006.

XY Ltd.'s Balance Sheet as at 31.3.2006 is summarised below :

`̀̀̀ in lakhs

Sources Share Capital

20 lakhs equity shares of ` 10 each fully paid 10 lakhs equity shares of ` 10 each ` 5 paid

Loans

200 50 100

Total 350

Uses Fixed Assets (Net) Net Current Assets

150 200

Total 350

An independent firm of merchant bankers engaged for the negotiation, have produced the following estimates of cash flows from the business of XY Ltd. :

Year ended By way of `̀̀̀ lakhs

31.3.07 31.3.08 31.3.09 31.3.10 31.3.11

after tax earnings for equity do do do do terminal value estimate

105 120 125 120 100 200

It is the recommendation of the merchant banker that the business of XY Ltd., may be valued on the basis of the average of (i) Aggregate of discounted cash flows at 8% and (ii) Net assets value. Present value factors at 8% for years. 1 - 5 : 0.93 0.86 0.79 0.74 0.68

You are required to : (i) Calculate the total value of the business of XY Ltd. (ii) The number of shares to be issued by AB Ltd.; and (iii) The basis of allocation of the shares among the shareholders of XY Ltd.



Q.12. Chennai Limited and Kolkata Limited have agreed that Chennai Limited will take over the business of Kolkata Limited with effect from 31st March, 2009. It is agreed that : (i) 10,00,000 shareholders of Kolkata Limited will receive shares of Chennai Limited. The swap ratio is determined on the basis of 26 weeks average market prices of

shares of both the companies. Average price have been worked out at ` 50 and ` 25 for the shares of Chennai Limited and Kolkata Limited respectively.

(ii) In addition to (i) above shareholders of Kolkata Limited will be paid cash based on the projected synergy that will arise on the absorption of the business of Kolkata Limited by Chennai Limited. 50% of the projected benefits will be paid to the shareholders of Kolkata Limited.

The following projection has been agreed upon by the management of both the companies.

Year ended 31.3. Benefit

2010 2011 2012 2013 2014

(in ` Lakhs) 50 75 90 100 105

The benefit is estimated to grow at the rate of 2% after 2014 perpetually. It has been further agreed that a discount rate of 20% should be used to calculate the

cash that the holder of each share of Kolkata Limited will receive. (i) Calculate the cash that holder of each share of Kolkata Limited will receive. (ii) Calculate the total purchase consideration. [Discounting factor : Discounting rate 20% : 1 year. 833, 2 year. 694, 3 year. 579,

4 year. 482, 5 year. 402, 6 year. 335; Discounting rate 18%; 1 year. 842, 2 year. 718,3 year. 609, 4 year. 516, 5 year. .437, 6 year. 370; Discounting rate 16% : 1 year. 862, 2 year. 743, 3 year. 641, 4 year. 552, 5 year. .476, 6 year. 410]

Q.13. Adonis Ltd., makes thermal clothing for winter sports and outdoor work, and is

considering acquiring Sking Ltd. which manufactures and sells ski clothing. Sking Ltd. is about one quarter of Adonis size and manufactures its entire product line in a small rented factory on a mountaintop in Manali. It costs about 10,00,000 a year in overhead to operate in the factory. Adonis Ltd. produces its output in a less popular in North but more popular north - east locations. Its factory has at least 50% excess capacity. Adonis plan is to acquire Sking Ltd., and combine production operations in its north - eastern factory, but otherwise run the companies separately.

Sking Ltd. beta is 2.0, Treasury bills currently yield 5% and the Nifty Index is yielding 9%. The corporate income tax rate for both firms is 40%. Because Sking Ltd. will no longer be maintaining its own production facilities, it can be assumed that only a minimal amount of cash will have to be reinvested. This amount is estimated at 1,00,000 per year.

The financial information for Sking Ltd. is as follows :

Revenue EAT Depreciation

` 1,25,00,000 ` 13,00,000

` 6,00,000

(a) Calculate the appropriate discount rate for evaluating the Sking Ltd. acquisition. (b) Determine the annual cash flow expected by Adonis Ltd. from Sking Ltd. if the

acquisition is made (considering the synergy). (c) Calculate the value of the acquisition to Adonis Ltd. assuming the benefits last for

(1) five years, (2) 10 years, and (3) 15 years. (d) Sking Ltd. has 2,50,000 shares outstanding. Calculate the maximum price Adonis

Ltd. should be willing to pay per share to acquire the firm under the three assumptions in part C.



(e) If Adonis Ltd. is willing to assume the benefits of the Sking Ltd. acquisition will last indefinitely without growth, what should it be willing to pay per share?

(f) Assume that the cash flow from the Sking Ltd. acquisition grows at 10% from its initial value for one year and then grows at 5% indefinitely (starting in the third year). Calculate the value of the firm and the implied stock price under these conditions. Use a terminal value at the beginning of the period of 5% growth. What price premium is implied in Rupees and as a percent of market price if Sking Ltd. stock is currently selling at ` 62?

Q.14. Zed Ltd. is considering the immediate purchase of some or all, of the shares of one of

two firms Red Ltd. and Yellow Ltd. Both Red and Yellow have 1,00,000 equity shares issued and neither company has any debt capital outstanding.

Both firms are expected to pay a dividend in 1 years’ time, Red's expected dividend amounting to ` 3 per share and Yellow's being ` 2.70 per share. Dividends will be paid annually and are expected to increase over time. Red's dividends are expected to display perpetual growth at a compound rate of 6 per cent per annum. Yellow's dividend will grow at a high annual compound rate of 331/3% until a dividend of ` 6.40 per share is reached in year 4.

Thereafter Yellow's dividend will remain constant. If Zed is able to purchase all the equity capital of either firm then the reduced

competition would enable Zed to save some advertising and administrative costs which would amount to ` 2,25,000 per annum indefinitely and, in year 2, to sell some office space for ` 8,00,000. These benefits and savings would only occur if a complete takeover were to be carried out. Zed would change some operations of any company completely taken over. The details are : (i) In case of Red : No dividend would be paid until year 2. Year 3 dividend would be

` 2.50 per share and dividends would then grow at 10% per annum indefinitely. (ii) In case of Yellow : No change in total dividends in years 1 to 4, but after year 4

dividend growth would be 25% per annum compound until year 7. Thereafter, annual dividends would remain constant at the year 7 amount per share.

An appropriate discount rate for the risk inherent in all the cash flows mentioned is 15%. You are required to present. (i) The valuation per share for a minority investment in each of the firms, Red and

Yellow, which would provide the investor with a 15% rate of return. (ii) The maximum amount per share which Zed should consider paying for each

company in the event of a complete takeover. Q.15. Y Ltd. which is specialized in manufacturing garments is planning for expansion to

handle a new contract which it expects to obtain. An investment bank have approached the company and asked whether the Co. had considered venture Capital financing. In 2001, the company borrowed ` 100 lacs on which interest is paid at 10% p.a. The Company shares are unquoted and it has decided to take your advice in regard to the calculation of value of the Company that could be used in negotiations using the following available information and forecast.

Company’s forecast turnover for the year to 31st March, 2005 is ` 2,000 lacs which is mainly dependent on the ability of the Company to obtain the new contract, the chance for which is 60%, turnover for the following year is dependent to some extent on the outcome of the year to 31st March, 2005. Following are the estimated turnovers and probabilities:



Year - 2005 Year - 2006

Turnover `̀̀̀ (in lacs)

Prob. Turnover `̀̀̀ (in lacs)

Prob.

2,000

1,500

1,200

0.6 0.3 0.1

2,500 3,000 2,000 1,800 1,500 1,200

0.7 0.3 0.5 0.5 0.6 0.4

Operating costs inclusive of depreciation are expected to be 40% and 35% of turnover respectively for the years 31st March, 2005 and 2006. Tax is to be paid at 30%. It is assumed that profits after interest and taxes are free cash flows. Growth in earnings is expected to be 40% for the years 2007, 2008 and 2009 which will fall to 10% each year after that. Industry average cost of equity (net of tax) is 15%.

Q.16. A valuation done of an established company by a well-known analyst has estimated a

value of ` 500 lakhs, based on the expected free cash flow for next year of ` 20 lakhs and an expected growth rate of 5%.

While going through the valuation procedure, you found that the analyst has made the mistake of using the book values of debts & equity in his calculation. While you do not know the book value weights he used, you have been provided with the following information: (i) Company has a cost of equity of 12% (ii) After tax cost of debt is 6% (iii) The market value of equity is three times the book of equity, while the market

value of debt is equal to the book value of debt. You required to estimate the correct value of the company.



Q.1. ABC Ltd. is a construction company following a residual dividend policy. The total

capital budget for next year can be ` 20 lakhs, ` 30 lakhs or ` 40 lakhs. The forecasted

level of potential retained earnings next year is ` 20 lakhs. The optimal/target capital structure is debt ratio of 40%. Compute the amount of the dividend and dividend payout ratio for each of the 3 capital expenditure amounts.

Q.2. Vouge Ltd. maintains a capital structure of 70% debt and 30% equity. The profit after

tax for the current year is ` 60,000. (i) How much capital expenditure can be incurred without raising fresh issue (a) If the

company adopts the residual approach and does not bother about capital structure? (b) If the company adopts the residual approach and bothers about the capital structure?

(ii) If the company plans to spend ` 1,50,000 in the upcoming year as capital expenditure, what dividend will it be in a position to pay if it follows the (a) residual approach and believes in not maintaing its capital structure intact? (b) residual approach and believes in maintaing its capital structure?

Q.3. Calculate the value of the share from the following information : Profit of the company ` 290 crores Equity capital of company ` 1,300 crores Par value of share ` 40 each Debt ratio of company 0.27 Long run growth rate of the co. 8% Beta 0.1 Risk free interest rate 8.7% Market returns 10.3% Capital expenditure per share ` 47 Depreciation per share ` 39 Change in working capital ` 3.45 per share Q.4. CMC plc has an all-common-equity capital structure. If has 200,000 share of ` 2 par

value equity shares outstanding. When CMC’s founder, who was also its research director and most successful inventor, retired unexpectedly to settle down in the South Pacific in late 2005, CMC was left suddenly and permanently with materially lower growth expectations and relatively few attractive new investment opportunities. Unfortunately, there was no way to replace the founder’s contributions to the firm. Previously, CMC found it necessary to plough back most of its earnings to finance growth, which averaged 12% per year. Future growth at a 5% rate is considered realistic; but that level would call for an increase in the dividend payout. Further, it now appears that new investment projects with at least the 14% rate of return required by CMC’s shareholders (ke = 14%) would amount to only ` 800,000 for 2006 in

comparison to a projected ` 2,000,000 of net income. If the existing 20% dividend payout were continued, retained earnings would be ` 16,00,000 in 2006, but, as noted, investments that yield the 14% cost of capital would amount to only ` 800,000. The one encouraging thing is that the high earnings from existing assets are expected to continue, and net income of ` 20,00,000 is still expected for2006. Given the dramatically changed circumstances. CMC’s board is reviewing the firm’s dividend policy.

DIVIDEND POLICY



(a) Assuming that the acceptable 2006 investment projects would be financed entirely by earnings retained during the year, calculate DPS in 2006, assuming that CMC uses the residual payment policy.

(b) What payout ratio does your answer to part a imply for 2006? (c) If a 60 % payout ratio is adopted and maintained for the foreseeable future, what is

your estimate of the present market price of the equity share? How does this compare with the market price that should have prevailed under the assumptions existing just before the news about the founder’s retirement? If the two values of P0 are different. Comment on why?

(d) What would happen to the price of the share if the old 20% payout were continued? Assume that if this payout is maintained, the average rate of return on the retained earnings will fall to 7.5% and the new growth rate will be G = (1.0- Payout ratio) × (ROE) = (1.0 – 0.2) (7.5%) = (0.8) (7.5%) = 6.0%.

Q.5. A Ltd. has earning of ` 4 per share this year. Dividend per share last year was ` 1.50

suppose the target pay-out ratio is 60% & the adjustment rate is 50%, what would be the dividend per share for the current year under Lintner's Model.

Q.6. The target payout ratio for Jupiter Ltd. is 0.4. The dividend per share for the current

year is ` 14. The dividend per share in previous year was ` 12. The Adjustment ratio is 0.60. The number of equity shares outstanding in the company is 10,00,000. If the P/E multiple is 9, applying Lintner Model of dividend policy to the company, compute the market capitalization of the company.

Q.7. Ghanshyam Limited is relatively a new company in the industry of automobiles. The

earnings per share of a company is ` 30 and dividend payout ratio is 60%. If the share

price of the company is ` 56 whereas cost of capital and internal rate of return is 15% and 18% respectively. What is the multiplier applicable to the company according to the Graham and Dodd model?

Q.8. ABC Ltd. has a capital of ` 10 lakhs in equity shares of ` 100 each. The shares are

currently quoted at par. The company proposes declaration of a dividend of ` 10 per share at the end of the current financial year. The capitalisation rate for the risk class to which the company belongs is 12%.

What will be the market price of the share at the end of the year if (i) A dividend is not declared? (ii) A dividend is declared?

Assuming that the company pays the dividend and has net profits of ` 5,00,000 and makes new investments of `10 lakhs during the period, how many new shares must be issued ? Use the M.M. model.

Q. 7. Diamond Engineering Company has 10,00,000 equity shares outstanding at the start of the

accounting year 2003. The ruling market price per share is ` 150. The Board of Directors of the Company contemplates declaring ` 8 share as dividend at the end of the current year. The rate

of Capitalization appropriate to the risk-class to which the company belongs is 12%. (a) Based on Modigliani-Miller Approach, calculate the market price per share of the company

when the contemplated dividend is (i) declared and (ii) not declared. (b) How many new shares are to be issued by the company at the end of the accounting year

on the assumption that the Net Income for the year is ` 2 crores? Investment budget is ` 4 crores and (i) the above dividends are distributed and (ii) they are not distributed.

(c) Show that the total market value of the shares at the end of the accounting year will remain the same whether dividends are either distributed or not distributed. Also find out the current market value of the firm under both situations.



Q.1. Your company is considering to acquire an additional computer to supplement its time

share computer services to its clients. It has two options : (i) To purchase the computer for ` 22 lakhs.

(ii) To lease the computer for three years from a leasing company for ` 5 lakhs as annual lease rent plus 10% of gross time - share service revenue. The agreement also requires an additional payment of ` 6 lakhs at the end of the third year. Lease rents are payable at the year - end, and the computer reverts to the lessor after the contract period.

The company estimates that the computer under review will be worth `10 lakhs at the end of third year.

Forecast Revenues are :

Year 1 2 3

Amount (` in lakhs) 22.5 25 27.5

Annual operating costs excluding depreciation / lease rent of computer are estimated at ` 9 lakhs with an additional ` 1 lakh for start-up and training costs at the beginning of the first year. These costs are to be borne by the lessee. Your company will borrow at 16% interest to finance the acquisition of the computer. Repayments are to be made according to the following schedule :

Year end 1 2 3

Principal (` '000) 500 850 850

Interest (` '000) 352 272 136

The company uses straight line method (SLM) to depreciate its assets and pays 50% tax on its income. The management approaches you to advice, which alternative would be recommended and why?

Note : The PV factor at 8% and 16% rates of discount are :

Year end 1 2 3

8% 0.926 0.857 0.794

16% 0.862 0.743 0.641

Q.2. Welsh Limited is faced with a decision to purchase or acquire on lease a mini car. The

cost of the mini car is ` 1,26,965. It has a life of 5 years. The mini car can be obtained on lease by paying equal lease rentals annually. The leasing company desires a return of 10% on the gross value of the asset. Welsh Limited can also obtain 100% finance from its regular banking channel. The rate of interest will be 15% p.a. and the loan will be paid in five annual equal installments, inclusive of interest. The effective tax rate of the company is 40%. For the purpose of taxation it is to be assumed that the asset will be written off over a period of 5 years on a straight line basis. (a) Advise Welsh Limited about the method of acquiring the car. (b) What should be the annual lease rental to be charged by the leasing company to

match the loan option? For your exercise use the following discount factors :

Years

Discount Rate 1 2 3 4 5

10% 0.91 0.83 0.75 0.68 0.62

15% 0.87 0.76 0.66 0.57 0.49

9% 0.92 0.84 0.77 0.71 0.65

LEASING DECISIONS & APV



Q.3. Kuber Leasing Ltd. Is in the process of making out a proposal to lease certain equipment to a user – manufacturer. The cost of the equipment is expected to be ` 10 lakhs and the primary period of lease is to be 10 years. Kuber Ltd. gives you the following additional information :

• SLM over 10 years period is acceptable under the Income – tax Act.

• The current effective tax rate is 40% and is expected to lower to 30% from the beginning of the 6th year of lease.

• Cut off rate is 10%.

• Lessees need to pay 1% of the value of the asset as lease management and processing fee.

• Annual lease rentals are to be collected at the beginning of the year. Compute annual lease rent. Q.4. (a) The pre – tax expected rate of return for the Hypothetical Industries Ltd. (HIL) is 24

per cent for a five year non – cancellable lease. The annual lease rental would be stepped at 10 per cent over the period. Compute the lease rental per ` 1,000.

(b) Assume that the lease rentals are deferred for the first two years. Compute the lease rentals per ` 1,000.

(c) The lease rentals will be stepped up by 25 per cent and then by 40 per cent and subsequently stepped down in the reverse order in the fifty year. Compute the lease rental per ` 1,000.

Q.5. GMBH Ltd. is in software development business. It has recently been awarded a

contract from an Asian country for computerization of its all offices and branches spread across the country. This will necessitate acquisition of a super computer at a total cost of `10 crores. The expected life of computer is 5 years. The scrap value is estimated at `5 crore. However, this value could even be much lower depending upon the developments taken place in the field of computer technology.

A leasing company has offered a lease contract will total lease of `1.5 crore per annum for 5 years payable in advance will all maintenance costs being borne by lesee.

The other option available is to purchase the computer by taking loan from the bank with variable interest payment payable semi – annually in arrears at a margin of 1% per annum above MIBOR. The MIBOR forecast to be at a flat rate of 2.4% for each 6 month period, for the duration of loan.

Tax rate applicable to corporation is 30%. For taxation purpose, depreciation on computer is allowed at 20% as per WDV method, with a delay of 1 year between the tax depreciation allowance arising and deduction from tax paid.

You are required to calculate : (a) Compound annualized post tax cost of debt. (b) NPV of lease payment Vs. purchase decisions at discount rate of 4% and 5%. (c) The break – even post – tax cost of debt at which corporation will be indifferent

between leasing and purchasing the computer. (d) Which option should be opted for?



Q.1. Determine the Risk Adjusted Net Present Value of the following projects :

A B C

Net cash outlays (`) Project life Annual cash inflow (`) Coefficient of Variation

1,00,000 5 years 30,000

0.4

1,20,000 5 years 42,000

0.8

2,10,000 5 years 70,000

1.2

The company selects the risk – adjusted rate of discount on the basis of the Coefficient of Variation:

Coefficient of Variation

Risk adjusted rate of discount rate of discount

Present value factor 1 to 5 years at risk adjusted

0.0 10% 3.791

0.4 12% 3.605

0.8 14% 3.433

1.2 16% 3.274

1.6 18% 3.127

2.0 22% 2.864

More than 2.0 25% 2.689

Q.2. ABC and Co. is considering two mutually exclusive machines X and Y. The company

uses a Certainty Equivalent approach to evaluate the proposals. The estimated cash flow and certainty equivalents for both machines are as follows :

Machine X Machine Y

Year Cash flow Certainty Equivalent Cash flow Certainty Equivalent

0 1 2 3 4

` - 30,000 15,000 15,000 10,000 10,000

1.00 0.95 0.85 0.70 0.65

` - 40,000 25,000 20,000 15,000 10,000

1.00 0.90 0.80 0.70 0.60

Which machine should be bought, if the risk free discount rate is 5 per cent? Q.3. XYZ Ltd. is evaluating two equal size mutually exclusive proposals X and Y for which

the respective cash flows together with associated probabilities are as follows :

Project X Project Y

Cash Flows (`̀̀̀) Probabilities Cash Flows (`̀̀̀) Probabilities

2,000 0.3 1,000 0.1

4,000 0.4 3,000 0.1

6,000 0.3 5,000 0.4

7,000 0.3

9,000 0.1

Find out the risks of the proposals in terms of the standard deviation and coefficient of variation.

RISK ANALYSIS



Q.4. A company is considering investing in a new product with an expected life of three years. It is estimated that if the demand for the product is favourable in the first year, then it is certain to be favourable in the subsequent years. And if it is low in the first year, it would remain low in years 2 and 3. The company feels that cash flows over time are perfectly correlated. The cost of the project is ` 50,000 and the possible cash flows for three years are :

Year 1 Year 2 Year 3

Cash flow Probability Cash flow Probability Cash flow Probability

---- 0.10 ` 5,000 0.15 ---- 0.15

` 10,000 0.20 20,000 0.20 ` 7,500 0.20

20,000 0.40 35,000 0.30 15,000 0.30

30,000 0.20 50,000 0.20 22,500 0.20

40,000 0.10 65,000 0.15 30,000 0.15

Assume a risk free discount rate of 5 per cent. Calculate the expected value and standard deviation of the probability distribution of possible net present values. Assuming a normal distribution, what is the probability of the project providing a net present value of (i) zero or less (ii) ` 15,000 or more?

Q.5. A firm has an investment proposal, requiring an outlay of ` 40,000. The investment

proposal is expected to have 2 year's economic life with no salvage value. In year I there is a 0.4 probability that cash inflow after tax will be ` 25,000 and 0.6 probability that cash inflow after tax will be ` 30,000. The probabilities assigned to cash inflows after tax for the year II are as follows : The Cash inflow year I ` 25,000 ` 30,000 The Cash inflow year II Probability Probability ` 12,000 0.2 ` 20,000 0.4 ` 16,000 0.3 ` 25,000 0.5

` 22,000 0.5 ` 30,000 0.1 The firm uses a 10% discount rate for this type of investment. Required :

(a) Construct a decision tree for the proposed investment project. (b) What net present value will the project yield if worst outcome is realised? What is

the probability of occurrence of this NPV? (c) What will be the best and the probability of that occurrence? (d) Will the project be accepted? (10% Discount factor 1 year 0.909 2 year 0.826)

Q.6. A company in the North of a country is engaged in the manufacture and installation of a

new leisure activity. Progress has been made in creating a market. A short lease on its existing temporary premises will expire at the end of this year and will not be renewable.

Market research has shown that the demand for new installation is likely to end after a further eight years. In this period it is foreseen that in the first four years there is a 70% chance that new work will be mainly in the south. Thereafter there is a forecast reversal of demand source with a 60% chance of most new work originating in the north.

No suitable rented accommodation is available. The cost of premises is ` 3,00,000 in the north and ` 4,00,000 in the south. Of these sums, 20% is the cost of land and the remainder the cost of specialised buildings. The buildings will have no further use after eight years. The land is assumed to retain its original value and will be sold when it is no longer required for the project.



To relocate after four years would involve dismantling and re - erecting buildings, a loss of business during the changeover, staff transfers and variations in the cost of services. The overall cost at the end of year four would be :

North to south ` 1,50,000 South to north ` 1,00,000

The annual net cash flow for the company is expected to be `1,20,000. The extra cost of transport and communication expense would reduce this annual income by ` 40,000 a year if the premises were located in the area away from the major business.

The cost of capital to the company is 12% per annum. You are required, from the information given, to :

(a) Prepare a decision tree of the options open to the company ; (b) Decide on a net present value (NPV) basis which option is the most attractive

financially. Q.7. A company is considering a project involving the outlay of ` 3,00,000 which it estimates

will generate cash flows over its two - year life with the probabilities shown below.

Cash flows for project Year 1

Cash flow Probability

`̀̀̀

1,00,000 2,00,000 3,00,000

0.25 0.50 0.25

1.00

Year 2 If cash flow in Year 1 is : there is a probability of :

that cash flow in Year 2 will be:

`̀̀̀ `̀̀̀

1,00,000 0.25 0.50 0.25

Nil 1,00,000 2,00,000

1.00

2,00,000 0.25 0.50 0.25

1,00,000 2,00,000 3,00,000

1.00

3,00,000 0.25 0.50 0.25

2,00,000 3,00,000 3,50,000

1.00

All cash flows should be treated as being received at the end of the year. The company has a choice of undertaking this project at either of two sites (A or B)

whose costs are identical and are included in the above outlay. In terms of the technology of the project itself, the location will have no effect on the outcome.

If the company chooses sits B, it has the facility to abandon the project at the end of the first year and to sell the site to an interested purchaser for ` 1,50,000. This facility is not available at site A.

The company's investment criterion for this type of project is 10% DCF. Its policy would be to abandon the project on site B and to sell the site at the end of the year 1 if its expected future cash flows for year 2 were less than the disposal value.

Required : (a) Calculate the NPV of the project on site A.



(b) (i) Explain, based on the data given, the specific circumstances in which the company would abandon the project on site B.

(ii) Calculate the NPV of the project on site B taking account of the abandonment facility.

(c) Calculate the financial effect of the facility for abandoning the project on site B stating whether it is positive or negative.

Ignore tax and inflation. Q.8. An investor has two alternative proposals for evaluation on the basis of the following

information:

Project A Project B

Cash inflows Probability Cash inflows Probability

` 75,000

` 25,000

0.6 0.4

` 52,500 1

His utility function states that he will get utilities of 6, 4, 2 and 1 from the first ` 25,000,

second ` 25,000, third ` 25,000 and the fourth ` 25,000 respectively. Evaluate the proposals with and without utility function.

Q.9. TMC is a venture capital financier. It received a proposal for financing requiring an

investment of ` 45 crores which returns ` 600 crores after 6 years, if succeeds. However, it may be possible that the project may fail at any time during the six years.

The following table provide the estimates of probabilities of the failure of the projects.

Year 1 2 3 4 5 6

Probability of failure 0.28 0.25 0.22 0.18 0.18 0.10

In the above table, the probability that the project fails in the second year is given that it has survived throughout year 1. Similarly, for year 2 and so forth.

TMC is considering an equity investment in the project. The beta of this type of project is 7. The market return and risk free rate of return are 8% and 6% respectively.

You are required to compute the expected NPV of the venture capital project and advice of TMC.

: 6 :

J. K. SHAH CLASSES FINAL C.A. - STRATEGIC FINANCIAL MANAGEMENT

REVISION NOTES – MAY ‘19

TABLE : AREAS UNDER THE STANDARD NORMAL CURVE FROM 0 TO Z.

Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359

.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753

.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141

.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517

.4 .1554 .1591 .1628 1664 .1700 .1736 .1772 .1808 .1844 .1879

.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224

.6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2518 .2549

.7 .2580 .2612 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852

.8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133

.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389

1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621

1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830

1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015

1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177

1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4252 .4306 .4319

1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441

1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545

1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633

1.8 .4641 .4649 4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706

1.9 4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767

2.0 4772 .4778 .4783 .4788 .4793 .4798 .4803 4808 .4812 .4817

2.1 .4821 4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857

2.2 4861 4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 4890

2.3 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .4916

2.4 .4918 .4920 .4922 .4925 .4927 .4931 .4931 .4932 .4934 .4936

2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952

2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964

2.7 4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974

2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981

2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986

3.0 .49865 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990

4.0 .4999683

IIIustration: For Z = 1.72, shaded area is .4573 out of total area of 1.



Foreign currency and foreign exchange : • In the context of India, any currency other than Indian rupees is foreign currency. • Foreign exchange includes currency, drafts, bills, letters of credits and traveler cheques

which are denominated and ultimately payable in foreign currencies What is a foreign exchange market : • The foreign exchange market is a decentralized worldwide market. • The participants in the foreign exchange market include central banks, commercial

banks, brokers etc. • The central banks monitor market movements and sentiments and intervene according to

government policy. • The function of buying and selling of foreign currencies in India is performed by

authorized dealers / moneychangers appointed by the RBI. • The foreign exchange department of the major banks are linked across the world on a 24

hour basis. • Major commercial centers are London, Amsterdam, Frankfurt, Milan, Paris, New York,

Toronto, Bahrain, Tokyo, Hong Kong and Singapore. Briefly describe the functions of a foreign exchange market : • Purchasing power is transferred across different countries which will enhance the

feasibility of international trade and overseas investments • The foreign exchange market acts as a central focal point wherein prices of various

currencies are discovered. • Enables the investors to hedge or minimize their risks • Enables the traders to arbitrage any inequalities • Provides an investment / trading avenue to entities who are willing to expose themselves

to this risk. What are the Determinants of Exchange rate

FOREIGN EXCHANGE RISK MANAGEMENT

Interest rate parity

Purchasing Power Parity

Balance of payment position

Government Intervention

Market Expectation

Overseas Investment

Speculation



A. Interest Rate Parity theorem: (IRP)

As per IRP “the size of the forward premium (or discount) should be equal to the interest rate differential between the two countries concerned”. When IRP exists, covered interest arbitrage is not feasible because any interest rate differential advantage will be offset by the discount on the forward rate. Thus, the act of covered interest arbitrage would a return that is no higher that what would be generated by a domestic investment.

B. Purchasing power parity (Inflation) theorem

• Difference in inflation rates between two countries is considered as the most important factor for variations in exchange rates.

• If domestic inflation is high, it means domestic goods are costlier than foreign goods. This results in higher imports creating more demand for foreign currency, making it costlier. (In other words the value of domestic currency will decline).

• If a basket of goods cost Rs470 in India and $10 in US then it is quite natural that the exchange rate should be Rs47/$1

• PPP theory can be expressed by the formula: PPPr = Spot rate (1+rh)

(1+rf) where rh is inflation rate at home; rf is the inflation rate of foreign country

Weakness of PPP theory : It is not only inflation, which affects foreign currency movements. PPP ignores substitution effects – i.e. instead of importing goods might be substituted. C. Balance of payments position : • The BOP position has a big impact on the value of a nation’s currency. • A big or consistent deficit would mount a pressure on the currency of a nation as

deficits require payments in foreign currency. • In the case of a fixed currency rate scenario – the local currency would be devalued

thereby making imports costlier and exports cheaper. • However in the free rate scenario a big or consistent deficit would be a forewarning

for depreciation of a nations currency

D. Government intervention : At times the government would intervene by purchasing or selling foreign exchange to

control pressures on the nation’s currency. F. Market expectation : Market expectation as regards interest rates, inflation, taxes, BOP positions etc would

affect the foreign exchange rates. G. Overseas investment : Overseas Investment flows have an impact of foreign exchange rate. E.g. if US

investments in India increases there would be dollar inflows putting downward pressure on dollar in India.

H. Speculation : Speculators including treasury managers of banks, by virtue of their buying and selling,

tend to influence the rates.



I. International Fisher Effect (IFE)

IFE uses interest rate rather than inflation rate differentials to explain why exchange rate change over time, but it is closely related to Purchasing Power Parity theory because interest rates are often highly co-related with inflation rates.

According to IFE “ nominal risk free interest rate contain a real rate of return and anticipated inflation”. This mean if investors of all countries required the same real rate of return, interest rate differentials between countries may be the result of differentials in expected inflation

What do you mean by Direct and Indirect quotes :

Direct quotes:

• Number of units of the domestic currency per unit of foreign currency

• E.g. 1$ = Rs 49.50 is a dollar direct quote of an Indian rupee in India. However the same quote when quoted in US is not a direct quote for an American.

Indirect quotes:

• Number of units of a foreign currency per fixed number of domestic currency;

• E.g. Rs 100 = $0.2245

What is Two way quotes

Bid price and offer price

• Bid is the price at which a dealer is willing to buy another currency and offer is the rate at which he is willing to sell the currency.

• E.g. a quote of Rs /$ is Rs42,50 / 42.55 it means that the dealer will buy $ at Rs 42.50 and sell dollar at 42.55

Spreads

• Spread is the difference between the bid rate and the offer rate and usually represents the profit margins that a dealer expects to make.

What is meant by Cross currency rates

• In India all buy and sell transactions are routed through the US $.

• Hence all deals involving any other currency would necessarily involve converting in US$ and then converting the US$ into INR.

• Thus if an Indian importer wishes to buy Yen he would first have to sell rupees and buy dollar; then he would sell dollar and buy yen.

• The banker would obtain the Yen / $ rate from Singapore or Tokyo and then apply the Rs /$ rate to determine the amount of rupees required to buy the desired Yen.

Spot rate, Forward rate, cash rate and Tom rate :

1. Spot rate : Rate quoted for transactions that will settled two business days from the transaction date (T+2)

2. Forward rate : Rate quoted for transactions that will be settled beyond two business days at a mutually agreed rate and date.

3. Cash rate : Rate quoted for transactions that will settled on the same day (T+0)

4. Tom rate : Rate quoted for transactions that will be settled in one business day form the date of transaction (T+1)



What is Appreciation and depreciation of currency : (A) Appreciation:

• A currency is said to have appreciated if it is able to purchase more of the other currency.

• E.g. if Rs /$ is 1$ = Rs45 and it changes to 1$ = Rs46 then dollar is said to have appreciated.

(B) Depreciation : • A currency is said to have depreciated if it is able to purchase less of the other

currency. • E.g. if Rs /$ is 1$ = Rs45 and it changes to 1$ = Rs44 then dollar is said to have

depreciated and rupee appreciated. What do mean by Premium and discount : • Premium :

➢ A currency is said to be at a premium if it is more expensive in the forward than in the spot

➢ If Rs / $ spot is 44.95/45.00 and 3 month forward is 45.2045.25 we say that dollar is at a premium

• Discount

➢ A currency is said to be at a discount when it is quoting higher in the spot and cheaper in the forward.

Briefly describe Arbitrage and the kinds of arbitrage operations Arbitrage means buying in one market & selling in another to take advantage of price differential For example a customer can make profits by purchase of dollars in one market where it is available at a cheaper rate and sell the dollars in another market (directly or through other currencies) at a higher rate. There are three types of arbitrages that are dominant in the market : 1. Geographical arbitrage : Buying currency in say London market & selling it in say

Tokyo 2. Triangular arbitrage : Involves three currencies and three markets (also known as

three point arbitrage) 3. Spot - forward Arbitrage (also known as Interest rate arbitrage) If the spot rate +

interest is greater or less than the forward rate there exists an arbitrage potential.

What are the various foreign currency accounts maintained by Banks : 1. Nostro Account : Nostro means “our account with you” Nostro account is the account maintained by the Bank in India with the bank

abroad. E.g. PNB may maintain a bank account with Citibank, New York. Such account

would obviously in dollars. All foreign exchange transactions routed through Nostro Accounts.The concept of Nostro Account and Exchange Position is explained in details towards the end of the notes.

2. Vostro Account : Vostro means “your account with us”. E.g. Citibank New York may maintain a Rupee account with SBI 3. Loro Account : Loro means “their account with you” E.g. SBI has an account with Citibank New York. When Syndicate Bank refers to

this account in any correspondence with Citibank New York it would refer it as Loro account.



Nostro Account and Exchange Position Explained.

Nostro Account refers to “Our Account with you”. For example if Bank of Baroda maintains a Dollar Account with CITIBANK (US), Bank of Baroda will refer it to as Nostro A/c : Citibank(US) meaning our account with Citibank. A Nostro A/c is a current account - no interest is earned on the balance kept in the account; but if the account is overdrawn then interest is charged.

The account is prepared in the books of the bank in which the account is maintained.A Nostro a/c is very similar to a passbook maintained by a customer in a bank - Hence actual inflow of foreign currency will be credited to the account and outflow will be debited.

Terms used with reference to Nostro A/c

Telegraphic Transfer (TT) - A mode of immediate transfer of funds (earlier done through telegrams / telex - now done online)

TT issuance / TT Sale / TT remittance: Suppose a customer of Bank of Baroda requires BoB to transfer immediately $100,000 to his associate in US. He will pay the Rupee equivalent to BoB (India) and BoB will instruct CITIBANK (US) to hand out $100,000 to the associate. In such a case CITIBANK (US) after handing out $100,000 will debit the Nostro A/c

TT payment / TT Purchase: Mr.Rastogi (a US citizen) remits $10,000 to his brother Ram in India. Ram will approach BoB which will hand out the Rupee equivalent of $10,000. BoB in turn will receive $10,000 from Mr Rastogi’s banker. Hence in this case $10,000 will be credited to the Nostro A/c

DD Payment / Encashment of DD/ DD Purchase: Desi Indian Ltd receives a DD of $5000 issued in its favour from Washington. Desi Indian Ltd will approach BoB to encash the DD - BoB will hand over the Rupee Equivalent of $5,000 and in turn will encash the DD of $5000. Hence the Nostro A/c will be credited.

DD issuance: Mr Bharat of New Delhi approaches BoB to get a DD issued for $1000 in favour of a supplier payable at Boston (USA). The Bank charges Rs.68000 and issues the DD. This transaction won’t be entered in the Nostro A/c on the date of issuance of DD. It will be entered on the day the amount of DD is paid. On that day the Nostro A/c will be debited with $1000

Forward Contracts: These are not entered into Nostro A/c on the day of the contract - these are entered on the day they are executed.

Bill of Exchange Purchased: These are not entered on the day of purchase - these are entered on the day of realisation

What is LIBOR and what is its Significance in International transactions:

a. LIBOR stands for London Interbank Offered Rate.

b. It is the base rate of interest rate with respect to which most international financial transactions are priced.

c. It is used as the base rate for a large number of financial products such as borrowings, lendings, swaps etc.

d. Banks and Financial institutions often use LIBOR as the base rate when setting or deciding interest rate of loans, savings, mortgages etc.



e. It is the average of quotes taken from 15 to 18 banks on 5 currencies (GBP, USD, JPY, Euro, CHF) and across 7 maturities (1 day, 1week, 1 month, 2 month, 3 month, 6 month and 12 months)

What is capital account convertibility and what are its basic objectives

Capital account convertibility (CAC) means the freedom to convert local financial assets into foreign financial assets and vice versa at market determined rates of exchange. This implies that Capital Account Convertibility allows anyone to freely move from local currency into foreign currency and back.

Objectives of capital account convertibility

• To deepen and integrate financial markets

• Increased access to global savings

• Discipline domestic policy makers

• Allow greater freedom to individual decision-making

• Facilitate resident Indians to invest their surplus outside the country

• Move capital from one country to another without hindrances



RISK MANAGEMENT - THEORY

What do you mean by Foreign exchange risk

Foreign exchange Risk (also known as FX Risk) is a financial risk that exists when a financial transaction is denominated in a currency other than the home currency.

The risk is that there may be an adverse movement in the exchange rate of the denomination currency in relation to the home currency before the date when the transaction is completed.

Investors and business exporting or importing goods and services or making foreign investments have an exchange rate risk which have severe financial consequences.

What are the Foreign exchange risk affecting Profit and loss account

i. Imports of raw materials

ii. Export of goods

iii. Sundry remittances for royalty

iv. Interest payment on outstanding FX loan

v. Translation of financial statements of offshore entities

vi. Depreciation on fixed assets financed through FX loans

What are the Foreign exchange risk affecting the Balance sheet

Imports of fixed assets through foreign exchange loan

Approvals of foreign exchange (loans pending draw down)

Recognition of exchange rate risk (when should the risk be recognized)

i. At the time of budgeting

ii. At the time of raising import orders

iii. At the time of receiving export orders

iv. At the time of approvals of foreign exchange loan

v. At the time of shipment of goods / drawdown of loan

vi. On the due date of payment

What are the different types of foreign exchange exposure

Transaction exposure

i. Occurs when a change in foreign exchange rate occurs between the time a transaction is executed and the time it is settled

ii. Thus this risk occurs whenever the cash flow is affected in a particular transaction

Translation exposure

Occurs when the assets and liabilities which are denominated in one currency are translated into another currency for inclusion in financial statement

Economic Exposure

This is the risk of a change in the foreign exchange rate due to change in the economic condition of one country



Write a brief note Foreign exchange risk management (FERM)

i. Also known as exposure management.

ii. Copes with the possibility of incurring a loss on account of a open or an unhedged position in foreign exchange.

iii. Especially important where

a. a large proportion of a corporate earnings / expenses are in foreign exchange; or

b. where any fluctuation in the FX has the potential to disturb the corporate ability to execute a strategic plan

What are the Fundamental hedging principles to be kept in mind

i. Hedging must be done centrally to avoid duplication.

ii. All currency exposures need to be included in the hedging programs.

iii. A portfolio approach is required to take the net effect of exposures into account.

iv. Before hedging the exposure using financial market products, the possibilities of exploiting built in hedge strategies need to be explored.

Briefly list the various Exchange rate risk management techniques

i. Forward contract

ii. Currency options

iii. Range forwards

iv. Money Market Hedge

v. Currency swaps

vi. Currency futures.

vii. Matching receipts and payments

viii. Leads and lags

ix. Netting

x. Arbitrage operations

Briefly list down the various techniques for managing Interest rate risks

i. Forward interest rate agreements

ii. Interest rate swaps

iii. Interest rate caps

iv. Interest rate floors

v. Interest rate collars

What are Forward contracts

i. An immediate firm and binding agreement between bank and customer to buy or sell an agreed amount of currency at a date of exchange and at a rate fixed at the time the contract is made.

ii. The time frame can vary from a few days to many years.

iii. Forwards (unlike futures) are not traded on the exchange.

iv. Hence the only way to exit a forward contract is to cancel the forward cover.

v. The decision to hedge would depend upon the cost of hedging (forward premia) and also the expected movement in the foreign exchange rates.

vi. A forward contract locks on to a particular exchange rate thereby insulating from exchange rate fluctuation.

vii. In India forward contracts are available for period’s up to 12 months.



viii. Forward premia are determined by demand and supply.

ix. Internationally the forward premia or discounts reflect the prevailing interest rate differentials and as such arbitrage opportunities are limited.

x. As a rule a currency with a higher interest rate trades at a discount to a currency with lower interest rates.

How do you Close out of forward contracts

When the customer cannot perform the forward exchange contract the bank will close out the contract in one of the following manner:

If the customer was to sell foreign exchange forward (Exporter)

The bank will sell foreign exchange spot and buy it forward from the customer

If the customer was to buy foreign exchange forward (Importer)

The bank will sell foreign exchange forward and buy back the same at spot rate

What are the Advantages / disadvantages of forward cover

Forward cover provides insurance to the taker and thereby acts as a hedge.

However by taking a forward cover one cannot take advantage of upswings or favorable movements in foreign exchange rates.

Currency futures

i. Closely related to currency forwards.

ii. Popularly known as futures contracts

iii. A standardized agreement to buy or sell a pre specified amount of foreign exchange in the futures market at some specified future date.

iv. Available for most hard currencies of the world say Yen, DM, £ sterling, $.

v. Futures being standardized are dealt on an organized exchange.

Difference between forward contracts and futures contract

(Important Theory question)

Criteria Forward contracts Futures contracts

Nature and size of

contract

Size and maturity not standardized Size and maturity are

standardized

Mode of trading Directly between the client and the

bank

Through the clearing house

Liquidity Relatively low liquidity High liquidity due to

standardization

Deposits /

Margins

Deposits / margins not required.

Not marked to market

Requires guarantee deposits /

margins. Marked to market

every day

Default risk Very High Relatively less due to mark to

market procedures

Actual delivery Closure involves actual delivery of

currencies

Position are reversed to close

the deal



What are Currency options

It is a financial instrument that provides the holder a right but not an obligation to buy or sell pre-specified amount of currency at a predetermined rate on a specified date.

What are the different types of currency options

Call options

i. The right to buy a particular currency at a specified rate on a particular date. or within a specified period.

ii. Such an option will be exercised only if the rate of the currency on the exercise date is higher than the option strike price

Put options

i. The right to sell a particular currency at a specified rate on a particular date. or within a specified period.

ii. Such an option will be exercised only if the rate of the currency on the exercise date is lower than the option strike price

Briefly describe the features of options trading

i. Hedges foreign exchange exposures while at the same time gives the opportunity to take advantages of favourable upswings.

ii. The cost of currency option is limited to the option premia.

iii. However the seller of the option runs an unlimited risk as against the risk run by the buyer which is limited to the option premia paid.

iv. In view of the high unlimited risk of the seller options are mainly dealt in the hard currencies and are traded on the OTC.

What are Currency swaps

i. A legal agreement between two parties to exchange the principal and interest rate obligation or receipts in different currencies.

ii. A currency swap is an agreement to exchange fixed or floating rate payments in one currency for fixed or floating payments in a second currency plus an exchange of the principal currency amount.

iii. Allows the customer to re-denominate a loan from one currency to another.

iv. Re-denomination done to reduce borrowing costs and also to hedge against a perceived foreign exchange fluctuation.

v. Currency swaps enables corporate to exploit their comparative advantage in raising funds in one currency to obtain savings in other currencies.

vi. A company has no longer got to live with a bad decision – if it feels that it has erred in the choice of currency it can always swap it.

What is meant by Money Market Hedge (MMH)

A money market hedge involves simultaneous borrowing and lending activities in two different currencies to lock in the home currency value of a future foregin currency cash flow. The simultaneous borrowing and lending activities enable a company to create a home made forward contract.



How to create a MMH in case we have a export receivable in $ (say):

a. Since we a have a receivable in $ (an asset) to create a MMH we need to create a liability in $ - i.e. we need to borrow in $.

b. The amount to be borrowed in $ will be the Present value of the $ receivable amount (@ borrowing rate).

c. The amount borrowed in $ will then be converted in home currency using spot rate and invested at the deposit rates of the home currency.

d. The export receivable realised will then be used to repay the borrowings.

How to create a MMH in case we have a import payable in $ (say)

a. Since we have a import payable (i.e liability) to create a MMH we need to create an asset (i.e Invest) in $.

b. The amount to be invested in $ will be the amount equal to present value of the Payable (@ deposit rate of $).

c. The requisite amount of $ required for making the investment will be purchased at spot rates and the domestic currency outlay so required (to purchase the $) will be borrowed at borrowing rate of domestic currency.

d. On the maturity date, the deposit maturity amount will be used to settle the import payable obligation.

What are the Internal measures for Reducing foreign exchange risks – [Important Theory Question]

A. Matching receipts and payments : Foreign exchange risk can be eliminated if the company has the same currency exposure for receipts as well as payments.

B. Invoicing or billing in the desired currency : One way to reduce the risks associated with FX is to raise the invoice in the home currency. However it may be impractical to adopt this system to international transaction unless the product of the company has got such a demand that its terms and conditions will be accepted by parties all over the world.

C. Leads and lags (leading and lagging): Sound financial management practices require that assets should be in strong currency while liability should be maintained in weak currency.

Leading and lagging refers to the technique of adjusting the timing of receipts and payments.

Leading: It is a process to collect the receivables from foreign debtors before they are due (if the home currency is expected to strengthen) and to pay the foreign currency creditors before their due date (if home currency is expected to depreciate)

Lagging: Lagging refers to delay the collection of receivables from foreign debtors (if the home currency is expected to weaken) and also to delay payment to creditors after their due date (if home currency is expected to appreciate)

D Netting and its Advantages

i. Very often we find MNCs have mutual trading amongst themselves.

ii. Foreign exchange risk exposure of such companies can be substantially reduced if the FX receivables and payables are settled on a net basis rather than making two way flow of moneys.

iii. To do netting it is important that the dates of settlement and the currency of settlement should be common.



Advantages of Netting:

a. Reduces the number of cross border transactions between group entities thereby decreasing the overall administration costs of such

b. Reduces the need for foreign exchange conversion and hence decreases transaction costs associated with foreign exchange conversion.

c. Improves cash flow forecasting since net cash transfers are made at the end of each period.

G. Indexation clauses

i. This is yet another way to hedge against foreign exchange fluctuation.

ii. The agreement of export or import includes an indexation clause which says that the contract price to be adjusted for any adverse movement in foreign exchange rate.

iii. Obviously such clause can be inserted depending upon the bargaining strength of the parties.

iv. Any clause which stipulates that the entire loss arising out of adverse movement in foreign exchange to be borne by one party will be perceived to be very harsh and is rarely adopted.

v. Normally a milder version, which says that any fluctuation beyond a certain threshold limit will be borne by one party.

H. Sharing risks This is a diluted form of indexation clause whereby both the parties to the contract agree to share the risks arising out of adverse movement in some predetermined ratio / manner.

I. Shifting the manufacturing base

i. This technique is normally useful for MNCs who have the ability to set up manufacturing bases across the globe and have sale around the world.

ii. In case the MNC has its production base in one country while the sales are predominantly in another country, the company may find it advantageous to shift the manufacturing base to the country of sale in order to avoid risks associated with foreign exchange fluctuations.

Briefly describe the various Mechanisms for Managing Interest rate risks

A. Forward Interest rate agreement (FRA)

FRA is a financial contract (for a specified period from the start date to the maturity date) between two parties to exchange interest payments for a notional principal amount on the settlement date.

B. Interest rate swaps (IRS)

IRS is a financial contract between two parties to exchange a stream of payments for a notional principal amount on multiple occasions during a specified period.

Accordingly on each payment date that occurs during the swap period cash payments are made by one party to another.

C. Interest rate caps (option)

An interest rate cap is a contract that enables borrowers with floating rate debt to limit or "cap" their exposure to rising interest rates.

Under this contract, the cap buyer is reimbursed for the amount by which the floating rate index exceeds a certain threshold.



An interest rate cap can be structured to protect customers from increases in a variety of floating rate indices, including LIBOR, commercial paper, prime and U.S. Treasury rates.

Typically, the buyer makes an up-front payment to purchase the cap. In general, the longer the term of the cap and the more protection offered by the cap, the more expensive the cap will be.

D. Interest rate floors:

It is a contract that enables lenders who have lent money at floating rates to limit their exposure to downward movement of interest rates. Under this contract, the floor buyer is reimbursed for the amount by which the floating rate falls short of the floor level.

E. Interest rate collars

An Interest rate collar can be created by a entity (which has purchased a cap) by selling a floor. The buyer of the cap needs to pay premium for the cap purchased. The amount of premium outflow on the cap purchased can be reduced by selling a floor and receiving a premium. By doing so the buyer of the cap sacrifices some of the gains that he can make on a downward interest move - and by sacrificing this amount he saves on the premium.



Changing of Quotes Q.1 Find the Re / $ quote from the given set of quote a. $ / Re = 71.25. b. $ / Re = 71.25 / 71.50 Calculation of Cross Currency Quotes Q.2 Find the Re / $ quote from the following set of quotes: ` / £ = 92.10 £ / CHF = 0.90 CHF / ¥ = 0.0090 ¥ / $ = s112 Q.3 Find the $ / £ quote from the following set of quotes ¥ / $ = 112.10 / 15 ¥ / CHF = 111.60 / 45 € / CHF = 0.88 / 0.90 € / £ = 1.20 / 1.21 (Solution : 1.3268 / 1.3793) Q.4 On December 27, 2017 a customer is Mumbai requested a bank to remit DG 2,50,000 to

Holland in payment of import of diamonds under an irrevocable LC. However due to bank strikes, the bank could effect the remittance only on January 3, 2018. The interbank market rates were as follows:

December 27 January 3

Mumbai $ / ` 100 = 3.15 / 3.10 3.12 / 3.07 London $ / £ = 1.7250 / 60 1.7175 / 85

DG / £ = 3.9575 / 90 3.9380 / 90

The bank wishes to retain an exchange margin of 0.125%. How much does the customer stand to gain or lose due to the delay.

Q.5 Given the following Swap points / Swap rate calculate the relevant forward rates: a. Spot ` / $ = 70.60 / 70.70 3 month swap point 5/10

∴ 3 Month forward rate =

b. Spot ` / $ = 70.60 / 70.70 3 month swap point 9/4


c. Spot ` / $ = 70.60 / 70.70 3 month swap rate 0.02/0.06


d. Spot ` / $ = 70.60 / 70.70 3 month swap rate 0.08/0.02


PROBLEMS



Geographical Arbitrage Q.6 Given the following set of quotes from two different markets what will be the arbitrage

action and the profits: Mumbai ₹ / $ = 71.25 / 71.50 New York ` / $ = 71.10 / 71.15 What will your answer be if the quotes were as under: Mumbai ₹ / $ = 71.25 / 71.50 New York ` / $ = 71.15 / 71.20 Interest Rate Arbitrage Q.7 Given the following information: Exchange rate Canadian $ 0.665 per DM (Spot) 3 Month forward Canadian $ 0.670 per DM Interest rates DM: 7% p.a Canadian $: 9% p.a What operations would be carried out to take the possible arbitrage gains? Premiums & Discounts (Appreciation / Depreciation of Currencies) Q.8 The following table shows interest rates for the US $ and French Francs (FF). The spot

exchange rate is 7.05 FF per US $ . Complete the following entries: 3 months 6 months 1 year Dollar interest rate (p.a) 11.5% 12.25% ? FF Interest rate (p.a) 19.5% ? 20% Forward FF per $ ? ? 7.52 Forward Discount per FF p.a ? -6.35% ?

Q.9 Fleur Du Lac, a French Company, has shipped goods to an American importer under a

letter of credit arrangement, which calls for payment at the end of 90 days. The invoice is for $ 1,24,000. Presently the exchange rate is 5.70 FF to the $. If the French Franc were to strengthen by 5% by the end of 90 days, what would be the transaction gain or loss in French Francs? If it were to weaken by 5% what would happen ?

Q.10 Exporters company, a UK company, is due to receive 5,00,000 Northland dollars (N$) in

6 months’ time for goods supplied. The company decides to hedge its currency exposure by using the forward market. The short term interest rate in the UK is 12% p.a and the equivalent rate in Northland is 15%. The spot rate of exchange is 2.5 N$ to the £ .

You are required: i. To calculate how much Exporters Company actually gains or loses as a result of the

hedging transaction if at the end of 6 months the £ in relation to the N$ had (i) gained 4% (ii) lost 2% or (iii) remained stable.

ii. You may assume that the forward rate of exchange simply reflects the interest differential in the two countries.

Q.11 A company operating a country having the dollar as its unit of currency has today

invoiced sales to an Indian company, the payment being due 3 months from the date of invoice. The invoice amount is $ 13750 and at today’s spot rate of $ 0.0275 per ` 1 is equivalent to `. 5,00,000.



It is anticipated that the exchange rate will decline by 5% over the 3 month period and in order to protect the $ proceeds, the importer proposes to take appropriate action through foreign exchange market.

The 3 month forward rate is quoted as $ 0.0273 per ` 1. You are required to calculate the expected loss and to show how it can be hedged by

forward contract. Money Market Hedge / Leading and Lagging Q.12 EXAMPLE ON MONEY MARKET HEDGE EXAMPLE (A) Payable of $ 10,00,000 due in 6 months’ time. Spot Rate : 1$ = 70.00/72.00 Deposit and borrowing rates are as under

India USA Deposit rate Borrowing rate Deposit rate Borrowing rate 3 months 8% 10% 3% 5%

Show how Foreign exchange risk can be hedged through a money market hedge. EXAMPLE (B) Receivable of $ 5,00,000 due in 6 months’ time. Spot Rate : 1$ = 72.00/75.00 Deposit and borrowing rates are as unders


Show how Foreign exchange risk can be hedged through a money market hedge. Q.13 The finance director of P Ltd has been studying exchange rates and interest rates

relevant to India and USA. P Ltd has purchased goods from the US C at a cost of $ 51 lakhs payable in dollars in 3 months’ time. In order to maintain profit margins, the finance director wishes to adopt, if possible, a risk free strategy that will ensure that the cost of the goods to P Ltd is no more than ` 22 crores.

Exchange rates (` / $ : Spot : 40-42) and 3 Months forward : ` / $ = 42-45 Interest rates available to P Ltd are as under:


Calculate whether it is possible for P Ltd to achieve a cost directly associated with this transaction of no more than ₹ 22 crores by means of a forward market hedge, market hedge or leading which is available @ 3%

Q.13 A X Ltd is supposed to make payment of $ 1,00,000 today when the spot rate is ` 40-42.

One month forward is available at $ 1 = ` 39-41 and the penal interest for late payment would at 12% p.a. Company’s cost of capital is 15%. You are required to advise the client whether to go for lagging or to make the payment right away



Q.14 Star trek Ltd is an Indian company. It has subsidiaries in US, UK and Singapore, named X, Y and Z respectively. The intercompany owing’s are as follows: Debtor Creditor Amount due X Y £ 1,00,000 X Z SG $ 30,000 Y X $ 70,000 Y Z SG $ 25,000 Z X $ 65,000

The relevant exchange rates are as follows: $ 1 = `. 46.15 £ 1 = `. 83.80 SG $ 1 = `. 27.70 If Startrek wants to do multilateral netting, ascertain the net payment for settlement to be

made mutually by the subsidiaries Nostro A/c & Vostro A/c Q.15 You as a dealer have the following position in Swiss francs (CHF) on October 31st: Balance in Nostro A/c (Cr) 1,00,000 Opening Position (Overbought) 50,000 Purchased a Bill on Zurich 80,000 Sold TT Forward 60,000 Forward Purchase Contract cancelled 30,000 Remitted by Telegraphic Transfer 75,000 Draft on Zurich Cancelled 30,000 What steps you would take if you required to maintain a credit balance of Swiss francs

30,000 in the Nostro Account and keep an overbought position of Swiss 10,000. Suppliers Credit Q.16 Alert Ltd is planning to import a multi-purpose machine from Japan at a cost of ¥ 3400

lakhs. The company can avail loans at 18% p.a with quarterly rests with which it can import the machine. However, there is an offer from Tokyo based branch of an Indian Bank extending credit of 180 days at 2% p.a against opening of an irrevocable letter of credit.

Other information: Present exchange rate ` 100 = ¥ 340 180 days forward rate ` 100 = ¥ 345 Commission charges for letter of credit at 2% for 12 months. Advise whether the offer from the foreign branch should be accepted. Q.17 Z Ltd importing goods worth $ 2 million requires 90 days to make the payment. The

overseas supplier has offered a 60 days interest free credit period and for additional credit for 30 days an interest of 8% per annum. The Bankers of Z Ltd offer 30 days loan at 10% per annum and their quote for foreign exchange is as follows:

Spot 1 $ = ` 56.50 60 days forward 1 $ = ` 57.10 90 days forward 1 $ = ` 57.50 You are required to evaluate the following options:

a. Pay the supplier in 60 days; or b. Avail the suppliers offer of payment after 90 days.



Hedge Using Futures Q.18 P Inc is a company operating in the USA which imports goods from Q Plc in the UK. P

Inc is due to pay £ 6,50,000 to Q Plc on 20th February 2017. It is now 12th November 2016. The following futures contracts (contract size £ 62500 are available on the Philadelphia exchange:

Expiry Current futures rate December 1.4900 $ / £ March 1.4960 $ / £ Illustrate how P Inc can use future contracts to reduce the transaction risk if on 20th

February the spot rate is 1.5030 $ / £ and March Futures are trading at 1.5120 $ / £. The spot rate on 12th November is 1.4850 $ / £

Q.19 XYZ Ltd is an export oriented business house based in Mumbai. The company invoices

in customers’ currency. Its receipt of $ 1,00,000 is due on 1st September 2017. Market information as on June 1, 2017

Exchange Rates Currency Futures $ / ` $ / ` Spot : 0.02140 Contract size ` 472000 1 Month forward 0.02136 June 0.02126 3 Month forward 0.02127 September 0.02118

Future Month Initial Margins Interest rate in India

June ` 10,000 7.50% September ` 15,000 8.00%

On September 1, 2017 the spot rate $ / ` is 0.02133 and currency future rate is 0.02134. Comment which of the following methods would be most advantageous to XYZ Ltd: a. Using Forward contracts b. Using Currency Futures c. Not hedging currency risks

Cancellation Extension of Forward contracts Cancellation on’s Due Date Q.20 On 15th January 2017 you as a banker booked a forward contract for $ 2,50,000 for your

import customer deliverable on 15th March 2017 at ₹ 65.3450. On due date customer requests you to cancel the contract. On this date quotation for $ in the interbank market is as follows:

Spot 1 $ = 65.2900 / 2975 Spot / April 3000 / 3100 Spot / May 6000 / 6100 Assuming that the flat charges for the cancellation is ` 100 and exchange margin is

0.10%, then determine the cancellation charges payable by the customer. Cancellation before due date Q.21 You as a banker has entered into a 3 months forward contract with your customer to

purchase AUD 1,00,000 at the rate of ₹ 47.2500. However after 2 months your customer comes to you and request cancellation of the contract. On that date quotation for AUD in the market is as follows:

Spot 1 AUD = ` 47.3000 / 3500 1 month forward 1 AUD = ` 47.4500 / 5200 Determine the cancellation charges payable by the customer



Extension before due date Q.22 Suppose you are a banker and one of your export customer has booked a $ 1,00,000

forward sale contract for 2 months with you at the rate of ` 62.52 and simultaneously you covered yourself in the interbank market at `. 62.59. However on the due date, after 2 months your customer comes to you and requests for cancellation of the contract and also requests for extension of the contract by one month. On this date quotation of $ in the market was as follows:

Spot `. 62.68 / 62.72 1 month forward `. 62.6400 / 62.7400 Determine the extension charges payable by the customer assuming exchange margin of

0.10% on buying as well as selling. Q.23 On 30th June 2017 when a forward contract matured for execution you are asked by an

importer customer to extend the validity of the forward sale contract for $ 10000 for a further period of 3 months.

Contracted rate $ 1 = ` 41.87 $ quotes on 30-6-2009 Spot `. 40.48 / 40.49 Premium July 0.1100 / 0.1300 Premium August 0.2300 / 0.2500 Premium September 0.3500 / 0.3750 Calculate the cost for your customer in respect of the extension for the forward contract.

Also calculate the new forward rate for the extended period. Bank’s margin 0.08% for Buying rate 0.25% for selling rate Q.24 X Ltd has imported goods costing $ 1,00,000 from an American company on 1/1/2017

payment to be made in 2 months’ time on 1/3/2017. The two months forward rates available on 1/1/2017 are 1 $ = ` 43-45. X Ltd enters into 2 months forward contract.

Now it is 1/3/2017 on which dates following rates are available Spot 1 $ = ` 46 - ` 48 1 month forward 1 $ = ` 46.10 - ` 47.20 The penal interest for late payment is 6% p.a and the company’s cost of capital is 18%.

You are required to advice the company whether to settle the deal today or go for lagging by extension of forward by 1 month.



Q.1. X Co., Ltd., invested on 1.4.2005 in certain equity shares as below :

Name of Co. No. of shares Cost (`̀̀̀)

M Ltd. 1,000 (` 100 each) 2,00,000

N Ltd. 500 (` 10 each) 1,50,000

In September, 2005, 10% dividend was paid out by M Ltd. and in October, 2005, 30% dividend paid out by N Ltd. On 31.3.2006 market quotations showed a value of ` 220 and ` 290 per share of M Ltd. and N Ltd. respectively.

On 1.4.2006, investment advisors indicate (a) that the dividends from M Ltd. and N Ltd. for the year ending 31.3.2007 are likely to be 20% and 35%, respectively and (b) that the probabilities of market quotations on 31.3.2007 are as below :

Probability factor Price / Share of M Ltd. Price / Share of N Ltd.

0.2 220 290

0.5 250 310

0.3 280 330

You are required to : (i) Calculate the average return from the portfolio for the year ended 31.3.2006 ; (ii) Calculate the expected average return from the portfolio for the year 2006-07 ; and (iii) Advise X Co. Ltd., of the comparative risk in the two investments by calculating the

standard deviation in each cases. Q.2. Suppose Mr. X in a world there are only two assets, gold and stocks. He is interested in

investing his money in one, the other or both assets. Consequently he collects the following data on the returns on the two assets over the last six years.

Gold Stock Market

Average return 8% 20%

Standard deviation 25% 22%

Correlation ---- -0.4

(a) Mr. X is constrained to pick just one, which one he would choose? (b) Mr. Y, a friend of Mr. X argues that this is wrong. He says that Mr. X is ignoring the

big payoffs that he can get on gold. How would Mr. X go about alleviating his concern?

(c) How would a portfolio composed to equal proportions in gold and stocks do in terms of mean and variance?

(d) Mr. X came to know that GPEC (a cartel of gold - producing countries) is going to vary the amount of gold it produces with stock prices in the country. (GPEC will produce less gold when stock markets are up and more when it is down). What effect will this have on his portfolios? Explain.

Q.3. P Ltd. and Q Ltd. have low positive correlation coefficient of + 0.5. Their respective risk

and return profile is as under : RP = 10% RQ = 15% sP = 20% sQ = 25% Compute the portfolio of P & Q to minimise risk.

PORTFOLIO MANAGEMENT



Q.4. Two particular securities P and Q lie on the Security Market Line. P has a Beta of 0.5, carries a risk premium of 4%. Q has an expected return of 20% along with the Beta of 1.75. In the light of this information, determine whether the securities given hereunder are overpriced or under - priced.

Security Expected Return Beta

1 20 2.00

2 14 0.75

3 15 1.25

4 5 - 0.25

5 31 3.25

Q.5. The following data relate to two securities, A and B.

A B

Expected Return 22% 17%

Beta Factor (b) 1.5 0.7

Assume : IRF = 10% and RM = 18%. Find out whether the securities, A and B are correctly priced ? Also show the graphic

presentation of the above situation. Q.6. The following details are given for X and Y companies' stocks and the Bombay Sensex

for a period of one year. Calculate the systematic and unsystematic risk for the companies' stocks. If equal amount of money is allocated for the stocks what would be the portfolio risk?

X Stock Y Stock Sensex

Average return 0.15 0.25 0.06

Variance of return 6.30 5.86 2.25

� 0.71 0.27

Correlation Co-efficient 0.424

Co-efficient of determination (r2) 0.18

Q.7. You are presented with the following information concerning the returns on the shares

of C Ltd. and on the market portfolio, according to the various conditions of the economy.

Condition of economy

Probability of condition occurring

Return on C Ltd. Return on the market

1 0.2 15% 10%

2 0.4 14% 16%

3 0.4 26% 24%

The current risk - free interest rate is 9 per cent. Required :

(a) Calculate the coefficient of correlation between the returns on C Ltd. and the market portfolio.

(b) Calculate the total risk (i.e., standard deviation) of C Ltd. and discuss why this is not the most appropriate measure of risk to be used in making investment decisions.

(c) Calculate the beta factor for C Ltd. and briefly discuss its significance. Is C Ltd. efficiently priced according to the CAPM and the information given above?



Q.8. Mr. X owns a portfolio with the following characteristics :

PARTICULARS SECURITY A SECURITY B SECURITY C

Factor 1 sensitivity 0.80 1.50 0

Factor 2 sensitivity 0.60 1.20 0

Expected return 15% 20% 10%

It is assumed that security returns are generated by a two factor model. (i) If Mr. X has ` 1,00,000 to invest and sells short ` 50,000 of security B and

purchases ` 1,50,000 of security A what is the sensitivity of Mr. X's portfolio to the two factors?

(ii) If Mr. X borrows ` 1,00,000 at the risk free rate and invests the amount he borrows

along with the original amount of ` 1,00,000 in security A and B in the same proportion as described in part (i), what is the sensitivity of the portfolio to the two factors?

(iii) What is the expected return premium of factor 2? Q.9. ABC Ltd. has a b of 1.20, IRF = 8% & Rm = 15%. What is the required rate on shares of

ABC? If the actual returns for 4 observations are as follows, what is the alpha value of shares of ABC?

Year Actual Returns

1 20.43

2 18.80

3 16.40

4 13.95

Q.10. With a risk - free rate of 10%, and with the market portfolio having an expected return

of 20% with a standard deviation of 8%, what is the Sharpe Index for portfolio X, with a mean of 14% and a standard deviation of 18%? For portfolio y, having a return of 20% and a standard deviation of 16%? Would you rather be in the market portfolio or one of the other two portfolios?

Q.11. The returns on stock A and market portfolio for a period of 6 years are as follows :

Year Return on A (%) Return on market portfolio (%)

1 12 8

2 15 12

3 11 11

4 2 - 4

5 10 9.5

6 - 12 -2

You are required to determine : (i) Characteristic line for stock A. (ii) The systematic and unsystematic risk of stock A.

Q.12. Ramesh wants to invest in stock market. He has got the following information about

individual securities: SECURITY EXPECTED RETURN BETA

A 15 1.5 40

B 12 2 20

C 10 2.5 30

D 9 1 10

E 8 1.2 20

F 14 1.5 30

Market Variance is 10% % , Risk Free Rate is 7 %. What should be the optimum portfolio assuming no short sales?



What is meant by Interest Rate Risk Interest rate risk refers to the risk that a business is exposed due to changes in interest rates. Interest rate movements affect different types of entities differently. For example a company with a high capital expenses and low margins would see its profits margins shrink in case of an upward move of interest rates. Similarly, banks who borrow money and lend it are affected in a different way. Banks would also be affected by interest rate movements to the extent such movements affect the valuation of bonds since banks hold a large portion of their funds in such bonds. What are the different types of Interest rate risk

Gap Exposure (typically more important for Banks)

A gap or mismatch risk arises from holding assets and liabilities (and off balance sheet items) with differing principal amounts or maturity dates thereby creating exposure due to sudden and unexpected changes in the interest rates

Where the bank holds more Rate sensitive Assets (RSA) than Rate sensitive Liabilities (RSL) there would be a positive Gap (meaning increase in interest rates could result in Net Interest Income going up) and vice versa.

Basis risk Market interest rates of various instrument seldom change by the same degree. The risk of different assets and liabilities may change in different magnitude is referred to as basis risk

For example: Assets may be linked to Fixed Interest rates while liabilities may be linked to floating rates.

Embedded option risk

There may be assets / liabilities which have an embedded option and any change in interest rates may trigger such embedded option resulting in losses

For example: A put table loan (i.e. a loan which can be repaid by the borrower at any time) will be triggered if the interest rates go down i.e. the borrower may decide to repay the high interest cost loan

Yield Curve risk In a floating rate scenario banks may price their assets and liabilities on different benchmarks like TBill yield, fixed deposit rates, call money rates etc. In such a case any non-parallel move in the yield curve i.e. one benchmark moves but the other does not may expose the entity to interest rate risk

These are more likely to happen when the economy is moving through business cycles

INTEREST RATE RISK MANAGEMENT



Price risk We know that yield and price of bonds are inversely related. Hence any movement in the interest rates results in an opposite movement in the price of the bonds

Banks hold a significant part of their funds in bonds and that too in the held for trading category. Any interest rate movement will affect the value of such bond portfolio

Reinvestment risk Reinvestment risk is the risk of interest rate movements at the time of reinvestment of cash flows

Any mismatch in cash flows could affect the returns of the bank if interest rates have moved in the interim period.

Hedging interest rate risk - Two broad methods

TRADITIONAL METHODS

Asset Liability Management (ALM) Asset Liability Management (ALM) can be defined as a mechanism to address the risk faced by a bank due to a mismatch between assets and liabilities either due to liquidity or changes in interest rates. Liquidity is an institution's ability to meet its liabilities either by borrowing or converting assets.

Forward Rate Agreements (FRAs) (Discussed in detail later in the chapter)

FRAs are Over the Counter (OTC) products and are not traded on the exchange. A FRA is an agreement between two parties through which a borrower / lender protects itself from unfavorable changes in interest rates



MODERN METHODS

(Detailed discussion given later in this chapter)

Interest rate futures An interest rate future is a futures contract with an underlying instrument that pays interest. The interest rate future allows the buyer and seller to lock in the price of interest bearing asset for a future date (and thereby lock in the yield or interest rates)

Interest rate options

Cap option. Cap option is usually purchased by a borrower whereby he gets reimbursed for any interest rise above the cap level. The buyer of the cap pays a premium to the seller of the cap. Refer Example 1 below

Floor option: Floor option is usually purchased by a lender whereby he gets reimbursed for any interest fall below the floor level. The buyer of the floor pays a premium to the seller of the floor. Refer Example 2 below

Interest rate collars It is a combination of a floor and a cap. The buyer of the cap (pays the premium) and simultaneously sells a floor (and receives a premium). Creation of a collar has the effect of reducing the premium outflow and creating a band within which the interest rate will move for the creator of the collar) Refer Example 3 below

Interest rate swaps In an interest rate swap, the parties to the agreement, termed the swap counter-parties, agree to exchange payments indexed to two different interest rates. Total payments are determined by the specified notional principal amount of the swap, which is never actually exchanged.

Swaptions An interest rate swaption is simply an option on an interest rate swap. It gives the holder the right but not the obligation to enter into an interest rate swap at a specific date in the future, at a particular fixed rate and for a specified term.



Example 1: CAP OPTION

Let’s say Mr X is a borrower who has borrowed money at LIBOR + 1%. Currently the LIBOR is at 4%, thereby making the current borrowing cost of Mr X 5%. Let’s presume that Mr X buys a Cap at LIBOR of 6%. If LIBOR goes above 6% say to 7% then Mr X will pay the lenders of money 8% (because he has borrowed at LIBOR + 1%) but on the other hand he will receive 1% from the seller of the cap the difference between LIBOR (7%) and the Cap rate (6%) thereby making his cost of borrowing 7+1-1 = 7%. If the LIBOR went to 10% (say) Mr X will pay the lenders of money L+1 i.e. 11% but on the other hand he will receive the difference between LIBOR(10%) and cap rate (6%) i.e. 4%. Hence his net borrowing cost will be again 7% i.e. 10+1-4 = 7%. If on the other hand LIBOR went down to say 2% he will pay the lenders of money 2+1 =3% and will not exercise the cap (since the LIBOR has not crossed the cap level of 6%) making his cost of borrowing 4%

Conclusion: Caps have the effect of freezing the upward movement of interest cost (in this case - 7%) while it allows the buyer of the cap option to take advantage of downward moves.

Example 2: FlOOR OPTION

Example: Let’s say Mr X is a lender who has lent money at LIBOR + 1%. Currently the LIBOR is at 7%, thereby making the current interest earning of Mr X 8%. Lets presume that Mr X buys a floor at LIBOR of 4%. If LIBOR goes below 4% say to 3% then Mr X will receive 4% from the borrower(because he has lent at LIBOR + 1%) but on the other hand he will receive 1% from the seller of the floor (the difference between LIBOR (3%) and the Floor rate (4%) thereby making his net interest income 3+1+1 = 5%. If the LIBOR went to 1 % (say) Mr X will receive from the borrower L+1 i.e. 2% but on the other hand he will receive the difference between LIBOR(1%) and floor rate (4%) i.e. 3%. Hence his net interest income will be again 5% i.e. 1+1+3% = 5%. If on the other hand LIBOR went up to say 10% he will receive from borrowers 10+1 =11% and will not exercise the floor (since the LIBOR has not crossed the floor level of 4%) making his net interest income 11%

Conclusion: Floors have the effect of freezing the downward movement of interest earnings (in this case - 5%) while it allows the buyer of the floor option to take advantage of upward moves.



Example 3: INTEREST RATE COLLARS Let us presume that Mr X has borrowed money at L+2%. Currently Libor is at 5%. Mr X decides to buy a cap of Libor at 7% and simultaneously sell a floor at Libor of 3%. Let us analyse what will be his net borrowing cost under different scenarios of Libor:

If Libor = Pay to Lenders (L+2%)

Receive on the Cap option

purchased @ 7%

Pay on the floor option sold @ 3%

Net borrowing cost

1% 3% Nil 2% 5%

2% 4% Nil 1% 5%

3% 5% Nil Nil 5%

4% 6% Nil Nil 6%

5% 7% Nil Nil 7%

6% 8% Nil Nil 8%

7% 9% Nil Nil 9%

8% 10% 1% Nil 9%

9% 11% 2% Nil 9%

10% 12% 3% Nil 9%

Hence we see from the above that by creating a floor Mr X has capped his lower level of interest rate at 5% (ie his cost of borrowings will never go below 5%) and has also capped the higher level of interest @ 9% (ie his cost of borrowings will never go beyond 5%) Swaptions An interest rate swaption is simply an option on an interest rate swap. It gives the holder the right but not the obligation to enter into an interest rate swap at a specific date in the future, at a particular fixed rate and for a specified term. There are two types of Swaption contracts: a. Fixed rate payer swaption gives the owner of the swaption the right but not the obligation

to enter into a swap where they pay the fixed leg and receive the floating leg. b. Fixed rate receive swaption gives the owner of the swaption the right but not the

obligation to enter into a sway in which they will receive the fixed leg and pay the floating leg.

Uses of swaption: a. Swaption can be used by traders (to speculate) as well as by corporates (to hedge). b. Swaptions are useful to borrowers to lock into a particular rate in case of adverse interest

rate movements. (They would pay fixed and receive floating) c. Swaptions are useful to investors / lenders to participate in upward interest rate

movements (they would pay floating and receive fixed). d. Swaptions can be useful for corporates tendering for contracts and who want to eliminate

the effect of adverse interest rate movements beyond a certain point. e. Swaptions also provide protection on callable / puttable bond issues



Forward rate Agreements A Forward Rate Agreement (FRA) is an agreement between two parties through which a borrower/ lender protects itself from the unfavourable changes to the interest rate. Unlike futures FRAs are not traded on an exchange thus are called OTC product. Main features of Forward rate agreements a. Normally it is used by banks to fix interest costs on anticipated future deposits or interest

revenues on variable-rate loans indexed to LIBOR. b. It is an off Balance Sheet instrument. c. It does not involve any transfer of principal. The principal amount of the agreement is

termed "notional" because, while it determines the amount of the payment, actual exchange of the principal never takes place.

d. It is settled at maturity in cash representing the profit or loss. A bank that sells an FRA agrees to pay the buyer the increased interest cost on some "notional" principal amount if some specified maturity of LIBOR is above a stipulated "forward rate" on the contract maturity or settlement date. Conversely, the buyer agrees to pay the seller any decrease in interest cost if market interest rates fall below the forward rate.

Interest rate futures: An interest rate future is a futures contract with an underlying instrument that pays interest. The interest rate future allows the buyer and seller to lock in the price of interest bearing asset for a future date (and thereby lock in the yield or interest rates). Futures use the inverse relationship between interest rates and bond prices to hedge against interest rate movements. A borrower will enter into a sell futures today. Then if the interest rates rise in the future, the value of future will fall (as it is linked to the underlying asset, bond prices) and hence a profit can be made when closing out the futures (i.e. buying the futures).



Question 1: In November 2012 a company’s corporate treasurer realises that in mid-December he will need to borrow $1 million for 3 months. He is concerned that interest rates might rise in the intervening period. The following data is available in November: - November spot $ interest rate 10% - December 3 month Euro Dollar futures 11% - The contract size for Euro dollar futures is $1 million. Required: Show how the treasurer might hedge his position using a futures market operation. Assume the funding requirement is on the last day of December futures trading. Illustrate your answer with reference to the following December spot rates: 9% 11% 13% Question 2: In UK, X Ltd has realised from its cash budget that it is likely to have a surplus of £ 100 lacs arising in 2 months’ time (May) for a period of 3 months. It is concerned that interest rates in the next 2 months may fall and wishes to hedge this risk using future contracts. June 3 months sterling interest rate futures contracts are available with a contract size of £ 5 lacs. They are currently priced at £ 96.00. Interest rate currently stands at 4%. Explain how X Ltd can hedge its interest rate exposure using futures contracts if in 2 months’ time the market interest rate has fallen to 3% and the futures price has moved to £ 97.00 Question 3: The monthly cash budget of HYK Communication plc shows that the company is likely to need £ 18 million in two months’ time for a period of four months. Financial markets have recently been volatile and finance director fears that the short-term interest rates could rise by as much as 150 tics that is 1.5%. Libor is currently at 6.5% and HYK plc can borrow at Libor + 0.75%. LIFFE £ 5,00,000 3 month future prices are as follows: December 93.40 March 93.10 June 92.75 Assume that it is now 1st December and that exchange traded future contracts expire at the end of the month. You are required to estimate the result of undertaking an interest rate futures on the London International financial futures exchange if LIBOR increases by 150 tics that is 1.5% and March future increases by 130 tics that is 1.3% Question 4 X Ltd would require Rs.500 crores after six month and is worried that it's cost of capital at that time might go up beyond 11% .Hence it decides to buy a Cap at 11% on 500 crores for five years interest to be paid at quarterly interval. It pays a premium of Rs.5 crores to Z limited. Y Ltd is expecting surplus of ` 100 crores after six months for three years and it is worried that interest rates may fall below 7%. Hence it buys a floor floor at 7% on ₹ 100 crores for three years on quarterly compounding basis and pays the premium of Rs.2 crores to X Ltd. You are required to bring out the cash flow implications for X Ltd and Y Limited if the interest rates after six months are as below: a. 6.5% -10.45% b. 7.5% -11.45% c. 06% - 10.5% d. 7.4% - 14% e. 5% -13%

PROBLEMS



Question 5. A Plc wishes to raise fixed interest debt capital. Because of its current poor credit rating it considers a debenture issue to be out of the question and the best fixed interest rate loan it can obtain is at 12.5% p.a. A Plc can however borrow at a variable rate of LIBOR + 0.5. B Plc can issue fixed rate debentures at 11% or alternatively borrow at a variable rate equivalent to LIBOR. B plc wants a floating rate loan. A and B arrange to swap with the following conditions (assume each firm requires £ 1 million of funds. i. A borrows £ 1 million at a variable rate of LIBOR + 0.5% ii. B borrows £ 1 million at the fixed rate of 11% iii. In the swap arrangement A agrees to pay B interest of 11.5% (fixed) on the £ 1 million

while B agrees to pay A an interest rate of LIBOR (variable) on the same sum. Required: a. Calculate the net cost of financing A & B b. Evaluate the effect on A and B of a LIBOR of (a) 8% (b) 17% c. Draft the scheme of swap if the bank arranging the swap, A Plc, B Plc are to share the net

gain in the ratio of 3:3:4 Question 6: Derivative Bank entered into a plain vanilla swap through an OIS (overnight Index Swap) on a principal of ` 10 crores and agreed to receive MIBOR overnight floating rate for a fixed payment on the principal. The swap was entered into on Monday 2nd August, 2010 and was to commence on 3rd August 2010 and run for a period of 7 days. Respective MIBOR rates for Tuesday to Monday were: 7.75%, 8.15%, 8.12%, 7.95%, 7.98%, 8.15% If Derivative Bank received ₹ 317 net on settlement, calculate Fixed rate and interest under both legs. Note:

a. Sunday is a holiday b. Work in rounded rupees and avoid decimal working Question 7: You are given the following interest rates by a bank: Period Rates 3 months 6% - 6.4% 6 months 8% - 10.2% Another bank has quoted 3/6 FRA as 6% - 7.2% Required A. Calculate 3/6 FRA in respect of deposits B. Verify whether there is any arbitrage opportunity if the client can borrow ₹ 1,00,000 now. C. Also, if yes, describe the actions to be taken by the arbitrager to avail arbitrage

opportunity.

Question 8: Consider the following data for Government Securities:

Face value Interest rate (%) Maturity (Years) Current Price (`̀̀̀)

1,00,000 0 1 91,000 1,00,000 10.5 2 99,000 1,00,000 11.00 3 99,500 1,00,000 11.50 4 99,900

Calculate the forward interest rates



Question 9: Electra space is a consumer electronics wholesaler. The business of the firm is highly seasonal in nature. In 6 months of a year the firm has a huge cash deposit and especially near Christmas time and other 6 months the firm faces a cash crunch leading to borrowing of money to cover up its exposure for running the business. It is expected that the firm shall borrow a sum of Euro 50 million for the entire period of slack season in about 3 months’ time. A Bank has given the following quotations: Spot 5.50% - 5.75% 3 x 6 FRA 5.59% - 5.82% 3 x 9 FRA 5.64% - 5.94% 3 months Euro 50000 futures contract maturing in 3 months’ time is quoted at 94.15 (5.85%) You are required to determine: (a) How a FRA shall be useful if the actual interest rate after 3 months turnout to be

(i) 4.5% (ii) 6.5% (b) How 3 month futures contract shall be useful for company if the interest rate turns out as

mentioned in (a) above Question 10 Suppose a life insurance company issued $ 100 million of 5 year guaranteed investment contracts that commit it can pay a fixed rate of 9% semiannually. Suppose the company is able to invest $ 100 million is a 5 year semiannual floating rate instrument yielding 6 month LIBOR + 1% a. Describe the interest exposure by the insurance company. At what point would the

company not be able to earn enough on the floating rate instrument to pay for its fixed obligations?

b. Suppose there is available in the market a 5 year floating interest rate swap with a notional amount $ 100 million with the following terms that i) receive fixed 8.5% every 6 months and ii) pay 6 month LIBOR, then how can the insurance company use this swap to hedge its interest rate exposure

Question 11 The following details are related to the borrowing requirements of two companies ABC Ltd and DEF Ltd :

Company Requirement Fixed rate offered Floating rate offered

ABC Ltd Fixed rupee rate 4.5% PLR + 2% DEF Ltd Floating rupee rate 5% PLR + 3%

Both companies are in need of ` 2,50,00,000 for a period of 5 years . The interest rates on the floating rate loans are reset annually. The current PLR for various period maturities are as follows :

Maturity (Years) PLR (%)

1 2.75% 2 3% 3 3.20% 4 3.30% 5 3.375%

DEF Ltd has bought an interest rate cap at 5.625% at an upfront premium of 0.25% per annum. a. You are required to exhibit how these two companies can reduce their borrowing cost by

adopting swap assuming that gains resulting from swap shall be shared equally among them.

b. Further calculate cost of funding to these two companies assuming that expectation theory holds good for 4 years.



SECTION 1 : FUTURES

Definition

A futures contract is a legal agreement, generally made on the trading floor of a futures exchange, to buy

or sell a particular commodity or financial instrument at a predetermined price at a specified time in the

future.

Common types of futures:

Some of the most common types of futures traded across the globe are:

a. Stock Futures

b. Index Futures

c. Commodity Futures

d. Currency Futures.

Advantages and Disadvantages of Futures

Advantages

a. It allows hedgers to shift risks to speculators.

b. It gives traders an efficient idea of what the futures price of a stock or value of an index is likely to

be.

c. Based on the current future price, it helps in determining the future demand and supply of the shares.

d. Since it is based on margin trading, it allows small speculators to participate and trade in the futures

market by paying a small margin instead of the entire value of physical holdings.

Disadvantages

However, one must be aware of the risks involved too.

a. The main risk stems from the temptation to speculate excessively due to a high leverage factor, which

could amplify losses in the same way as it multiplies profits.

b. Further, as derivative products are slightly more complicated than stocks or tracking an index, lack of

knowledge among market participants could lead to losses.

c. Since these are exchange traded products - they have standard lot sizes and expiry dates. This might

pose a problem for matching the risk exposures in terms of quantity (or value) and time

Pricing of Futures

The most commonly used model for pricing of futures is known as the “Cost of Carry model”. According

to cost of carry model the price of Futures = Spot price + Net Cost of Carry. The formula can be modified

slightly by expanding the term Net cost of carry as Cost of Carry - Carrying return.

In other words :

Future = Spot + (Cost of carry - Carrying return)

Carry Cost refers to the cost of holding the asset till the futures contract matures. This could include

storage cost, interest paid to acquire and hold the asset, financing costs etc.

DERIVATIVES : FUTURES & OPTIONS



Carry Return refers to any income derived from the asset while holding it like dividends, bonuses etc.

While calculating the futures price of an index, the Carry Return refers to the average returns given by the

index during the holding period in the cash market. A net of these two is called the net cost of carry.

Mathematically the basic pricing model can be expressed as follows :

Futures = Spot (1+r)n

However, this basic model undergoes slight modification depending on the type of futures being calculate

e.g stock futures, index futures or commodity futures. This modification is required to factor in storage

costs (typically in case of commodities) and dividend returns (in case of stocks / index).

Hence we can state as under:

Commodity futures:

Futures = (Spot + Present Value of Storage) (1+r)n

Stock futures:

Futures = (Spot - Present Value of Dividends) (1+r)n

Index futures

Futures = Spot [1+(r-d)]n

What is continuous compounding

Continuous compounding is the mathematical limit that compound interest can reach. It is an extreme

case of compounding since most interest is compounded on a monthly, quarterly or semiannual basis.

Hypothetically, with continuous compounding, interest is calculated and added to the account's balance

every infinitesimally small instant. While this is not possible in practice, the concept of continuously

compounded interest is important in finance and is very frequently used in valuation of derivatives.

Continuous compounding can be expressed as:

Amount = Principal x ern

Where e = 2.7183 (constant); r = continuously compounded rate of interest (CCRI) and n = time

If futures price is to be computed using a continuously compounded rate then the models can be

expressed as under:

Stock futures :

Futures = (Spot - PV of Dividend) x ern

Commodity futures :

Futures = (Spot + PV of Storage) x ern

Index futures:

Futures = Spot x e(r-d)n

Margins

Since futures are exchange traded products, they are subject to initial margins and mark to market

margins (MTM margins).

Initial Margin : This is the margin required to be paid at the initiation of the trade. Normally it is at 10%

of the trade value. Both the buyer as well as seller are required to pay the initial margins.



Mark to Market Margin (MTM Margin): Every day the trade in futures is marked to market and the

resultant profit or loss is debited or credited to the clients account. This process is known as marking to

market and the resultant debits or credits are called as Mark to Market margins.

Top up Margin : If the balance in the margin account goes below the maintenance levels (i.e the level

which if breached would trigger the margin call) the client is required to bring in additional margins of

such amount as is required to bring the balance in margin account back to the initial margin levels.

DISTINCTION BETWEEN FUTURES AND FORWARDS:

Parameter Forwards Futures

Nature A telephonic contract An exchange traded product

Standardisation Individually tailor made for every customer and therefore has no standard size

Since they are exchange traded - size (lots) are standardised.

Settlement Normally settled by actual delivery

Cash settled - rarely settled by delivery

Settlement Settlement takes place between two parties directly

Since they are exchange traded, settlement takes place through clearing houses

Transaction cost Cost of forward contract is based on bid- ask spread

Entails brokerage fees

Marking to market No marking to market Marked to market on a daily basis

Margins No Margins required Initial Margins to be put up at the time of executing the trade

Credit risk Subject to counter party risks No counter party risks since transaction happens through an exchange and broker



SECTION 2 : OPTIONS

What are options?

In finance, an option is a contract which gives the buyer (the owner or holder of the option) the right, but not the obligation, to buy or sell an underlying asset or instrument at a specific strike price on a specified date, depending on the form of the option. The seller has the corresponding obligation to fulfil the transaction—to sell or buy—if the buyer (owner) "exercises" the option. An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put.

DEFINITION OF VARIOUS TERMS USED IN OPTIONS

Call option Gives the buyer the right but not the obligation to buy the underlying security at a specific price for a specified time. The seller of the call option (writer) has the obligation to sell the underlying asset if the buyer exercises his options

Put option Gives the buyer the right but not the obligation to sell the underlying security at a specific price for a specified time. The seller of the call option (writer) has the obligation to buy the underlying asset if the buyer exercises his options

Option

premium

Premium is the price at which the contract trades. The premium is the price of the option and is paid by the buyer of the option to writer or seller of the option. The writer gains the premium irrespective of whether the option is exercised or not.

Strike Price

/Exercise

price

It is the specified price at which the underlying asset is to be bought or sold by the buyer if he exercises his option

Contract

Size

The number of shares of the underlying asset covered by the options contract.

Open

Interest

Number of outstanding contract options in the exchange market. In the futures market it refers to the number of long or short positions undertaken but not squared off.

American

option

An option which can be exercised at any time between the date of purchase and the expiration date.

European

option

An option which can be exercised only on the expiration date.

Expiration

Date

The last day (in case of American option) or the only day in case of European option on which the option can be exercised. In India this date is the last Thursday (or previous business day if Thursday is a holiday) of the expiration month



At the money, In the money & Out of the money

In the money

If by exercising the option the buyer makes a profit then the option is in the money

At the money

If by exercising the option the buyer neither makes a profit nor a loss then the option is at the money

Out of money

If by exercising the option the buyer makes a loss then the option is out of the money

Option premium and its constituents

Option premium consists of two components: Intrinsic value + Time value

Intrinsic value

• Intrinsic value is that part of option premium which represents the extent to which the option is in the money.

• The balance is the time value of money. • An option which is out of money or at the money has zero intrinsic value. • Intrinsic value can never be negative.

Time Value

a. Also called as the extrinsic value of option

b. Represents the probability of the change in the underlying price that determines the value of the option during the remaining time till expiration.

c. This value depends on the time to expiration and the volatility of the underlying.

d. If an option is at the money or out of money the entire premium represents the time value.

e. Time value can also be never negative.

f. All options will have time value right upto the date they expire.

g. However as this time is constantly eroding, the time value of option declines over the balance period.

h. That is why options are referred to as wasting assets.

i. The decay begins slowly but starts accelerating towards the end causing the option to quickly lose value. This is because the market makers decide that it is unlikely that the underlying will gain value.

Table showing Intrinsic Value

If the option is Does it have Intrinsic

Value

Does it have Time Value

IN THE MONEY YES YES

AT THE MONEY NO YES

OUT OF MONEY NO YES

Option spreads

Option spreads means taking position in two or more options of the same type (calls or puts) on the same underlying.



Vertical spread [Price spread]

• Two legs have different strike price but the same expiration date. • E.g. Buying a December Call with a strike price of Rs.100 and sell a December Call on the same

script with a strike price of Rs.110.

Horizontal spread [Time spread]

• Two legs having the same strike price but different expiration date. • E.g. Buying a December call option for Rs.100 and selling a January Call option Rs.100

Diagonal spread [Price & Time Spread]

• Two legs having different strike prices and different expiration dates. • E.g. Buying a December call option for Rs.100 and selling a December Call for Rs.110

Other option strategies

Bull Put / Call Spread & Bear Put / Call Spread

Bull Call / Put spread Bear Call put spread

Purchase and sale of put / call at different strike price

Purchase and sale of put / call at different strike price

Same Expiry date Same Expiry date

Purchased put/ call to have a lower strike price than the sold put / call

Purchased put/ call to have a higher strike price than the sold put / call

Example Purchase a Dec call at Rs.100 and sell a Dec Call at Rs.110; [Bull Call Spread] or Purchase a Dec put at Rs.35 and sell a Dec put at Rs.37 [Bull Put Spread]

Example: Purchase a Dec call at Rs.100 and sell a Dec Call at Rs.90 [Bear Call Spread] Purchase a Dec put at Rs.35 and sell a Dec put at 33 [Bear Put Spread]

Straddle and Strangle

This strategy is adopted where the direction of the market is not known but the volatility is there in the underlying. Long straddle: purchasing a call and put option with the same exercise price. Short straddle: selling a call and put option with the same exercise price is a short straddle. Long strangle: Purchasing a call and put option with different strike price Short strangle: Selling a call and put option with different strike price



Put Call Parity theorem

A portfolio comprising a call option and an amount of cash equal to present value of option’s strike price has the same expiration value as a portfolio comprising a corresponding put option and the underlying. If the expiration values of the two portfolios are the same then their present value must also be the same.

This is called put call parity.

If two portfolios are going to have the same expiration value then they must have the same value today. If this is not the case then the investor can make an arbitrage profits. Put call parity is not based on any option pricing model. It has been derived purely using arbitrage arguments Let us make the following terminology for building a model: Sp = Spot price today P = Price of Put C = Price of call X = Strike Price St = Market price on the strike day Using the above Put Call parity theorem can be expressed as : Put + Stock = Call + Investment in Present Value of Strike Price ; i.e P + S = C + PV(X)

Option Pricing Models

There are 3 main models which can be used for pricing options : 1) Binomial Riskless Model 2) Binomial Risk Neutral Model 3) Black Scholes Model

Binomial Riskless Model

Binomial option pricing is a simple but powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes and other complex option-pricing models that require solutions to stochastic differential equations, the binomial option-pricing model (two- state option-pricing model) is mathematically simple. It is based on the assumption of no arbitrage. The assumption of no arbitrage implies that all risk-free investments earn the risk-free rate of return and no investment opportunities exist that require zero amount of investment but yield positive returns. A model which ensures that the expiration values of any portfolio is the same irrespective of any price. Let us make the following assumptions: i) CMP of stock = Rs. 100 ii) Possible moves = Rs.110 or Rs.90 iii) Strike price of call option = Rs.100 iv) Price of Call = “C” v) rate of interest = 6% CCRI vi) Time to expiry = 1 month



Our final objective is to find out the value of “C” i.e the option price

Step I Create a portfolio buying “h” number of shares at the CMP of Rs.100. Current value of portfolio = Rs.100h

Step 2 Protect the above portfolio by selling a call at a price “C”. Now the value

of the portfolio will be ₹ .100 h - C

THE IMPACT OF TWO POSSIBLE MOVES ARE ANALYSED BELOW

If stock price goes to `.110 If stock price goes to ` 90

Portfolio Value = ` 110h - C; or

` 110h - ` 10

[Since Call would have a value of ` 10]

Portfolio Value = ` 90h - C; or

` 90h -` 0

[Since Call would have a value of ` 0]

Step 3 Since the values must be equal in a risk less model we can state that:

` 110h - ` 10 = ` 90h - ` 0 Solving the above we get h = 0.5

Step 4 Substituting the value of h in ` 110 h - ` 10 or alternatively substituting the

value of h in ` 90h - ` 0 we get the portfolio value on expiry as ` 45

Step 5 If the Value of portfolio on expiry is ` 45, then the value of portfolio today must

be equal to the Present Value of ` 45 which is ` 45 x e-rt where r = 6% CCRI and t = 1/12

Step 6 But we know that the value of portfolio today is ` 100 h - C [refer step 2]

Step 7 Hence we can say that ₹ 100h - C = ₹ 45 x e-rt Solving the equation given that h = 0.5, e = 2.7183, r = 6% CCRI and t = 1/12 we get the value of C = Rs 5.22

Binomial Risk Neutral model

In the risk less hedge approach, the probability of the stock price increasing, Pu, or the probability of the stock price decreasing, Pd = 1-Pu, did not enter into the analysis at all. In the risk neutral approach, given a stock price process (tree) we try to estimate these probabilities for a risk neutral individual and then use these risk neutral probabilities to price a call option. In the above example for the Riskless model, the model ignored the probability of the prices hitting the level of Rs.110 or Rs.90. The risk neutral valuation approach takes into consideration the probability of a stock price moving up or down and factors the same in calculating the price of an option.

Example explaining the concept

Let Pu be the probability of price going up; then the probability of price going down i.e Pd = 1- Pu

Let us make the following assumption: i. CMP = Rs.75 ii. Upward possible price = Rs.95 iii. Downward possible price = Rs.63 iv. Call option strike price = Rs.65 (one month) v. Risk free rate = 6%



We know that : CMP of Stock = Present Value of Future expected values i.e CMP = PV of [(upward price x pu) + (downward price x pd)] i.e CMP = PV of [(upward price x pu) + (downward price x (1-pu)] Hence Rs.75 today = PV of expected values Now, Expected values = Pu (95) + Pd(63); or P(u)(95) + (1-Pu)(63) PV of expected values = [P(u)(95) + (1-Pu)(63)]*e

-rt

i.e Rs.75 = [P(u)(95) + (1-Pu)(63)]*e-rt

Solving the above equation for r =6% and T= 1 month we get the values of Pu and Pd

Pu = 0.38675 and Pd = (1-0.38675) i.e. 0.61325

Now we calculate the expected value of Call

If price of stock on expiry

Value of Call with strike price = ₹ 65

Probability Expected value

95 30 0.38675 11.6025

63 0 0.61325 0

Expected value of call on expiry 11.6025

Hence value of call today = Present value of 11.6025 @ 6% per annum

for 1 month : ` 11.6025 x e-rt ` 11.54

Black Scholes Model

a) First propogated in 1973 by Fischer Black and Myron Scholes. b) It has become the standard for valuing options c) Predominantly used for calculating European Options d) It utilizes the stock price, strike price, expiration date, risk free return, and the standard deviation

(volatility) of the stock’s return. The formula for Black Scholes model is: C = S.N.(d1) – Xe

-rt.N(d2) Where C = Value of Option S = Spot price X = Strike price R = risk free interest rate T = time till expiration N = area under normal curve D1 = [(Log s/x) + (r +

2/2)T ] T1/2 D2 = D1 - T

1/2

Valuing Real Options

Real Options Valuation, also often termed real options analysis,(ROV or ROA) applies option valuation techniques to capital budgeting decisions.A real option itself, is the right — but not the obligation — to undertake certain business initiatives, such as deferring, abandoning, expanding, staging, or contracting a capital investment project. For example, the opportunity to invest in the expansion of a firm's factory, or alternatively to sell the factory, is a real call or put option, respectively. Real options are generally distinguished from conventional financial options in that they are not typically traded as securities, and do not usually involve decisions on an underlying asset that is traded as a financial security. A further distinction is that option holders here, i.e. management, can directly influence



the value of the option's underlying project; whereas this is not a consideration as regards the underlying security of a financial option. Moreover, management cannot lookup for a volatility as uncertainty, instead their perceived uncertainty matters in real options reasoning’s. Unlike financial options, management also have to create or discover real options, and such creation and discovery process comprises an entrepreneurial or business task. Real options are most valuable when uncertainty is high; management has significant flexibility to change the course of the project in a favorable direction and is willing to exercise the options.

Option Greeks

Gamma

Gamma is a measure of rate of change of delta for small changes in underlying stock price - in other words it is delta of the delta. While using delta to hedge the portfolio we need to keep in mind that we should keep the gamma very low . If gamma is very high then a small change in the underlying would result in delta going haywire and therefore your hedge might collapse.

Theta

Theta measures the change in option price if the period to maturity reduces by one day. In simple words it is a measure of time decay. Now we know that time decay of an option is inevitable and bound to take place. So there is no point in hedging for the same. All options – both Calls and Puts lose value as the expiration approaches. The Theta or time decay factor is the rate at which an option loses value as time passes. Theta is expressed in points lost per day when all other conditions remain the same. Time runs in one direction, hence theta is always a positive number, however to remind traders it’s a loss in options value it is sometimes written as a negative number. A Theta of -0.5 indicates that the option premium will lose -0.5 points for every day that passes by. For example, if an option is trading at Rs.2.75/- with theta of -0.05 then it will trade at Rs.2.70/- the following day (provided other things are kept constant). A long option (option buyer) will always have a negative theta meaning all else equal, the option buyer will lose money on a day by day basis. A short option (option seller) will have a positive theta. Theta is a friendly Greek to the option seller. Remember the objective of the option seller is to retain the premium. Given that options loses value on a daily basis, the option seller can benefit by retaining the premium to the extent it loses value owing to time. For example if an option writer has sold options at Rs.54, with theta of 0.75, all else equal, the same option is likely to trade at – =0.75 * 3 = 2.25 = 54 – 2.25 = 51.75 Hence the seller can choose to close the option position on T+ 3 day by buying it back at Rs.51.75/- and profiting Rs.2.25 …

Rho

Rho measures the change in option price given a one percentage change in risk free interest rate. In other words it measures how sensitive the option value is to change in interest rates. For example a Rho of 0.05 indicates that the options theoretical value will increase by 0.05 if interest rate is decreased by 1

Vega

Vega indicates the change in value of option for one percentage change in volatility. The option's vega is a measure of the impact of changes in the underlying volatility on the option price. Specifically, the vega of an option expresses the change in the price of the option for every 1% change in underlying volatility.

Example of Vega

A stock XYZ is trading at ₹ 46 in May and a JUN 50 call is selling for ₹ 2. Let's assume that the vega of the option is 0.15 and that the underlying volatility is 25%. If the underlying volatility increased by 1% to 26%, then the price of the option should rise to ₹ 2 + 0.15 = ₹ 2.15. However, if the volatility had gone down by 2% to 23% instead, then the option price should drop to ₹ 2 - (2 x 0.15) = $1.70



SECTION A : FUTURES

Q.1 Spot price of Infosys is ` 2000. Interest rate prevailing is 14% per annum. Expected dividend after 2

months is ` 10 per share. Calculate what should be the expected price of Infosys today in the 3 months futures markets.

Q.2 For X Ltd, spot rate = ` 70, continuous compounded rate of interest is 8%. Calculate price of future

with 3 months expiry if the stock pays a dividend of ` 1.5 on expiry [e0.02 = 1.02020].

Q.3 Stock index currently stands at ` 3500. The risk free interest rate is 8% per annum & the dividend yield on the index is 4% per annum. Calculate the 4 month index future if the of 8% is CCRI [e0.0133 = 1.014].

Q.4 The current price of cotton is ` 400 per bale. The storage cost is ` 100 per bale per year payable in arrears. Assuming that interest rates are 10% per annum [CCRI], calculate the one year future price per bale of cotton [e0.10 = 1.1051].

Q.5 On 31-7-2017 the value of stock index is 2600. The risk free return is 9% per annum. The dividend

yield on this stock index is as follows :

Month Dividend yield

January 2%

February 5%

March 2%

April 2%

May 5%

June 2%

July 2%

August 5%

September 2%

October 2%

November 5%

December 2%

Assuming that interest is continuously compounded, what will be the future price of contract deliverable on 31-12-2011. Given e0.02417 = 1.02446 or say 1.0245

Q.6 The following data relates to ABC Ltd’s share prices

Current price per share = ` 180

Price per share in the futures markets - 6 months = ` 195 It is possible to borrow money in the market for securities transaction at the rate of 12% per annum.

Required:

a. Calculate the theoretical minimum price of 6 months futures. b. Explain if any arbitrage opportunities exist.



Margins on Futures

Q.7 On November 15, when the spot price for TELCO is ₹ 473 per share, Mr X buys 15 contracts of July TELCO futures at ₹ 491. Assume that the initial margin for TELCO futures is ₹ 800 per contract, and the maintenance margin is ₹ 600 per contract. Given that each contract is 50 shares. Daily settlement prices for the next few days are as follows :

Nov 15th ₹ 496 Nov 16th ₹ 503 Nov 17th ₹ 488 Nov 18th ₹ 485 Nov 19th ₹ 491 Assume that Mr X withdraws profits from his margin account only once on Nov 16th when he

withdraws half the maximum amount allowed. Compute the balance in the account at the end of each of these days. Find his profit or loss at the end of Nov 19th.

Futures & Hedging

Q.8 Ram buys 10000 shares of X Ltd at ₹ 22 and obtains a complete hedge of shorting 400 Nifties at ` 1100 each. He closes out his position at the closing price of the next day at which point the share price of X Ltd has dropped 2% and the Nifty futures has dropped 1.5%. What is the overall profit / loss on this set of transaction.

Q.9 BSE Index 5000

Value of Portfolio `. 10,10,000 Risk free interest rate 9% per annum Dividend yield on Index 6% per annum Beta of portfolio 1.5 We assume that a futures contract on the BSE index with 4 months maturity is used to hedge the

value of portfolio over next 3 months. One future contract is for delivery of 50 times the index. Based on the above information, calculate: a. Price of future contract. b. The gain on short position of futures if index turns out to be 4500 in 3 months

Q.10 A company is long on 10 MT of copper at ` 474 per kg (spot) and intends to remain so for the ensuing quarter. The standard deviation of change of its spot and future prices are 4% and 6% respectively, having a co-relation co-efficent of 0.75. What is the hedge ratio? What is the amount of the copper futures it should short to achieve a perfect hedge.

Q.11 A High Networth Individual (HNI) is holding the following portfolio is Rupees crores:

Investment in diversified equity shares 80.00 Cash and Bank Balance 20.00 Total 100.00

The Beta of the portfolio is 0.8. The index futures is selling at 5500 levels. The HNI wants to increase the beta of the portfolio for he believes tha the market would up from the current level. How many index futures he should buy / sell so that the beta is increased to 1.20. One index futures consists of 100 units.

Q.12 On April 1, 2015 an investor has a portfolio consisting of eight securities as shown below: The cost of capital for the investor is 20% per annum continuously compounded. The investor fears

a fall in the prices of the shares in the near future. Accordingly he approaches you for the advice to protect the interest of his portfolio. You can make use of the following information: a. The current NIFTY value is 8500 b. NIFTY futures can be traded in units of 25 only. c. Futures for May are currently quoted at 8,700 and futures for June are being quoted at 8850.



You are required to calculate : i. The beta of his portfolio. ii. The theoretical value of the futures contracts expiring in May and June iii. Given that e0.03 = 1.03045, e0.04 = 1.04081, e0.05 = 1.05127 iv. The number of NIFTY contracts that he would have to sell if desires to hedge until June in

each of the following cases: a. His total portfolio b. 50% of his portfolio c. 120% of his portfolio

Security Market

Price

No of shares Beta value

A 29.40 400 0.59

B 318.70 800 1.32

C 660.20 150 0.87

D 5.20 300 0.35

E 281.90 400 1.16

F 275.40 750 1.24

G 514.60 300 1.05

H 170.50 900 0.76



SECTION B : OPTIONS

ITM / ATM / OTM / Time value & Intrinsic Value

Q.13 Given the following data determine the value of the call option at their expiration dates:

Option Market price per

share on Expiry

Exercise price of

the option

A 10 12

B 25 21

C 48 52

D 7 5

Q.14 State whether each one of the following is In the Money (ITM), At the Money (ATM) or Out of Money (OTM)

Option Exercise price Spot

Call 60 55

Call 50 50

Call 110 105

Call 40 35

Put 110 100

Put 105 115

Put 12 15

Put 25 20

Q.15 A stock with a current market price of ` 50 has the following exercise price and call option

premium. Compute the intrinsic value and time value:

Exercise price 45 48 50 52 55

Premium 9 6 4 3 2

Q.16 A stock with a current market price of ` 50 has the following exercise price and put option premium. Compute the intrinsic value and time value:

Exercise price 45 48 50 52 55

Premium 1 2 3 5 7



Pay off tables / Spreads / Strategies

Q.17 The equity shares of Ramacast Ltd are being sold at ` 210. A 3 month call option is available for a

premium of ` 6 per share and a 3 month Put is available for a premium of ` 5 per share. Find out the net pay off of the option holder of the call option and put option given that (i) the strike price in

both the case is ` 220, and (ii) the share price on expiry is `200 or ` 210 or`220 or ` 230 or ` 240

Q.18 Equity shares of Casio Ltd are being currently sold for ` 90 per share. Both the call option and the

put option for 3 month period are available for a strike price of ` 97 at a premium of ` 3 and ` 2

respectively. Prepare the payoff table if price of share on expiry ranges between 80 to ` 120 in ticks

of ` 10 if an creates a (i) Strip or (ii) Strap

Q.19 A trader buys for ` 3 a call with a strike price of ` 30 and sells for ` 1 a call with a strike price of ` 35. Calculate his net pay off if the stock price at the end of expiration period is:

a. Less than or equal to ` 30

b. More than or equal to ` 35

c. About ` 30 but below ` 35

Q.20 A trader buys for ` 1 a call with a strike price of ₹ 35 and sells for ₹ 3 a call with a strike price of ` 30. Calculate his net pay off if the stock price at the end of expiration period is:

a. Less than or equal to ` 30

b. More than or equal to ` 35

c. About ` 30 but below ` 35

Q.21 Suppose that a certain stock is currently worth ` 61. A trader feels that a significant price move in the next 6 months is unlikely. The market price of 6 month calls are as follows:

Strike Price (`̀̀̀) Call Price (`̀̀̀)

55 10

60 7

65 5

Create a Butterfly spread for the investor and show the payoff of the overall strategy presuming that

price of share on expiry could range between ` 30 to ` 80 in ticks of ` .5

Put Call Parity / Arbitrage

Q.22 You are given the following information about ABC Ltd’s share and call option:

Current share price ` 90

Option Strike Price ` 110

Risk free interest rate 10%

Time to option expiry 1 year

Call Premium 12

Put Premium 21

You are required to analyses if there is any arbitrage opportunity



Q.23 You are given the following information about ABC Ltd’s share and call option:

Current share price ` 90

Option Strike Price ` 110

Risk free interest rate 10%

Time to option expiry 1 year

Call Premium 12

Put Premium 24

You are required to analyses if there is any arbitrage opportunity

Option valuation: Binomial / Black Scholes

Q.24 Consider a two year American call option with a strike price of ` 50 on a stock the current price of which is also ₹ 50. Assume that there are two time periods of one year and in each year the stock price can move up or down by equal percentage of 20%. The risk free interest rate is 6%. Using Binomial risk neutral model calculate the value of call and probability of price moving up and down. Also draw a two-step binomial tree showing prices and payoffs at each.

Q.25 An equity share is currently selling for Rs. 80. In a year’s time. It can rise by 30 percent or fall by

15 percent. The exercise price of a call option on this share is Rs.90.

What is the value of the call option if the risk-free rate is 8 percent? Use the Binomial Method risk less model

Q.26 X Ltd’s share is currently trading at ` 220. It is expected that in 6 months’ time it could double or

halve. One year call option on X Ltd’ share has an exercise price of ` 165. Assuming the risk free rate of interest to be 20% calculate:

(a) value of call option of X Ltd’s share.

(b) Option delta for the second 6 month in case the stock price rises to ` 440 or falls to ` 110

(c) Now suppose in 6 months the share price is ` 110. How at this point can we replicate portfolio

of call options and risk free lending.

Q.27 (i) The shares of TIC Ltd are currently priced at ₹ 415 and call option exercisable in three months’ time has an exercise rate of ` 400. Risk free interest rate is 5% p.a (CCRI) and standard deviation of share price is 22%. Based on the assumption that TIC is not going to

declare any dividend over the next 3 months is the option worth buying at ` 25. (ii) Calculate the aforesaid call option based on Black Scholes Model if the current market price

of share is ` 380

(iii) What would be the worth of Put option if the current price is considered ` 380.

(iv) If TIC share price at present is taken at ₹ 408 and a dividend of ` 10 is expected to be paid in 2 months’ time then calculate the value of call option.

Q.28 From the following data for a certain stock, find the value of call option:

Price of stock now = ` 80

Exercise price = ` 75 Standard Deviation = 0.40 Maturity period = 6 months Annual Interest rate = 12% CCRI

Given :



No of S.D from mean (z) Area of the left or right (one tail)

0.25 0.4013

0.30 0.3821

0.55 0.2912

0.60 0.2578

e0.06 = 1.060 and Ln 1.0667 = 0.0645

Q.29 You are trying to value a long term call option on the Standard and Poor 500, expiring in 2 months with a strike price of $ 900. The index is currently at $ 930 and the annualized standard deviation in stock prices is 20% per annum. The average dividend yield on the index is 0.3% per month, and expected to remain unchanged over the next month. The treasury bond rate is 8%. a. Estimate the value of the long term call option. b. Estimate the value of a put option with the same parameters.

Q.30 IPL is already in Production of Fertiliser and is considering a proposal of building a new plant to

produce pesticides. Suppose the Present value of proposal is ₹ 100 crores without the abandonment option. However, if market conditions for pesticide turns out to be favourable the PV of the proposal shall increase by 30%. On the other hand if the market conditions remain sluggish the PV of the proposal shall be reduced by 40%. In case company is not interested in continuation of the

project it can be disposed off for ` 80 crores. If the risk free rate of interest is 8% then what will be the value of abandonment option.

Q.31 ABC Ltd is a pharmaceutical company possessing a patent of a drug called “Aidrex” a medicine for

aids patients. Being an approach drug ABC Ltd holds the right of production of drugs and its marketing. The period of the patent is 15 year after which any other pharmaceutical company can produce the drug with the same formula. It is estimated that company shall required to incur $ 12.5 million for development and marketing of the drug. As per survey conducted the present value of expected cash flow from the sale of drug during 15 years shall be $ 16.70 million. Cash flow from the previous similar type of drug have exhibited a variance of 26.8% of the present value of cash flows. The current yield on Treasury Bonds of similar duration (15 years) is 7.8%. Determine the value of the patent.

Arbitrage between Futures and Options

Q.41 You are given the following information about ABC’s futures and options:

March futures price = ` 123 Details of March options are as under:

Strike Price = ` 150

Call Premium = ` 20

Put Premium = ` 50 Explain if any arbitrage opportunity exists Q.42 You are given the following information about ABC’s futures and options:

March futures price = ` 122 Details of March options are as under: Strike Price = ` 130

Call Premium = ` 8

Put Premium = ` 10 Explain if any arbitrage opportunity exists

: 18 :



TABLE : AREAS UNDER THE STANDARD NORMAL CURVE FROM 0 TO Z.

Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359

.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753

.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1103 .1141

.3 .1179 .1217 .1255 .1293 .1331 .1368 .1406 .1443 .1480 .1517

.4 .1554 .1591 .1628 1664 .1700 .1736 .1772 .1808 .1844 .1879

.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224

.6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2518 .2549

.7 .2580 .2612 .2642 .2673 .2704 .2734 .2764 .2794 .2823 .2852

.8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133

.9 .3159 .3186 .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389

1.0 .3413 .3438 .3461 .3485 .3508 .3531 .3554 .3577 .3599 .3621

1.1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830

1.2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015

1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177

1.4 .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4252 .4306 .4319

1.5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441

1.6 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545

1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 .4616 .4625 .4633

1.8 .4641 .4649 4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706

1.9 4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767

2.0 4772 .4778 .4783 .4788 .4793 .4798 .4803 4808 .4812 .4817

2.1 .4821 4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857

2.2 4861 4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 4890

2.3 .4893 .4896 .4898 .4901 .4904 .4906 .4909 .4911 .4913 .4916

2.4 .4918 .4920 .4922 .4925 .4927 .4931 .4931 .4932 .4934 .4936

2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952

2.6 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964

2.7 4965 .4966 .4967 .4968 .4969 .4970 .4971 .4972 .4973 .4974

2.8 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981

2.9 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986

3.0 .49865 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990

4.0 .4999683

IIIustration: For Z = 1.72, shaded area is .4573 out of total area of 1.

: 19 :



AREAS UNDER THE

STANDARD NORMAL CURVE

from - �� to x

x 0 1 2 3 4 5 6 7 8 9

0.0 .5000 .5040 5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359

0.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5754

0.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141

0.3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517

0.4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879

0.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224

0.6 .7258 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7518 .7549

0.7 .7580 .7910 .7939 .7967 .7996 .8023 .8051 .8078 .8106 .8133

0.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389

1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621

1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830

1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015

1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177

1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319

1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441

1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545

1.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 9616 .9625 .9633

1.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706

1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767

2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817

2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857

2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890

2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .9916

2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936

2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952

2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964

2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974

2.8 .9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .9981

2.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986

3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990

3.1 .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993

3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .9995

3.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997

3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998

3.5 .9998 .9998 .9998 .9998 .9998 .9998 .9998 .9998 .9998 .9998

3.6 .9998 .9998 .9999 .9999 .9999 .9999 .9999 .9999 .9999 .9999

3.7 .9999 .9999 .9999 .9999 .9999 .9999 .9999 .9999 .9999 .9999

3.8 .9999 .9999 .9999 .9999 .9999 .9999 .9999 .9999 .9999 .9999

3.9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

: 20 :



LOGARITHMS

0 1 2 3 4 5 6 7 8 9Mean Differences

1 2 3 4 5 6 7 8 9

10 0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 4 8 12 17 21 25 29 33 37

11 0414 0453 0492 0531 0569 0607 0645 0682 0719 0755 4 8 11 15 19 23 26 30 34

12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 3 7 10 14 17 21 24 28 31

13 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 3 6 10 13 16 19 23 26 29

14 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 3 6 9 12 15 18 21 24 27

15 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 3 6 8 11 14 17 20 22 25

16 2041 2068 2095 2122 2148 2175 2201 2227 2253 2279 3 5 8 11 13 16 18 21 24

17 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 2 5 7 10 12 15 17 20 22

18 2553 2577 2601 2625 2648 2672 2695 2718 2742 2765 2 5 7 9 12 14 16 19 21

19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 2 4 7 9 11 13 16 18 20

20 3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 2 4 6 8 11 13 15 17 19

21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 2 4 6 8 10 12 14 16 18

22 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 2 4 6 8 10 12 14 15 17

23 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 2 4 6 7 9 11 13 15 17

24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 2 4 5 7 9 11 12 14 16

25 3979 3997 4014 4031 4048 4065 4082 4099 4116 4133 2 3 5 7 9 10 12 14 15

26 4150 4166 4183 4200 4216 4232 4249 4265 4281 4298 2 3 5 7 8 10 11 13 15

27 4314 4330 4346 4362 4378 4393 4409 4425 4440 4456 2 3 5 6 8 9 11 13 14

28 4472 4487 4502 4518 4533 4548 4564 4579 4594 4609 2 3 5 6 8 9 11 12 14

29 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 1 3 4 6 7 9 10 12 13

30 4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 1 3 4 6 7 9 10 11 13

31 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 1 3 4 6 7 8 10 11 12

32 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 1 3 4 5 7 8 9 11 12

33 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 1 3 4 5 6 8 9 10 12

34 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 1 3 4 5 6 8 9 10 11

35 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 1 2 4 5 6 7 9 10 11

36 5563 5575 5587 5599 5611 5623 5635 5647 5658 5670 1 2 4 5 6 7 8 10 11

37 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 1 2 3 5 6 7 8 9 10

38 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 1 2 3 5 6 7 8 9 10

39 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 1 2 3 4 5 7 8 9 10

40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 1 2 3 4 5 6 8 9 10

41 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 1 2 3 4 5 6 7 8 9

42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 1 2 3 4 5 6 7 8 9

43 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 1 2 3 4 5 6 7 8 9

44 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 1 2 3 4 5 6 7 8 9

45 6532 6542 6551 6561 6571 6580 6590 6599 6609 6618 1 2 3 4 5 6 7 8 9

46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 1 2 3 4 5 6 7 7 8

47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 1 2 3 4 5 5 6 7 8

48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 1 2 3 4 4 5 6 7 8

49 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 1 2 3 4 4 5 6 7 8

50 6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 1 2 3 3 4 5 6 7 8

51 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 1 2 3 3 4 5 6 7 8

52 7160 7168 7177 7185 7193 7202 7210 7218 7226 7235 1 2 2 3 4 5 6 7 7

53 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 1 2 2 3 4 5 6 6 7

54 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 1 2 2 3 4 5 6 6 7

: 21 :



0 1 2 3 4 5 6 7 8 9 Mean Differences

1 2 3 4 5 6 7 8 9

55 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 1 2 2 3 4 5 5 6 7

56 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 1 2 2 3 4 5 5 6 7

57 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 1 2 2 3 4 5 5 6 7

58 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 1 1 2 3 4 4 5 6 7

59 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 1 1 2 3 4 4 5 6 7

60 7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 1 1 2 3 4 4 5 6 6

61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 1 1 2 3 4 4 5 6 6

62 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 1 1 2 3 3 4 5 6 6

63 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 1 1 2 3 3 4 5 5 6

64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 1 1 2 3 3 4 5 5 6

65 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 1 1 2 3 3 4 5 5 6

66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 1 1 2 3 3 4 5 5 6

67 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 1 1 2 3 3 4 5 5 6

68 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 1 1 2 3 3 4 4 5 6

69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 1 1 2 2 3 4 4 5 6

70 8451 8457 8463 8470 8476 8482 8488 8494 8500 8506 1 1 2 2 3 4 4 5 6

71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 1 1 2 2 3 4 4 5 5

72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 1 1 2 2 3 4 4 5 5

73 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 1 1 2 2 3 4 4 5 5

74 8692 8698 8704 8710 8716 8722 8727 8733 8739 8745 1 1 2 2 3 4 4 5 5

75 8751 8756 8762 8768 8774 8779 8785 8791 8797 8802 1 1 2 2 3 3 4 5 5

76 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 1 1 2 2 3 3 4 5 5

77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 1 1 2 2 3 3 4 4 5

78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 1 1 2 2 3 3 4 4 5

79 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 1 1 2 2 3 3 4 4 5

80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 1 1 2 2 3 3 4 4 5

81 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 1 1 2 2 3 3 4 4 5

82 9138 9143 9149 9154 9159 9165 9170 9175 9180 9186 1 1 2 2 3 3 4 4 5

83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 1 1 2 2 3 3 4 4 5

84 9243 9248 9253 9258 9263 9269 9274 9279 9284 9289 1 1 2 2 3 3 4 4 5

85 9294 9299 9304 9309 9315 9320 9325 9330 9335 9340 1 1 2 2 3 3 4 4 5

86 9345 9350 9355 9360 9365 9370 9375 9380 9385 9390 1 1 2 2 3 3 4 4 5

87 9395 9400 9405 9410 9415 9420 9425 9430 9435 9440 0 1 1 2 2 3 3 4 4

88 9445 9450 9455 9460 9465 9469 9474 9479 9484 9489 0 1 1 2 2 3 3 4 4

89 9494 9499 9504 9509 9513 9518 9523 9528 9533 9538 0 1 1 2 2 3 3 4 4

90 9542 9547 9552 9557 9562 9566 9571 9576 9581 9586 0 1 1 2 2 3 3 4 4

91 9590 9595 9600 9605 9609 9614 9619 9624 9628 9633 0 1 1 2 2 3 3 4 4

92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 0 1 1 2 2 3 3 4 4

93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 0 1 1 2 2 3 3 4 4

94 9731 9736 9741 9745 9750 9754 9759 9763 9768 9773 0 1 1 2 2 3 3 4 4

95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 0 1 1 2 2 3 3 4 4

96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 0 1 1 2 2 3 3 4 4

97 9868 9872 9877 9881 9886 9890 9894 9899 9903 9908 0 1 1 2 2 3 3 4 4

98 9912 9917 9921 9926 9930 9934 9939 9943 9948 9952 0 1 1 2 2 3 3 4 4

99 9956 9961 9965 9969 9974 9978 9983 9987 9991 9996 0 1 1 2 2 3 3 3 4

LOGARITHMS

: 22 :



ANTILOGARITHMS


1 2 3 4 5 6 7 8 9

.00 1000 1002 1005 1007 1009 1012 1014 1016 1019 1021 0 0 1 1 1 1 2 2 2

.01 1023 1026 1028 1030 1033 1035 1038 1040 1042 1045 0 0 1 1 1 1 2 2 2

.02 1047 1050 1052 1054 1057 1059 1062 1064 1067 1069 0 0 1 1 1 1 2 2 2

.03 1072 1074 1076 1079 1081 1084 1086 1089 1091 1094 0 0 1 1 1 1 2 2 2

.04 1096 1099 1102 1104 1107 1109 1112 1114 1117 1119 0 1 1 1 1 2 2 2 2

.05 1122 1125 1127 1130 1132 1135 1138 1140 1143 1146 0 1 1 1 1 2 2 2 2

.06 1148 1151 1153 1156 1159 1161 1164 1167 1169 1172 0 1 1 1 1 2 2 2 2

.07 1175 1178 1180 1183 1186 1189 1191 1194 1197 1199 0 1 1 1 1 2 2 2 2

.08 1202 1205 1208 1211 1213 1216 1219 1222 1225 1227 0 1 1 1 1 2 2 2 3

.09 1230 1233 1236 1239 1242 1245 1247 1250 1253 1256 0 1 1 1 1 2 2 2 3

.10 1259 1262 1265 1268 1271 1274 1276 1279 1282 1285 0 1 1 1 1 2 2 2 3

.11 1288 1291 1294 1297 1300 1303 1306 1309 1312 1315 0 1 1 1 2 2 2 2 3

.12 1318 1321 1324 1327 1330 1334 1337 1340 1343 1346 0 1 1 1 2 2 2 2 3

.13 1349 1352 1355 1358 1361 1365 1368 1371 1374 1377 0 1 1 1 2 2 2 3 3

.14 1380 1384 1387 1390 1393 1396 1400 1403 1406 1409 0 1 1 1 2 2 2 3 3

.15 1413 1416 1419 1422 1426 1429 1432 1435 1439 1442 0 1 1 1 2 2 2 3 3

.16 1445 1449 1452 1455 1459 1462 1466 1469 1472 1476 0 1 1 1 2 2 2 3 3

.17 1479 1483 1486 1489 1493 1496 1500 1503 1507 1510 0 1 1 1 2 2 2 3 3

.18 1514 1517 1521 1524 1528 1531 1535 1538 1542 1545 0 1 1 1 2 2 2 3 3

.19 1549 1552 1556 1560 1563 1567 1570 1574 1578 1581 0 1 1 1 2 2 3 3 3

.20 1585 1589 1592 1596 1600 1603 1607 1611 1614 1618 0 1 1 1 2 2 3 3 3

.21 1622 1626 1629 1633 1637 1641 1644 1648 1652 1656 0 1 1 2 2 2 3 3 3

.22 1660 1663 1667 1671 1675 1679 1683 1687 1690 1694 0 1 1 2 2 2 3 3 3

.23 1698 1702 1706 1710 1714 1718 1722 1726 1730 1734 0 1 1 2 2 2 3 3 4

.24 1738 1742 1746 1750 1754 1758 1762 1766 1770 1774 0 1 1 2 2 2 3 3 4

.25 1778 1782 1786 1791 1795 1799 1803 1807 1811 1816 0 1 1 2 2 2 3 3 4

.26 1820 1824 1828 1832 1837 1841 1845 1849 1854 1858 0 1 1 2 2 3 3 3 4

.27 1862 1866 1871 1875 1879 1884 1888 1892 1897 1901 0 1 1 2 2 3 3 3 4

.28 1905 1910 1914 1919 1923 1928 1932 1936 1941 1945 0 1 1 2 2 3 3 4 4

.29 1950 1954 1959 1963 1968 1972 1977 1982 1986 1991 0 1 1 2 2 3 3 4 4

.30 1995 2000 2004 2009 2014 2018 2023 2028 2032 2037 0 1 1 2 2 3 3 4 4

.31 2042 2046 2051 2056 2061 2065 2070 2075 2080 2084 0 1 1 2 2 3 3 4 4

.32 2089 2094 2099 2104 2109 2113 2118 2123 2128 2133 0 1 1 2 2 3 3 4 4

.33 2138 2143 2148 2153 2158 2163 2168 2173 2178 2183 0 1 1 2 2 3 3 4 4

.34 2188 2193 2198 2203 2208 2213 2218 2223 2228 2234 1 1 2 2 3 3 4 4 5

.35 2239 2244 2249 2254 2259 2265 2270 2275 2280 2286 1 1 2 2 3 3 4 4 5

.36 2291 2296 2301 2307 2312 2317 2323 2328 2333 2339 1 1 2 2 3 3 4 4 5

.37 2344 2350 2355 2360 2366 2371 2377 2382 2388 2393 1 1 2 2 3 3 4 4 5

.38 2399 2404 2410 2415 2421 2427 2432 2438 2443 2449 1 1 2 2 3 3 4 4 5

.39 2455 2460 2466 2472 2477 2483 2489 2495 2500 2506 1 1 2 2 3 3 4 5 5

.40 2512 2518 2523 2529 2535 2541 2547 2553 2559 2564 1 1 2 2 3 4 4 5 5

.41 2570 2576 2582 2588 2594 2600 2606 2612 2618 2624 1 1 2 2 3 4 4 5 5

.42 2630 2636 2642 2649 2655 2661 2667 2673 2679 2685 1 1 2 2 3 4 4 5 6

.43 2692 2698 2704 2710 2716 2723 2729 2735 2742 2748 1 1 2 3 3 4 4 5 6

.44 2754 2761 2767 2773 2780 2786 2793 2799 2805 2812 1 1 2 3 3 4 4 5 6

.45 2818 2825 2831 2838 2844 2851 2858 2864 2871 2877 1 1 2 3 3 4 5 5 6

.46 2884 2891 2897 2904 2911 2917 2924 2931 2938 2944 1 1 2 3 3 4 5 5 6

.47 2951 2958 2965 2972 2979 2985 2992 2999 3006 3013 1 1 2 3 3 4 5 5 6

.48 3020 3027 3034 3041 3048 3055 3062 3069 3076 3083 1 1 2 3 4 4 5 6 6

.49 3090 3097 3105 3112 3119 3126 3133 3141 3148 3155 1 1 2 3 4 4 5 6 6

: 23 :



ANTILOGARITHMS


1 2 3 4 5 6 7 8 9

.50 3162 3170 3177 3184 3192 3199 3206 3214 3221 3228 1 1 2 3 4 4 5 6 7

.51 3236 3243 3251 3258 3266 3273 3281 3289 3296 3304 1 2 2 3 4 5 5 6 7

.52 3311 3319 3327 3334 3342 3350 3357 3365 3373 3381 1 2 2 3 4 5 5 6 7

.53 3388 3396 3404 3412 3420 3428 3436 3443 3451 3459 1 2 2 3 4 5 6 6 7

.54 3467 3475 3483 3491 3499 3508 3516 3524 3532 3540 1 2 2 3 4 5 6 6 7

.55 3548 3556 3565 3573 3581 3589 3597 3606 3614 3622 1 2 2 3 4 5 6 7 7

.56 3631 3639 3648 3656 3664 3673 3681 3690 3698 3707 1 2 3 3 4 5 6 7 8

.57 3715 3724 3733 3741 3750 3758 3767 3776 3784 3793 1 2 3 3 4 5 6 7 8

.58 3802 3811 3819 3828 3837 3846 3855 3864 3873 3882 1 2 3 4 4 5 6 7 8

.59 3890 3899 3908 3917 3926 3936 3945 3954 3963 3972 1 2 3 4 5 5 6 7 8

.60 3981 3990 3999 4009 4018 4027 4036 4046 4055 4064 1 2 3 4 5 6 6 7 8

.61 4074 4083 4093 4102 4111 4121 4130 4140 4150 4159 1 2 3 4 5 6 7 8 9

.62 4169 4178 4188 4198 4207 4217 4227 4236 4246 4256 1 2 3 4 5 6 7 8 9

.63 4266 4276 4285 4295 4305 4315 4325 4335 4345 4355 1 2 3 4 5 6 7 8 9

.64 4365 4375 4385 4395 4406 4416 4426 4436 4446 4457 1 2 3 4 5 6 7 8 9

.65 4467 4477 4487 4498 4508 4519 4529 4539 4550 4560 1 2 3 4 5 6 7 8 9

.66 4571 4581 4592 4603 4613 4624 4634 4645 4656 4667 1 2 3 4 5 6 7 9 10

.67 4677 4688 4699 4710 4721 4732 4742 4753 4764 4775 1 2 3 4 5 7 8 9 10

.68 4786 4797 4808 4819 4831 4842 4853 4864 4875 4887 1 2 3 4 6 7 8 9 10

.69 4898 4909 4920 4932 4943 4955 4966 4977 4989 5000 1 2 3 5 6 7 8 9 10

.70 5012 5023 5035 5047 5058 5070 5082 5093 5105 5117 1 2 4 5 6 7 8 9 11

.71 5129 5140 5152 5164 5176 5188 5200 5212 5224 5236 1 2 4 5 6 7 8 10 11

.72 5248 5260 5272 5284 5297 5309 5321 5333 5346 5358 1 2 4 5 6 7 9 10 11

.73 5370 5383 5395 5408 5420 5433 5445 5458 5470 5483 1 3 4 5 6 8 9 10 11

.74 5495 5508 5521 5534 5546 5559 5572 5585 5598 5610 1 3 4 5 6 8 9 10 12

.75 5623 5636 5649 5662 5675 5689 5702 5715 5728 5741 1 3 4 5 7 8 9 10 12

.76 5754 5768 5781 5794 5808 5821 5834 5848 5861 5875 1 3 4 5 7 8 9 11 12

.77 5888 5902 5916 5929 5943 5957 5970 5984 5998 6012 1 3 4 5 7 8 10 11 12

.78 6026 6039 6053 6067 6081 6095 6109 6124 6138 6152 1 3 4 6 7 8 10 11 13

.79 6166 6180 6194 6209 6223 6237 6252 6266 6281 6295 1 3 4 6 7 9 10 11 13

.80 6310 6324 6339 6353 6368 6383 6397 6412 6427 6442 1 3 4 6 7 9 10 12 13

.81 6457 6471 6486 6501 6516 6531 6546 6561 6577 6592 2 3 5 6 8 9 11 12 14

.82 6607 6622 6637 6653 6668 6683 6699 6714 6730 6745 2 3 5 6 8 9 11 12 14

.83 6761 6776 6792 6808 6823 6839 6855 6871 6887 6902 2 3 5 6 8 9 11 13 14

.84 6918 6934 6950 6966 6982 6998 7015 7031 7047 7063 2 3 5 6 8 10 11 13 15

.85 7079 7096 7112 7129 7145 7161 7178 7194 7211 7228 2 3 5 7 8 10 12 13 15

.86 7244 7261 7278 7295 7311 7328 7345 7362 7379 7396 2 3 5 7 8 10 12 13 15

.87 7413 7430 7447 7464 7482 7499 7516 7534 7551 7568 2 3 5 7 9 10 12 14 16

.88 7586 7603 7621 7638 7656 7674 7691 7709 7727 7745 2 4 5 7 9 11 12 14 16

.89 7762 7780 7798 7816 7834 7852 7870 7889 7907 7925 2 4 5 7 9 11 13 14 16

.90 7943 7962 7980 7998 8017 8035 8054 8072 8091 8110 2 4 6 7 9 11 13 15 17

.91 8128 8147 8166 8185 8204 8222 8241 8260 8279 8299 2 4 6 8 9 11 13 15 17

.92 8318 8337 8356 8375 8395 8414 8433 8453 8472 8492 2 4 6 8 10 12 14 15 17

.93 8511 8531 8551 8570 8590 8610 8630 8650 8670 8690 2 4 6 8 10 12 14 16 18

.94 8710 8730 8750 8770 8790 8810 8831 8851 8872 8892 2 4 6 8 10 12 14 16 18

.95 8913 8933 8954 8974 8995 9016 9036 9057 9078 9099 2 4 6 8 10 12 15 17 19

.96 9120 9141 9162 9183 9204 9226 9247 9268 9290 9311 2 4 6 8 11 13 15 17 19

.97 9333 9354 9376 9397 9419 9441 9462 9484 9506 9528 2 4 7 9 11 13 15 17 20

.98 9550 9572 9594 9616 9638 9661 9683 9705 9727 9750 2 4 7 9 11 13 16 18 20

.99 9772 9795 9817 9840 9863 9886 9908 9931 9954 9977 2 5 7 9 11 14 16 18 20



Question 1: It is around February end and the spot $/ £ rate is $1.4/1. You are convinced that the £ will weaken by May end to about $ 1.3 / £ 1. Sterling December put options with a strike price of $ 1.39 are being traded at a premium of £ 500 per contract. The sterling contract size is £ 25000. You are required to work out possible pay offs if the spot rate at expiration is (a) $1.3 (b) $1.5 and (c) $1.39 Question 2: A company is tendering for the sale of equipment’s to a US company for $ 3 million, settlement due in 3 months’ time. The current spot rate is $ 1.58 per 1 £. However the company is worried about the dollar weakening against the Pound thus making the sale less profitable. The company has been offered a 3 month put option on US dollar at $1.60 per £ 1 costing 2 cents per Pound. What is the total premium outflow? Question 3: Hessey international plc has recently purchased a consignment of cleaning fluid from a United States supplier for $3,00,000 payable in 3 months’ time. Recently the company has experienced foreign exchange losses on similar deals and the financial director has decided that henceforth all transaction exposure will be covered. After discussion with the bank the following data have been made available: Foreign exchange market

$ / £

Spot rate 1.5000 - 1.5050

3 month forward premium on $ 1.00 - 0.80 cents

Money Market Base rates are 18% per annum both in UK and USA. Hessey can borrow at 2% above and deposit at 2% below the relevant base rate in either countries Option The Bank has offered a call option on $300000 at an exercise price of $ 1.49 / £ at a cost of £ 3000 payable in arrears. The financial director is also aware that transaction exposure may be hedged by the use of financial futures exchanges but is uncertain of the advantages they offer as exposed to services offered by banks. You are required: (a) To calculate the net cost of the transaction assuming it was covered in:

(i) The forward foreign exchange market. (ii) The money market

(b) To explain to the financial director the nature of the foreign exchange risk cover provided by the call option and calculate the exact future spot rate at which the option would start to give a cheaper cost than the forward contract

CURRENCY OPTIONS & SWAPS



Question 4: XYZ Ltd a US firm will need £ 3,00,000 in 180 days. In this connection the following information is available: Spot 1 £ = $2.00 180 day forward rate of £ as of today = $1.96 Interest rates are as follows:

UK US

180 day deposit rate 4.5% 5%

180 day borrowing rate 5% 5.5%

A call option of £ that expires in 180 days has an exercise price of $1.97 and a premium of $0.04. XYZ Ltd has forecast the spot rates 180 days hence as below:

Future rate Probability

$1.91 25%

$1.95 60%

$2.05 15%

Which of the following strategy would be most preferable to XYZ Ltd : (a) forward market (b) Money market hedge (c) Option contract (d) No hedging Show calculation in each case. Question 5: On 19th April following are the spot rates: Spot EUR / $ 1.20000; USD / INR = 44.8000 Following are the quotes of European Options:

Currency Pair Call / Put Strike Price Premium Expiry Date

EUR / USD Call 1.2000 $ 0.0375 July 19

EUR / USD Put 1.2000 $ 0.04 July 19

USD / INR Call 44.8000 ₹ 0.12 Sep 19

USD / INR Put 44.8000 ₹ 0.04 Sep 19

(i) A trader sells an at the money spot straddle expiring at 3 months (July 19). Calculate gain or loss if 3 months later the spot rate is EUR / USD = 1.2900.

(ii) Which strategy gives a profit to the dealer if 5 months later (Sep 19) expected spot rate is USD / INR = 45.00. Also calculate the profit for a transaction of USD 1.5 million.



Question 6: Apple Inc, a US based Company wishes to lend $500,000 to its Japanese subsidiary. At the same time Toyota Motors, a Japan based company, is interested in making a medium term loan of approximately the same amount to its USA subsidiary. The two parties are brought together by an investment bank for the purpose of making parallel loans. Apple Inc will lend $500,000 to the US subsidiary of Toyota Motors for 4 years at 13%. Principal and interest are payable only at the end of the fourth year with interest compounding annually. Toyota motors will lend the Japanese subsidiary of Apple Inc 70 million Yen for 4 years at 10%. Again the principal and interest (annual compounding) are payable at the end. The current exchange rate is 140 Yen to the $. However the dollar is expected to decline by 5 Yen to the Dollar per year over the next 4 years. a. If these expectations prove to be correct what will be the dollar equivalent of principal and

interest payments to Toyota Motors at the end of 4 years . b. What total dollars will Apple Inc receive at the end of 4 years from the payment of

principal and interest on its loan by the US subsidiary of Toyota Motors . c. Which party is better off with the parallel loan arrangement. What would happen if the

yen did not change in value. Question 7: A German firm buys a call on $ 10,00,000 with a strike of DM 1.60 / $ and a premium of DM 0.03 / $. The interest opportunity cost is 6% per annum and the maturity is 180 days. (a) What is the break even maturity spot rate beyond with the firm makes a net gain? (b) Suppose the 6 month forward rate at the time the option was bought was DM 1.62 / $,

What is the range of maturity spot rate for which the option would prove better than the forward cover? For what range of values would the forward cover be better?



Q.1. Z Ltd. is foreseeing a growth rate of 12% per annum in the next 2 years. The growth

rate is likely to fall to 10% for the third year and fourth year. After that the growth rate is expected to stabilise at 8% per annum. If the last dividend paid was ` 1.50 per share and the investors' required rate of return is 16%, find out the intrinsic value per share of Z Ltd. as of date. You may use the following table :

Year 0 1 2 3 4 5

Discounting Factor at 16% 1 0.86 0.74 0.64 0.55 0.48

Q.2. SP Industries has been growing at the rate of 15% per year and this trend is expected

to continue for 5 more years. Thereafter, it is likely to grow at the rate of 8% which is the industry average. The investor expects a return of 12%. The dividend paid per share last year (D0) corresponding to period 0 is 5. Determine at what price an investor will be ready to buy the shares of the company at the end of year 0,1,2,3,4,5.

Present value of Re.1 at 12%. Year 1 0.893, Year 2 0.797, Year 3 0.712, Year 4 0.636, Year 5 0.567.

Q.3. A company has a book value per share of ` 137.80. Its return on equity is 15% and it

follows a policy of retaining 60% of its earnings. If the opportunity cost of capital is 18%, what is the price of the share today?

Q.4. Shares of Voyage Ltd. are being quoted at a price-earnings ratio of 8 times. The

company retains 45% of its earnings which are ` 5 per share. You are required to compute

(1) The cost of equity to the company if the market expects a growth rate of 15% p.a. (2) If the anticipated growth rate is 16% per annum, calculate the indicative market

price with the same cost of capital. (3) If the company's cost of capital is 20% p.a. & the anticipated growth rate is 19%

p.a., calculate the market price per share. Q.5. A Co. has invested Rs.500 lakhs in assets. There are 50 lakh shares outstanding. The

par value per share is ` 10. It earns a rate of 15% on its investment & has a policy of retaining 50% of the earnings. If the appropriate discount rate of the firm is 10%. What is the price of its share using Gardon's Model? What will happen to the price of the share if the Co. has a payout of 80% & 20%.

Q.6. Omega Foods currently pay a dividend of ` 2.00 per share. The growth rate, which is

currently 20%, is expected to decline linearly over the next ten years to a stable rate of 5% thereafter. The required rate of return is 12%. Calculate the current value of Omega.

Q.7. Piyush Loonker and Associates presently paid a dividend of ` 1.00 per share and has a

share price of ` 20.00. (i) If this dividend were expected to grow at a rate of 12% per annum forever, what is

the firm’s expected or required return on equity using a dividend-discount model approach?

(ii) Instead of this situation in part (i), suppose that the dividends were expected to grow at a rate of 20% per annum for 5 years and 10% per year thereafter. Now what is the firm’s expected, or required, return on equity?

VALUATION OF SECURITIES



Q.8. AXLES Limited has issued 10,000 equity shares of ` 10 each. The current market price per share is ` 30. The company has a plan to make a rights issue of one new equity

share at a price of ` 20 for every four shares held. You are required to : (i) Calculate the theoretical post-rights-price per share; (ii) Calculate the theoretical value of the rights alone, (iii) Show the effect of the rights issue on the wealth of a shareholder who has 1,000

shares assuming he sells the entire rights; and (iv) Show the effect if the same shareholder does not take any action and ignores the

issue. Q.9. ABC Limited's shares are currently selling at ` 13 per share. There are 10,00,000

shares outstanding. The firm is planning to raise ` 20 lakhs to Finance a new project. Required : What is the ex-right price of shares and the value of a right, if

(i) The firm offers one right share for every two shares held. (ii) The firm offers one right share for every four shares held. (iii) How does the shareholders' wealth change from (i) to (ii)? How does right issue

increases shareholders' wealth? Q.10. Monopolo Ltd. has a paid – up ordinary share capital of ` 2,00,00,000 represent by

4,00,000 shares of ` 50 each. Earnings after tax in the most recent year were ` 75,00,000 of which ` 25,00,000 was distributed as dividend. The current price / earnings ratio of these shares, as normally reported in the financial press, is 8.

The company is planning a major investment that will cost ` 2,02,50,000 and is expected to produce additional after tax earnings over the foreseeable future at the rate of 15% on the amount invested.

It was proposed by CFO of company to raise necessary finance by a rights issue to the existing shareholders at a price 25% below the current market price of the company’s shares. (a) You have been appointed as financial consultant of the company and are required

to calculate: (i) The current market price of the shares already in use. (ii) The price at which the rights issue will be made. (iii) The number of new shares that will be issued. (iv) The price at which the shares of the entity should theoretically be quoted on

completion of the rights issue (i.e. the ‘ex – rights price’), assuming no incidental costs and that the market accepts the entity’s forecast of incremental earnings.

(b) It has been that, provided the required amount of money is raised and that the market is made aware of the earning power of the new investment, the financial position of existing shareholders should be the same whether or not they decide to subscribe for the rights they are offered.

You are required to illustrate that there will be no change in the existing shareholders’ wealth.

Q.11. The stock of the Sonic Plc is selling for £ 50 per common stock. The company then

issues rights to subscribe to one new share at £ 40 for each five rights held. (a) What is the theoretical value of a right when the stock is selling rights – on? (b) What is the theoretical value of one share of stock when it goes ex – rights? (c) What is the theoretical value of a right when the stock sells ex – rights at £ 50? (d) John Speculator has 1,000 at the time Soni Plc. Goes ex – rights at £ 50 per

common stock. He feels that the price of the stock will rise to £ 60 by the time the



rights expire. Compute his return on his £ 1,000 if he (1) buys Soni Plc stock at £ 50, or (2) buys the rights at the price computed in part (c), assuming his price expectations are valid.

Q.12. Rahul Ltd. has surplus cash of ` 100 lakhs and wants to distribute 27% of it to the

shareholders. The company decides to buy back shares. The Finance Manager of the company estimates that its share price after re-purchase is likely to be 10% above the buyback price if the buyback route is taken. The number of shares outstanding at present is 10 lakhs and the current EPs is ` 3.

You are required to determine : (i) The price at which the shares can be re- purchased , if the market a capitalization

of the company should be 210 lakhs after buyback, (ii) The number of shares that can be re-purchased, and (iii) The impact of share re0purchase on the EPS, assuming that net income is the

same. Q.13. The earnings per share of a company are ` 8 and the rate of capitalisation applicable

to the company is 10%. The company has before it an option of adopting a payout ratio of 25% or 50% or 75%. Using Walter's formula of dividend payout compute the market value of the company's share if the productivity of retained earnings is (i) 15% (ii) 10%, and (iii) 5%.

What inference can be drawn from the above exercise? Q.14. ABC and Co. has been following a dividend policy which can maximize the market

value of the firm as per Walter's model. Accordingly, each year, at dividend time the capital budget is reviewed in conjunction with the earning for the periods and alternative investment opportunities for the shareholders.

In the current year, the firm expects earnings of ` 5,00,000. It is estimated that firm can earn ` 1,00,000 if the profits are retained. The investor have alternative investment opportunities that will yield them 10% return. The firm has 50,000 shares outstanding. What should be the dividend payout ratio in order to maximize the wealth of the shareholders? Also find out the current market price of the share.

Q.15. A share with par value of ` 100 has current market price of ` 500. Annual dividend is

20%. Bonus shares are expected to be issued during the 5th year @ one share for 4 held. One shareholder intends to sell the shares at the end of 8th year. Price of a share is expected to be ` 900 at the end of the 8th year. Shareholders are required to bear incidental expenses on sale & purchase of shares @ 10% of Market Price of share. Dividend rate will remain same even after the bonus issue. Required rate of return is 10%. Ignore taxation. Should the share be purchased and if yes, at what maximum price?

Documents

FINAL CA...XYZ Ltd has issued convertible debentures with interest rate of 12%. Every debenture has an option to convert to 20 equity shares at any time until the date of maturity