SFM Material

LEGEND for CA Strategic Financial Management

LEGEND ACADEMY FOR CA

Strategic Financial Management

- CA. Alok Agarwal

____________________________________________________________LEGEND ACADEMY FOR CABandari Arcade, 5th Floor, Above IDBI Bank Opposite: SR Nagar Bus Stop, Hyderabad. Ph: 90004 64672, 90000 13135, E-mail: [email protected], Website: www.legendforca.com

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http://www.legendforca.com/

mailto:[email protected]


DIVIDEND POLICY

Problem No 1A company has a book value per share of Rs.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 under:

a. Walter’s Dividend Modelb. Gordon’s Model

Problem No 2

A firm pays 18% dividend on its equity having a face value of Rs.100. Find out the price of one equity share if the expectation of shareholder is 12% with consistent dividend forever.

Problem No 3

A Co., pays the first dividend by Y4 at 18% on its face value of Rs.100/-. It expects to maintain the same rate of dividend thereafter. What is the price of the share if the cost of equity if 12%?

Problem No 4

A company wants to declare 3 years holiday for dividends with lots of capital investments program in the offing. It is also decided to declare consistently 14% dividend for the face value of each equity share of Rs.10, thereafter. Find the present value per share of the company if the required rate of return of equity share is 9%.

Problem No 5

The chairman of a company wanted to know the opinion of his policy of not declaring dividend. He feels money with the company is more productive than with the shareholders. However agrees to declare dividend consistency after 20 years @ Rs.40 forever. He also suggests another policy of declaring only Rs.6 consistently forever. In either of the policies consider only a cost of capital of 11%. Which of the policies would be attractive for the shareholders? Suggest. Problem No 6 A company had just paid a dividend pf Rs.6. Earnings and dividends are expected to grow @ 15%. Find out the price per share of the company if the required rate of return is 18%.

Problem No 7

Dolphin Products Corporation currently pays a dividend of Rs.2 per share and this dividend is expected to grow at a 15% annual rate for 3 years, then at a 10% rate for the next 3 years, after which it is expected to grow at a 5% rate for ever.

(a) What value would you place on the stock if an 18% rate of return were required?

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Problem No 8

Sigma 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 stabilize at 8% per annum. If the last dividend paid was Rs.2.50 per share and the investor’s required rate of return is 15%, find out the intrinsic value per share of Z Ltd as of date.

Determine the price at which an investor may be ready to buy the shares of the company at the end of period Po (i.e., now) and P1, P2, P3, P4, and P5.

Problem No 9Sai Chemicals has a current cash dividend of Rs.2 per share. You estimate that cash dividend grow at a rate of 12% for each of the three years and then at 6% per year for each of two more years. After you expect them to grow at 2 percent per year infinity.

a. What is the current market value of Sai Chemical’s share if the required rate of return is 14 percent?

b. What is the market price if everything is the same as in (a) except that after year 5 three is no expected growth in cash dividend?

Problem No 10

This risk free return is 10% and the risk premium is 5% with beta of a company is 1.6 the company had declared the latest dividend at Rs.3 (2007) whereas it had declared a dividend of Rs.2.115 in the year 2001. The company’s earnings and the dividend experienced constant growth. Find out the intrinsic value of the shares. Take into account the following PV table value if useful.

% of Cost of Capital PV at the end of 6 years 5% 0.746 6% 0.705 7% 0.666

Problem No 11

A company’s share is quoted in market at Rs.60 currently. A company currently paid a dividend of Rs.5 per share and investors expect a growth rate of 12 percent per year.

Compute:

a. The company’s cost of capitalb. If anticipated growth rate is 13 percent pa. Calculate the indicated market price per share.c. If the company’s cost of capital is 18 percent and anticipated growth rate is 15 percent pa,

calculate the market price per share, if dividend of Rs.5 per share is to be maintained.

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Problem No 12

Sheetal has invested in Manali Chemicals Ltd. The capitalization rate of the company is 15 percent and the current dividend is Rs.3.00

a. Calculate the value of the company’s equity share if the company is slowly sinking with an annual decline rate 5% in the dividend

b. Calculate the value of the equity share of Manali Chemicals Ltd, if the company shows no growth but is able to maintain its dividend.

Problem No 13

A company wants to declare 2 years holiday for dividends with lots of capital investments program in the offing. It is also decided to declare dividend of Rs.14, with a growth rate of 9% for ever on account of investments taken up now. Find the present value per share of the company if the required rate of return of equity share is 19%. In case the investment program is not taken up, there will be no holiday for dividend. The company just paid Rs.16 per share. Growth rate would be 6% forever without investment program. Find out the advantage / disadvantage of taking up investment program on the value per share of the company. Make suitable assumptions if required.

Problem No 14

Most Corporation had a net income of Rs. 8, 00,000 in 19X1. Earnings have grown at an 8% annual rate. Dividends in 19X1 were Rs. 3, 00.000. In 19X2, the net income was Rs. 11, 00,000. This, of course was much higher than the typical 8 percent annual growth rate. It is anticipated that earnings will go back to the 8% rate in future. The investment in 19X2 was Rs. 7,00,000

How much dividend should be paid in 19X2 assuming a) stable dividend payout ratio of 25 % b) stable rupee dividend policy is maintained c) residual dividend policy is maintained and 40 % of the 19X2 investment is financed with debt d) the investment for 19X2 is to be financed with 80% debt and 20% retained earnings. Any net income not invested is paid out in dividends.

Problem No 15

Buena Terra Corporation is reviewing its capital budget for the upcoming year. It has paid a $3.00 dividend per share (DPS) for the past several years, and its shareholders expect the dividend to remain constant for the next several years. The company’s target capital structure is 60 percent equity and 40 percent debt; it has 1,000,000 shares of common equity outstanding; and its net income is $8 million. The company forecasts that it would require $10 million to fund all of its profitable (i.e., positive NPV) projects for the upcoming year.

a. If Buena Terra follows the residual dividend model, how much retained earnings will it need to fund its capital budget?b. If Buena Terra follows the residual dividend model, what will be the company’s dividend per share and payout ratio for the upcoming year?c. If Buena Terra maintains its current $3.00 DPS for next year, how much retained earnings will be available for the firm’s capital budget?d. Can the company maintain its current capital structure, maintain the $3.00 DPS, and maintain a $10 million capital budget without having to raise new common stock?

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e. Suppose that Buena Terra’s management is firmly opposed to cutting the dividend, that is, it wishes to maintain the $3.00 dividend for the next year. Also, assume that the company was committed to funding all profitable projects and was willing to issue more debt (along with the available retained earnings) to help finance the company’s capital budget. Assume that the resulting change in capital structure has a minimal impact on the company’s composite cost of capital, so that the capital budget remains at $10 million. What portion of this year’s capital budget would have to be financed with debt?f. Suppose once again that Buena Terra’s management wants to maintain the $3.00 DPS. In addition, the company wants to maintain its target capital structure (60 percent equity, 40 percent debt) and maintain its $10 million capital budget. What is the minimum dollar amount of new common stock that the company would have to issue in order to meet each of its objectives?g. Now consider the case where Buena Terra’s management wants to maintain the $3.00 DPS and its target capital structure, but it wants to avoid issuing new common stock. The company is willing to cut its capital budget in order to meet its other objectives. Assuming that the company’s projects are divisible, what will be the company’s capital budget for the next year?h. What actions can a firm that follows the residual dividend policy take when its forecasted retained earnings are less than the retained earnings required to fund its capital budget?

Problem No 16

The earnings per share of a company are Rs.8 and the rate of capitalization 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%.

Explain fully what inferences can be drawn from the above exercise?

Problem No 17

The following information is available in respect of the rate of return on investments (r), the capitalization rate (k) and earnings per share (E) of Hypothetical Ltd.

R= (i) 12% (ii) 10% (iii) 8%; k=10% E=Rs.20

Determine the value of its shares, assuming the following:

Situation 1 2 3 4 5 6 7Rentention Ratio (b) 10 20 30 40 50 60 70D/P ratio (1-b) 90 80 70 60 50 40 30

Problem No 18

From the following information supplied to you, determine the theoretical market value of equity shares of a company as per Walter’s Model:

--------------------------------------------------------- Earning of the company Rs.500, 000 Dividends paid Rs.300, 000

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Number of shares outstanding 100, 000 Price earning ratio 8 Rate of return on investment 15% ---------------------------------------------------------

Are you satisfied with the current dividend policy of the firm? If not, what should be the optimal dividend payout ratio in this case?

Problem No 19

Orix telecommunications has a target capital structure which consists of 70% debt and 30% equity. The company anticipates that its capital budget for the upcoming year will be Rs.30, 00,000. If Orix reports net income of Rs.20, 00,000 and it follows a residual dividend payout policy, what will be its dividend payout ratio?

Problem No 20

A Ltd has made a profit of Rs.1, 20,000. Its gearing ratio is 0.4 which is to be maintained. It cost of capital is: debt 10%, equity 22%, retained earnings 20%. Four projects are under consideration.

Investment Required Rate of Return on InvestmentA Rs.60, 000 19%B Rs.50, 000 18%C Rs.80, 000 17%D Rs.20, 000 16%

What amount should be paid as dividend?

Problem No 21

What will be the dividend per share of Manik Industries for the year 2003 given the following information about the company? ------------------------------------------- EPS of 2007 =Rs.5 ------------------------------------------- DPS for 2006 = Rs.2 Target payout ratio = 0.6 Adjustment rate = 0.7 -------------------------------------------- Apply the Lintner Model. ------------------------------------------

Problem No 22

ABC Ltd has a capital of Rs.10 lakhs in equity shares of Rs.100 each. The shares currently quoted at par. The company proposes declaration of a dividend of Rs.10 per share at the end of the current financial year. The Capitalization rate for the risk class to which the company belongs is 12%.

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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?(iii) Assuming that the company pays the dividend and has net profits of 5, 00,000 and

makes new investments of Rs.10 lakhs during the period, how many new shares must be issued? Use the M.M. model.

Problem No 23

Jasper Ltd had issued 30 Lacs ordinary shares of Re.1 each that are at present selling for Rs.4 per share. The company plans to issue rights to purchase one new equity share at a price of Rs.3.2 per share for every three shares held. A share holder who owns 900 shares thinks that he will suffer a loss in his personal wealth because new shares are being offered at a price lower than market value. On the assumption that the actual market value of the shares will be equal to the Ex-rights price. What could be the effect on the share holders’ wealth if A) He sells all the rights; B) he exercises half of the rights and sells other half C) He does nothing at all.

Problem No 24

A Ltd is an all equity financed company. The current market price of shares is Rs.180 it has just paid a dividend of Rs.15 per share and expected future growth in dividend is 12 percent. Currently, it is evaluating a proposal requiring funds of Rs.20 lacs, with annual inflows of Rs.10 lacs for 3 years. Find out the Net Present Value of the proposal, if

(i) It is financed from retained earnings and (ii) It is financed by issuing fresh equity at market price with a floatation cost 5 percent

of issue price

Problem No 25

XYZ Ltd has just paid a dividend of Rs.2 per share. The market expects this dividend to grow constantly in each future year at the rate of 6% p.a. The cost of capital is currently 8%. As soon as the dividend was paid, a new project has come up for the consideration of the company. This project requires retaining all the earnings for a period of 3 years. First dividend shall be paid @ Rs.2.50 per share at the end of 4th year and dividend will grow @ 7% thereafter.

An investor holds 1000 shares in that company and has a personal commitment to meet every year for a sum of Rs.2000.

a. What is the price of the company’s share?b. How would you advise the investor to meet the personal commitment when there is no

dividend for 3 years period?c. Determine the wealth of the investor at the end of year 3.

Problem No 26

The company has flush cash position to carry out buy back operations. Advice the minimum buy back price to be offered

Number of shares prior to buy 10L

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backShares to be bought back 1LMPS prior to buy back Rs.378

Problem No 27

Following are the details regarding 3 companies A, B and C Ltd.

Details A B CInternal Rate of Return 15% 5% 10%Cost of Equity Capital 10% 10% 10%Earnings per Share Rs. 8 Rs. 8 Rs. 8

Calculate the value of an equity share of each of three companies applying Walter’s Formulae when dividend payout ratio (D/P) is

i. 50 % ii. 75 % iii. 25 %

What conclusions do you draw?

Problem No 28

Components Manufacturing Corporation (CMC) has an all-common-equity capital structure. It has 200,000 shares of $2 par value common stock outstanding. When CMC’s founder, who was also its research director and most successful inventor, retired unexpectedly to the South Pacific in late 2001, 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 plow back most of its earnings to finance growth, which averaged 12 percent per year. Future growth at a 5 percent 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 percent rate of return required by CMC’s stockholders (ks _ 14%) would amount to only $800,000 for 2002 in comparison to a projected $2,000,000 of net income. If the existing 20 percent dividend payout were continued, retained earnings would be $1.6 million in 2002, but, as noted, investments that yield the 14 percent cost of capital would amount to only $800,000. The one encouraging point is that the high earnings from existing assets are expected to continue, and net income of $2 million is still expected for 2002. Given the dramatically changed circumstances, CMC’s management is reviewing the firm’s dividend policy.

a. Assuming that the acceptable 2002 investment projects would be financed entirely by earnings retained during the year, calculate DPS in 2002, assuming that CMC usesthe residual dividend model.b. What payout ratio does your answer to part a imply for 2002?c. If a 60 percent payout ratio is maintained for the foreseeable future, what is your estimate of the present market price of the common stock? 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 stock if the old 20 percent payout were continued?

Assume that if this payout is maintained, the average rate of return on the retainedearnings will fall to 7.5 percent and the new growth rate will be

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g = (1.0 - Payout ratio) (ROE) = (1.0 - 0.2) (7.5%) = (0.8) (7.5%) = 6.0%.

Merger, acquisitions and Restructuring

Problem No 1

Find out the NPV of merger with respect to A Ltd and B Ltd.

A Ltd. B Ltd. Merged CompanyValue of the Company Rs.40 Lacs Rs.10 Lacs 60 Lacs

Compensation paid to B Ltd for takeover is Rs. 12Lacs

Problem No 2

X Ltd is considering the proposal to acquire Y Ltd. and their financial information is given below: X Ltd Y LtdNo of Equity Shares 10,00,000 6,00,000Market Price per Share Rs. 30 18Market Capitalization Rs. 3,00,00,000 1,08,00,000

X Ltd intend to pay Rs. 1,40,00,000 in cash for Y Ltd’s market price reflects only its value as a separate entity.

Calculate the Cost of merger:

(i) When Merger is financed by cash(ii) When Merger is financed by 500,000 shares (in the merged entity)

Problem No 3

X Ltd wants to take over Y Ltd and the financial details of both are follows:

X Ltd Y LtdRs. Rs.

Preference share capitalEquity share capital of Rs 10 eachShare premium Profit and loss A/c.10% Debentures

Fixed assetsCurrent assets

Profit after tax and Preference divided

20,000 -1,00,000 50,000- 200038,000 400015000 50001,73,000 61,0001,22,000 35,000 51,000 26,0001,73,000 61,00024,000 15,000

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Market price 24 27

What should be share exchange ratio should be offered to the shareholders of Y Ltd. if based on (i) net asset value, (ii) ESP, and (iii) market price. Which should be preferred from the point of view of X Ltd?

Problem No 4

B Co. is being acquired by A Co. on a share exchange basis. Their selected data are as follows:Determine (a) pre-merger, market value per share, and (b) the maximum exchange ratio A Co. should offer without the dilution of (i) EPS (ii) market value per share.

A BProfit after tax (Rs.lac) 56 21Number of shares (lac) 10 8.4Earnings per share (Rs) 5.6 2.5Price-earnings ratio 2.5 7.5

Problem No 5

If the cost of merger is computed as Rs 277.5 lacs after acquiring S Ltd, what is the exchange ratio worked out by the acquiring company B Ltd. from the following information?

MPS of B Ltd (Before Acquisition) Rs.192.50MPS of S Ltd(Before Acquisition) Rs.88No. of shares of B Ltd. (Before Acquisition) 20LacsNo of shares of S Ltd. (Before Acquisition) 15Lacs

It is also estimates that the synergy value is measured at present value of Rs.687.5 Lacs

Problem No 6

Telco Plans to acquire Proton. The following information is provided as following:

Telco ProtonMPS Rs.300 Rs.200EPS Rs.25 Rs.20No of ES 20Lacs 10LacsPE ratio 12 10

(a) What is the maximum exchange ratio acceptable to the shareholders of Telco if the PE Ratio after on a acquisition is 11 with no synergy gain?

(b) What is the minimum exchange ratio acceptable to shareholders of Proton if the PE ratio after acquisition is 11.5 times with 5% synergy gain?

Problem No 7

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Big Ltd is determined to report earnings per share of Rs. 2.67; it therefore acquires the Small Ltd. You are given the following facts:

Big Ltd Small Ltd Merged FirmEarning Per Share 2 2.50 2.67Price per Share 40 25 ?Price-earnings ratio 20 10 ?Number of Shares 100,000 200,000 ?Total earnings 200,000 500,000 ?Total Market value 40,00,000 50,00,000 ?

Once again there are no gains from merging In exchange for Small Ltd shares, Big Ltd issues just enough of its own shares to ensure its Rs.2.67 earnings per share objective.

(a) Complete the above table for the merged firm.(b) How many shares of Big Ltd are exchanged for each share of Small Ltd?(c) What is the cost of the merger to Big Ltd?(d) What is the change in the total market value of the Big Ltd. shares that were

outstanding before the merger?

Problem No 8

Post Merger AnalysisYou have been provided the following financial data of two companies:

Krishna Ltd Rama LtdEarning after taxes Rs.7,00,000 Rs.10,00,000Equity shares outstanding 2,00,000 4,00,000Earning per share 3.5 2.5Price-earning ratio 10 times 14 timesMarket Price per Share Rs.35 Rs.35

Company Rama Ltd is acquiring the company Krishna Ltd exchanging its shares on a one-to-one basis for company Krishna Ltd.’s shares, The exchange ratio is based on the market prices of the shares of the two companies.

You are required to calculate-(i) The EPS subsequent to merger,(ii) Change in EPS for the share holders of Rama Ltd and Krishna Ltd.,(iii) The market value of the post-merger firm,(iv) The profits accruing to share holders of both the Companies.

Problem No 9

X Ltd. made an attempt to acquire Y Ltd. Following information is available for both the Companies:

X Ltd. Y Ltd.Price for Share (Rs) 30 20

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P/E ratio 5 4No. of Shares (lakhs) (FV of Rs 10) 3.0 2.0Reserve & Surplus (Rs lakhs) 30 20Promoters’ holding (lakh shares) 1.2 0.75

Directors of both the Companies have decided that a workable swap ratio is to be based on weights of 30%, 30% and 40% respectively for Earning, Book Value and Market Price of share of each company.

Find out the following:(i) Swap ratio(ii) After merger, Promoter’s holding %(iii) Post merger EPS(iv) Gain in Capital market Value of merged company, assuming Price Earnings ratio will remain same

Problem No 10

The following information is provided related to the acquiring Firm Mark Limited and the target Firm Mask Limited:

: 93JainFirm Mark Limited Firm Mask Limited

Earnings after tax (Rs.) 2,000 lakhs 400 lakhsNumber of shares outstanding 200 lakhs 100 lakhsP/E ratio (times) 10 5

Required: (i) What is the Swap Ratio based on current market prices?(ii) What is the EPS of Mark Limited after acquisition?(iii) What is the expected market price per share of Mark Limited after acquisition,

assuming P/E ratio of Mark Limited remains unchanged?(iv) Determine the market value of the merged firm(v) Calculate gain/ loss for shareholders of the two independent companies after

acquisition.

Problem No 11

Blue Dart is analyzing the possible acquisition of Pioneer Couriers. Neither firm has debt. The forecasts of Blue Dart show that the purchase would increase its annual after –tax cash flow by Rs.600,000 indefinitely. The current market value of Pioneer is Rs. 20 million. The current market value of Blue Dart is Rs.35 million. The appropriate discount rate for the incremental cash flow is 8%.

a. What is the synergy from the merger?b. What is the value of Pioneer to Blue Dart?

Blue Dart is trying to decide whether it should offer 25% of its share or Rs.15 Million in cash to Pioneer.

c. What is the cost to Blue Dart of each alternative?d. What is the NPV to Blue Dart of each alternative?

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e. Which alternative should Blue Dart use?

Problem No 12

Dividend Growth ModelChennai Limited and Kolkata Limited have agreed that Chennai Limited will take over the business of Kolkata Limited with effect from 31st December, 2001. It is agreed that.

1. Shareholders of 10,00,000 shares 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 prices have been worked out at Rs. 50 and Rs 25 for the shares of Chennai Limited and Kolkata Limited respectively.

2. In addition to (i) above shareholder 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 share holder of Kolkata Limited.

The following projection has been agreed upon by the management of both the companies. Year 2002 2003 2004 2005 2006 Benefit (in Rs.Lacs) 50 75 90 100 105

The benefit is estimated to grow at the rate of 2% from 2007 onwards. 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.

1. Calculate the cash that holder of each share of Kolkata Limited will receive.2. Calculate the total purchase consideration.

Problem No 13

Nivea Ltd is investigating the possible acquisition FLP Ltd. Following is the data:

___________________________________________________ Nivea Ltd FLP ____________________________________________________ Earnings per share 5 1.50 Dividend per share 3 0.80 Number of shares 1,000,000 600,000 Share price 90 20 ____________________________________________________

You estimate that investors currently expect a steady growth of about 6% in FLP earnings and dividends. Under new management this growth rate would be increased to 8% per year, without any additional capital investment required.

(a) What is the gain from the acquisition?

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(b) What is the cost of the acquisition if Nivea Ltd pays Rs. 25 in cash for each share of FLP?

(c) What is the cost of the acquisition if Nivea Ltd offers one share of Nivea Ltd for every three shares of FLP?

(d) How would the cost of the cash offer and the share offer alter if the expected growth rate of FLP were not changed by the merger?

Problem No 14

Going PrivateAlpha Limited a chain of restaurants is considering going private limited. The President Bidhu Das believes that with the elimination of Share holder servicing costs and other costs associated with public ownership the company could save Rs. 800,000 per annum before taxes. In addition the company believes management incentives and hence performance will be higher as a private company. As a result, annual profits are expected to be 10% greater than present after-tax profits of Rs.9 million The effective tax rate is 30 %, the price / earnings ratio of the Share is 12, and there are 10 million shares outstanding. What is the present market price per share? What is the maximum Rupees premium above this price that the company could pay in order to take the company into private Limited?

Problem No 15 Timex products has estimated the following anticipated incremental benefits and investments for a potential target:

Year ΔPBT (in Rs) Δ Dep*(in Rs.) (Investment (in Rs.) 1 80000 20000 150000 2 80000 50000 100000 3 135000 50000 50000 4 190000 50000 0 5 195000 50000 0 6-10 200000 20000 0*Δ depreciation is for the investment in the column immediately to the right.

a) If Timex’s tax rate is 0.40, Calculate the incremental after-tax cash flows, Δ CF, from the target.b) The Value of Timex before the merger is Rs 2.4 million, while the target’s market value is Rs.1 million. The market price per share of Timex’s share is Rs. 50, and the required rate of return is 15 percent. Calculate the NPV for both a cash-financed and a Share-financed acquisition if Timex anticipates paying a 15% premium above the current market value of the target.

Problem No 16

Master Corporation wants to buy certain fixed assets of Smith Corporation. However, Smith Corporation wants to dispose of its entire business. The balance sheet of Smith follows-

ASSETS Rs. Cash 2,000Accounts receivable 8,000

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Inventories 20,000Equipment 1 10,000Equipment2 20,000Equipment3 35,000Buildings 90,000Total assets 185,000LIABILITES AND EQUITYTotal liabilities 80,000Total stockholders equity 105,000Total liabilities and stock holders’ equity 185,000

Master needs only equipment 1 and 2 and the building. The other assets excluding cash can be sold for Rs. 35000 .Smith wants Rs. 48,000 for the entire business. It is anticipated that the after-tax cash inflows from the new equipments will be Rs. 30,000 a year for the next 8 years. The cost of capital is 12 percent.(a) What is the initial net cash outlay?(b) Should the acquisition be made?

Problem No 17

Demerger AnalysisThe following information relates to Fortune India Limited having two divisions viz. Pharma Division and Fast Moving Consuming Goods Division (FMCG). Paid up share capital of Fortune India Ltd is consisting of 3000 lacs equity shares of Re.1 each. Fortune India Ltd decided to de-merge Pharma division as Fortune Pharma Ltd with effect from 1.4.2005. Details of Fortune India Ltd as on 31.03.2005 and of Fortune Pharma Ltd as on 1.4.2005 are as below:

Rs in lacs Particular Fortune Pharma Ltd Fortune India LtdOutside LiabilitiesSecured Loan 400 3000Unsecured Loan 2400 800Current Liabilities &Provisions 1300 21200Assets Fixed Assets 7740 20400Investments 7600 12300Current Assets 8800 30200Loans & Advances 900 7300Deferred Tax/ Miscellaneous exp 60 (200)

Boards 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 Ltd. For that purposes following points are to be considered:

1. Transfer of Liabilities and asset at book values 2. Estimated Profit for the year 2005-06 is Rs 11400 Lacs for Fortune India Ltd and

Rs.1470 Lacs for Fortune Pharma Ltd.3. Estimated Market Price of Fortune Pharma Ltd is Rs.24.50 per share.

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4. Average P/E Ration 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. Book value per share of both the Companies immediately after Demerger.

Problem No 18

The following is the balance sheet of A Ltd.

Liabilities Amount Assets Amount Rs.13% Preference Share Capital 1, 00,000 Fixed Assets 19, 00,000Equity Shares (Rs.10 each) 20, 00,000 Investments 1, 00,000Retained earnings 4, 00,000 Stock 5, 00,00012% Debentures 3, 00,000 Debtors 4, 00,000Current liabilities 2, 00,000 Bank 1, 00,000 30,00,000 30,00,000

X Ltd. agreed to take over A Ltd. for which the purchase consideration was agreed as follows:

1. Rs. 3,30,000 in 13% Debentures of X Ltd. for redeeming 12 % Debentures of A Ltd.2. Rs. 1,00,000 in 12 % Convertible Preference shares for the Preference shares of A Ltd.3. 1, 50,000 Equity Shares of X Ltd. at the market price of Rs.15 each.4. X Ltd. to meet acquisition cost of Rs. 30,0005. The break- up figure of eventual disposition by X Ltd. of the un-required current assets

and current liabilities of A Ltd. Is as follows: Investment Rs. 125000; Debtors Rs. 350000; Inventories 425000; and Current Liabilities Rs. 190000.

A Ltd is expected to generate yearly operating cash flows (after tax) of Rs. 700000 per annum for 6 years and that the fixed assets of A Ltd. are expected to expected to fetch Rs.3,00,000 at the end of 6 years. Evaluate the proposals given that the cost of capital of X Ltd’s 15%

Problem No 19

Following are the financial statement 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 14, 00,000 10, 00.000Total fixed assets (net) 10, 00,000 5, 00,000Total Assets 24, 00,000 15, 00,000

------------------------------------------------------------

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Equity capital (10 each) 10, 00,000 8, 00,000 Retained earnings 2, 00,000 - 14% Loan term debt 5, 00,000 3, 00,000 Total current liabilities 7, 00,000 4, 00,000 ------------------------------------------------------------- 24, 00,000 15, 00,000 --------------------------------------------------------------

Income Statements _______________________________________________________ A Ltd. B Ltd. Rs. Rs. _____________________________________________________ Net sales 34, 50,000 17, 00,000 Cost of goods sold 27, 60,000 13, 60,000 Gross profit 6, 90,000 3, 40,000 Opening expenses 2, 00,000 1, 00,000 Interest 70,000 42,000 Earnings Before taxes 4, 20,000 1, 98,000 Taxes (50%) 2,10,000 99,000 Earning after taxes (EAT) 2,10,000 99,000 Additional Information: Number of equity shares 1,00,000 80,000 Dividend payment ratio 40% 60% Market prices per share (MPS) Rs.40 Rs.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 ERS and PE components, and also segregate their EPS figures into return on equity (ROE) and book value /intrinsic value per shares (BVPS) components

ii. Estimate future ERS growth rates for each firmiii. 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 ratios, 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.

Problem No 20

A ltd. is considering the purchasing of T Ltd. The cash inflows after taxes for T Ltd. are estimated to be Rs. 15 lacs per year in the future. This forecast by A ltd. includes expected merger synergic gains. T Ltd. currently has total assets of Rs.50 lacs with 20% of the total assets being financed with debts funds. A Ltd’s pre-merger weighted average cost of capital is 15%

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i. Based on A Ltd. pre-merger cost of capital, what is the maximum purchase price that A Ltd. would be willing to pay to acquire T Ltd.?

ii. Assume that by acquiring T Ltd. A Ltd. will move toward an optimal capital structure such that its weighted average cost of capital will be 12% after the acquisition. Under these conditions, what would be the maximum price A Ltd. should be willing to pay?

iii. Assume that cash flows for T Ltd. estimated at Rs. 15 lacs for the coming year, will grow at a rate of 20% per year for the following two years, and will be on level thereafter. Each rupee increase in cash flows will require Re. 0.7 incremental investment in assets. Estimate the maximum purchase price for T Ltd. based on a 12% cost of capital.

Problem No 21

In 2007, Vishnu Ltd. acquired Ravana Ltd. after a hotly contested takeover for approximately Rs. 110 per share. The free cash flows of the two firms-before and after merger-were projected as follows: Free Cash Flow (Rs. million)Year/Firm 1 2 3 4 5 Terminal value*Vishnu 4684 4918 5164 5422 5693 82756Ravana 471 509 550 594 641 8102Combined 5195 5558 5948 6364 6809 96672(Post-merger)*Terminal value as at the end of the 5th year.

Cost of equity and debt of the individual firms and the combined firm (after merger) were estimated as given under:

Vishnu Ravana CombinedCost of equity 14.23% 15.33% 14.34%Cost of debt 5.40% 6.00% 5.42%Debt/ (Debt + equity) 21% 9% 20%

At the time of merger deal Ravana had 70.6 million outstanding shares and Rs. 537 million worth of outstanding debt:

(a) What is the minimum price per share Vishnu could have offered to Ravana?(b) Do you think the price paid by Vishnu was justifiable? Give reasons

Problem No 22

The chief executive of a Amazon Inc. thinks that shareholders always look for the earnings per share. Therefore, he considers maximization of the earnings per share (EPS) as his Company’s objective. His Company’s current net profits are Rs. 80 Lakh and EPS is Rs.4. The current market price is Rs. 42. He wants to buy another to buy another firm which has current income of Rs. 15.75 Lakh, EPS of 10.50 and the market price per share of Rs. 85.

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(i) What is the maximum exchange ratio which the chief executive should offer so that he could Keep EPS at the current level?

(ii) If the chief executive borrows funds at 15 per cent rate of interest and buys out the other company by paying cash, how much should he offer to maintain his EPS? Assume a tax rate of 52%

Problem No 23

OCTL is considering the cash acquisition of R Ltd for Rs.750,000 The acquisition is expected to result in incremental cash flows of Rs 125,000 in the first year, and this amount is expected to grow at a 6 per cent compound rate. In the absence of the acquisition OCTL expects net cash flows of Rs 600,000 this coming year (after capital expenditures), and these are expected to grow at a 6 per cent compouned rate forever. At present, investors and creditors require a 14 percent overall rate of return for OCTL, R Ltd is much more risky, and the acquisition of its will raise the company’s overall return to 15 per cent.

(a) Should OCTL acquire R Ltd?(b) Would you answer be the same if the overall required rate of return stayed the same?

Business Valuation

Goodwill Valuation

Problem No 24

Laxmi Private Limited is negotiating to sell their business to a public limited company. The following is a summarized extract from the Balance Sheet as on 31st March, 2006 of Laxmi Private Limited.

RsCapital 1,000 shares of Rs. 1000 each Free Reserve

Fixed Assets at depreciated costCurrent Assets(-) Current Liabilities

Rs 7,20,000 1,60,000

10,00,000 2,00,00012,00,0006,40,000

5,60,00012,00,000

The profits of Laxmi Private Limited for the last five years it has been in existence, after eliminating any extraneous or non-recurring debits and credits, were Rs. 90,000; Rs. 1,30,000; Rs.1,15,000; Rs 2,40,000 and Rs 2,75,000. A return of 10% on the capital employed is considered to be reasonable in this particular business and it is expected that future requirements as to capital will not vary materially from the capital employed as on 31st March.

Ignoring any extraneous factors that may affect the position, suggest the amount that should reasonably be paid to the private company for good will for acquiring the company.

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Problem No 25

Mr. Dinesh a successful entrepreneur has gathered the latest financial information pertaining to an unlisted company. Mr. Dinesh intention is to buy this company.

Liabilities Rs.000 Assets Rs.000Equity (FV Rs.1)ReservesTerm loansTrade creditsOverdraftTax payable

300730350430320110

Land and BuildingPlant and MachineryStockDebtorsCash

45072043560035

2240 2240

Amount/Rs.Pre tax Profits Present yearPre tax profits Last yearPost tax profits Present yearDividends declared Present year A year ago

640,000341,000384,000300,000200,000

Additional Information:Profits are expected to grow annually at a rate of 8%Average earnings per share of comparable listed companies is Re.0.15Earnings yield for companies in the same risk class 10%Market value of land and buildings has fallen by 20%Cost of equity 16%Replacement cost of plant 900Realizable value 648Obsolete element in the stock valuation 75This obsolete element cab be sold for 3Debtors can be realized In fullAverage pre tax return on net realizable assets 12%Tax Rate 40%

Required: Compute the price that can pay for this business, using:

1) Net realizable value of assets method2) Earnings capitalization model3) Fair value model (Berliner method)4) Dividend valuation model5) Price earnings model6) An average price that you would recommend of models 3 to 5 are used.

For this computation assume the following: Last two year average pre-tax earnings will be capitalized (15%) PE multiple will be on earnings after reckoning growth for only one year

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PE multiple of unlisted companies is normally 90% of Listed companies Dividends will grow at the same rate as earnings

Problem No 26

Given below is the balance sheet of S Ltd. as on 31.3.2008 –

Liabilities Rs. Lakhs Assets Rs. Lakhs

Share Capital 100 Land and Buildings 40

Reserves and Surplus 40 Plant and Machinary 80

Creditors 30 Investments 10

Stock 20

Debtors 15

Cash and Bank 5

170 170

You are required to work out the value of the company shares on the basis of Net Asset Method and Profit Earning Capacity Method (Capitalization) Method and arrive at the fair price of the shares, by considering the following information –(i) Profit for the current year Rs. 64 lakhs includes Rs. 4 lakhs extraordinary income and Rs. 1 lakh income from investments of surplus funds unlikely to recur(ii) In subsequent years, additional advertisement expenses of Rs. 5 lakhs are expected to be incurred each year(iii) Market value of Land and Buildings and P&M have been ascertained at Rs. 96 lakhs and Rs. 100 Lakhs respectively. This will entail additional depreciation of Rs. 6 lakhs each year(iv) The capitalization rate applicable to similar business is 15%

Problem No 27

The total value both equity and debt of two companies, Sun Ltd and Moon Ltd, are expected to fluctuate according to the state of the economy.

Economic StateRecession Slow Growth Rapid growth

Probability 0.15 0.65 0.20Total Value:Sun Ltd (Rs In lakh) 126 165 225Moon Ltd (Rs.In lakh) 189 240 360

Currently Sun Ltd has Rs 135 lakh of debt and Moon Ltd’s 30 lakh of debt.

21


If the two companies were to merge and assuming that no operational synergy occurs as a result of the merger, calculate the expected value of debt and equity of the merged company.

Explain the reasons for any difference that exists form the expected values of debt and equity if they do not merge.

Economic Value Added

Problem No 28

The following data relates to Morning Glory Limited.

Profit and Loss A/c20 × 1 Rs. In lakh

20 × 2 Rs. in lakh

Turnover 1990 2360Pre-tax accounting profit 420 530Taxation 125 160Profit after tax 294 370Dividends 100 120Retained Earnings 194 250

20 × 1 Rs. In lakh

20 × 2 Rs. In lakh

Fixed assets 740 960Net current Assets 800 1000

1540 1960Financed by Shareholders Funds 1190 1440Medium and long term Bank Loan 350 520

1540 1960

Pre-tax accounting profit is taken after deducting the economic depreciation of the company’s fixed assets (also the depreciation used for tax purposes).

Additional Information:

i) Economic depreciations were Rs 190 lakh in 20×1 and Rs. 210 lakh in 20 × 2.ii) Interest expenses were Rs.26 lakh in 20×1 and Rs 36lakh in 20×2iii) Other non-cash expenses were Rs.64 lakh in 20×1 and Rs 72 lakh in 20×2.iv) The tax rate in 20×1 and 20×2 was 30%v) Morning Glory Limited has non-capitalized valued at Rs.70 lakh in each year, 20 ×0 to 20×2.vi) The Company’s pre-tax cost of debt was estimated as 7% in 20×1 and 8% in 20×2.vii) The company’s cost of equity was estimated as 14% in 20×1 and 16% in 20×2.viii) The target capital structure is 75% equity and 25%debt.ix) Balance sheet capital employed at the end of 20×0 was a Rs 1390 lakh.

Estimate the economic value added for Morning Glory Limited for 20×1 and 20×2.

Problem No 29

Calculate the EVA from the following data:

22


(Rs.Crores) 2001Average Debt 50Average Equity 2766Cost of Debt Post tax% 7.72Cost of Equity% 16.70Weighted Average Cost of Capital % 16.54Profit after tax, before exceptional item 1541Interest after taxes 5

Brand Valuation

Problem No 30

Consider the extract of profit & Loss Statements of ABC Ltd for the past three years:

Year ended 31.03 2005 2006 2007 2008 (Projected)

Sales 2526 2730 2975 3010Other Income 30 35 32 40PBIT 126 140 149 158Interest 20 24 21 25Tax 21 28 32 27Profit after tax 74 88 96 106

Inflation index for the past three years: 31.03.2005 100 31.03.2006 105 31.03.2007 109

Sales figures include sale proceeds from unbranded product as well, on which the company earns a modest profit of 3%. Unbranded sales were:

Year ended Rs. in lacs31.03.2005 25031.03.2006 24031.03.2007 26531.03.2008 280

The average capital employed of ABC Ltd (calculated on past three year’s figures) is Rs 1200 lacs. ABC Ltd estimates that 5% return on average capital employed is the minimum level of earnings the company would have got by selling equivalent unbranded products. The marketing department of ABC Ltd assigns the score of 74 out of 100 for its brand strength and recommends a multiple of 15 to be applied on earnings to value brand. Show the brand valuation by following earnings multiple methods.

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Problem No 31

ABC Ltd. Is run and managed by an efficient team that insists on reinvesting 60% of its earnings in projects that provide an ROE of 10%, despite the fact that the firm’s capitalization rate (K) is 15%. The firms current year’s earnings is Rs. 10 per share.

At what price will the stock of ABC Ltd. Sell? What is the present value of growth opportunities? Why would such a firm be a takeover target?

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CAPITAL BUDGETING

Problem No 1

Find out the cash flow for investing decision.

Sales CostProfit before interest and taxInterestProfit before taxTaxProfit after tax

400 5000 2250270 2750 1000130 2250 1250 30 675 250100 1575 1000 40 575 300 60 1000 700

Problem No 2

Find out the missing figures from the following.

S. No. Real Cost Inflation rate Money Rate1 10 5 ?2 8 ? 17.723 ? 6 12.35

Problem No 3

PQR Company is examining an investment proposal requiring an initial outflow of Rs.8 lacs and expected inflow in real terms (i.e. today’s purchasing power) is Rs.2, 80,000 per year for the next 4 years. The company’s out of pocket monetary cost capital is 9% and inflation is expected to be 3.2% p.a. over the next four years.

(i) Compute the company’s real (net of inflation) cost of capital.(ii) What is the present value of cash inflows if real cost of capital is taken into

consideration?(iii) Compute nominal cash inflow from real cash inflows and also calculate present value

on the basis of nominal cash inflows.

Problem No 4

A company is considering a new project requiring an outlay of Rs.1 Lac. The firm’s existing cost a capital is 10% for its market value of Rs.10 lacs. The new project under consideration would place the firm into a new higher risk category, requiring a revised cost of capital at 11%.

1) What is the new project’s minimum required rate of return?2) In case, the expected annual incremental cash flow due to the new project (perpetuity) is

Rs.30000. Should the company accept the project?

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Problem No 5

One project of a company is doing poorly and is being considered for replacement. Three mutually exclusive projects A,B & C have been proposed. The projects are proposed to require Rs.200000 each and have an estimated life of 5, 4, 3 years respectively and have no salvage value. The company’s required rate of return is 10%. The anticipated cash inflows after taxes for the three projects are as follows:

Year A B C 1 50000 80000 100000 2 50000 80000 100000 3 50000 80000 10000 4 50000 30000 --- 5 190000 --- ---

Rank each project applying the methods of Pay-back, Average rate of return.

Problem No 6

Zenith Industries Ltd. are thinking of investing in a project costing Rs.. 20 lakhs. The life of the project is five years and the estimated salvage value of the project is zero. Straight line method of charging depreciation is followed. The tax rate is 50%. The expected cash flows before tax are as follows:

Year 1 2 3 4 5Estimated cash flow before depreciation 4 6 8 8 10

You are required to determine the:(i) Payback period for the investment(ii) Average rate of return on the investment(iii) Net present value at 10% cost of capital(iv)Benefit-cost ratio.

Problem No 7

United Industries Ltd has an investment budget of Rs. 100 lakhs for 2005-06. It has short listed two projects A and B after completing the market and technical appraisals. The management wants to complete the financial appraisal before making the investment. Further particulars regarding the two projects are given below:

Particulars A BInvestment required 100 90Average annual cash inflow before dep and tax (estimate) 28 24

Salvage value –Nil for both projects Estimate life – 10 years for both projects

P.V. of an annuity of Re. 1 for ten years at different discount rates is given below:

26


Rate % 10 11 12 13 14 15Annuity - 10 years 6.145 5.899 5.650 5.426 5.216 5.019

The company follows straight line method of depreciation. Its tax rate is 50%.You are required to calculate:

a. Payback period andb. I.R.R of the two projects.

Problem No 8

The cash flows of two mutually exclusive projects are as under:

t0 t1 t2 t 3 t 4 t 5 t 6

Project ‘P’Project ‘J’

(40,000)(20,000)

13,0007,000

8,00013,000

14,00012,000

12,000--

11,000--

15,000--

Required:

(i) Estimate the net present value (NPV) of the Project ‘P’ and ‘J’ using 15% as the burled rate.

(ii) Estimate the internal rate of return (IRR) of the Project ‘P’ and ‘J’.

(iii) Why there is a conflict in the project choice by using NPV and IRR criterion?

(iv) Which criteria you will use in such a situation? Estimate the value at that criterion. Make a project choice.

The present value interest factor values at different rates of discount are as under:

Rate of discount

t0 t1 t2 t 3 t 4 t 5 t 6

0.150.180.200.240.26

1.001.001.001.001.00

0.86960.84750.83330.80650.7937

0.75610.71820.69440.65040.6299

0.65750.60860.57870.52450.4999

0.57180.51580.48230.42300.3968

0.49720.43710.40190.34110.3149

0.43230.37040.33490.27510.2499

Problem No 9

Following are the data on a capital project being evaluated by the management of M Ltd.

Project M Annual Cost saving = Rs.40, 000 Useful life = 4 years IRR = 15% Profitability Index = 1.064 NPV = ? Cost of capital (%) = ? Cost of project (Rs.) = ?

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Payback period = ? Salvage value = 0

Find out the missing values considering the following table of discount factor only. ___________________________________________ Discount factor 15% 14% 13% 12% ____________________________________________ 1 year 0.869 0.877 0.885 0.893 2 year 0.756 0.769 0.783 0.797 3 year 0.658 0.675 0.693 0.712 4 year 0.572 0.592 0.613 0.636 _____________________________________________ 2.855 2.913 2.974 3.038 _____________________________________________

Problem No 10

Following cash flow details are available for project A and B having an initial outlay of Rs.5.4 crores and 4.7 crores respectively.

Project A Project B Years PAT Depreciation Interest PAT Depreciation Interest 0 (540) (470) 1 185 50 60 100 45 50 2 110 50 50 105 45 40 3 195 50 40 135 45 30 4 225 50 30 125 45 20 5 175 50 20 175 45 10

Tax rate is at 30%

Cost of capital is to be applied at 20%. Only one of the two projects can be chosen.

Which of the projects is to be chosen based on (a) NPV (b) PI (benefit cost ratio)?

Problem No 11

S Ltd. has Rs.10,00,00 allocated for capital budgeting purposes. The following proposals and associated profitability indexes have been determined:

Project Amount (Rs.) Profitability Index123456

3,00,0001,50,0003,50,0004,50,0002,00,0004,00,000

1.220.951.201.181.201.05

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Which of the above investments should be undertaken? Assume that projects are indivisible and there is no alternative use of the money allocated for capital budgeting.

Problem No 12

Five Projects M, N, O, P and Q are available to a company for consideration. The investment required for each project and the cash flows it yields are tabulated below. Projects N and Q are mutually exclusive. Taking the cost of capital @ 10%, which combination of projects should be taken up for a total capital outlay not exceeding Rs.3 lakhs on the basis of NPV and Benefit-Cost Ratio (BCR)?

Project Investment Cash flow p.a. No. of years P.V. @ 10%MNOPQ

50,0001,00,0001,20,0001,50,0002,00,000

18,00050,00030,00040,00030,000

10481625

6.1453.1705.3357.8249.077

Problem No 13

A project analyst is allotted with Rs.7000 for independent capital investment projects. He had prepared certain computations for your perusal. The details are as follows:

Projects DISCCO DISCCI NPV Profitability Index Rank (PI) A 4000 4801 801 =4801 / 4000 → 1.20 2 B 5000 5600 600 1.12 4 C 2000 2377 377 1.19 3 D 1800 2274 474 1.26 1

You are asked to find out the best combination of projects on the following assumptions:a. Projects are divisible.b. Projects are indivisible

Problem No 14

The Anson Company is evaluating three investment situations:

(1) Produce a new line of aluminum skillets (2) Expand its existing cooker line to include several new sizes, and

(3) Develop a new higher-quality line of cookers.

If only the project in question is undertaken the expected present values and the amounts of investment. _____________________________________________ Project Investment Required Present value of Future cash flows

29


______________________________________________ 1 2, 00,000 2, 90,000 2 1, 15,000 1, 85,000 3 2, 70,000 4, 00,000 _____________________________________________

(i) If projects 1 and 2 are jointly undertaken, there will be no economies; the investments required and present values will simply be the sum of the parts.

(ii) With projects 1 and 3 economies are possible In investment because one of the machines acquired can be used in both production processes.

(iii) The total investment required for projects 1 and 3 combined is Rs.4,50,000; (iv) If projects 2 and 3 are undertaken there are economies to be achieved in marketing

and producing the projects but not in investment. (v) The expected present value of future cash flows for projects 2 and 3 is Rs.6, 20,000. (vi) If all three projects are undertaken simultaneously, the economies noted will still

hold. However, an Rs.1,25,000 extensions on the plant will be necessary, as space is not available for all three projects.

Which project or projects should be chosen?

Problem No 15

Following are the cash flows for G Ltd: ----------------------------------- Year Cash flow (Rs) ----------------------------------

0 (1, 00,000) 1 30, 0002 40, 0003 50, 0004 60, 000

-----------------------------------Discount rate is 15%.

i. Find the modified IRR (MIRR)ii. Compute NPV using Front end and Back end analysis

Problem No 16

SS Engineering Ltd is considering including two pieces of equipment, a truck and for overhead pulley system, in this year’s capital budget. The projects are independent. The cash outlay for the truck is Rs.17, 100, and that for the pulley system is Rs.22, 430. The firm’s cost of capital is 14 percent. After-tax cash flows, including depreciation, are as follows: _______________________________ Year Truck Pulley ________________________________ 1 Rs.5, 100 Rs.7, 500 2 Rs.5, 100 Rs.7, 500 3 Rs.5, 100 Rs.7, 500

4 Rs.5, 100 Rs.7, 500 5 Rs.5, 100 Rs.7, 500

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_________________________________

Calculate the IRR, the NPV and the MIRR for each project, and indicate the correct accept / reject decision for each.

Problem No 17

Devaraj Ind. Ltd must choose between a gas-powered and an electric-powered fork-lift truck for moving material to its factory. Since both fork-lifts perform the same function the firm will choose only one. The electric powered truck will cost more, but it will be less expensive to operate. It will cost Rs.22, 000, whereas the gas-powered truck will cost Rs.17, 500. The cost of capital that applies to both investments is 12 percent. The life for each type of truck is estimated to be 6 years, during which time the net cash flows for the electric-powered truck will be Rs.6, 290 per year and those for the gas-powered truck will be Rs.5, 000 per year. Annual net cash flows include depreciation expenses.

Calculate the NPV and IRR for each type of truck, and decide which to recommend.

Problem No 18 Office Automation company Ltd is obliged to choose between two copies HP or Epson. HP costs less than Epson, but its economic life is shorter. The costs and maintenance expenses of these two copiers are given as follows. These cash flows are expressed in real terms.

Copier Year 0 Year 1 Year 2 Yea 3 Year 4 Year 5 HP Rs.700 Rs.100 Rs.100 Rs.100 --- ---- Epson Rs.900 Rs.110 Rs.110 Rs.110 Rs.110 Rs.110

The inflation rate is 5% and the nominal discount rte is 14%. Assume that revenues are the same regardless of the copier, and that whichever copier the company chooses, it will buy the model forever. Which copier should the company choose? Ignore taxes and depreciation.

Problem No 19

Photolysis Ltd uses a 10% discount rate for project appraisal. It is considering purchasing a machine which, when it comes to the end of its economic life, is expected to be replaced by an identical machine and so on, continuously. The machine has a maximum life of three years but, as its productivity declines with age, it could be replaced after either just one of two years. The financial details are as follows (all figures in Rs.000).

Years 0 1 2 3Outlay -1000Revenues +900 +800 +700Costs -400 -350 -350Scrap value +650 +400 +150

What is the appropriate replacement cycle?

Problem No 20

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To carry out identical tasks, a company uses several machines of the same type, but of varying ages. They have a maximum life of five years. Typical financial data for a machine are given below.

Time Now After After After After After Rs. 1 yr Rs. 2 yrs. Rs. 3 yrs. Rs. 4 yrs. Rs. 5 yrs. Rs.Initial cost 10, 000 Maintenance and serviceCosts 1, 000 1, 500 2, 000 2, 500 3, 000 5, 000Resale value if sold 7, 000 5, 000 3, 500 2, 500 2, 000

The rate of interest is 15%

These machines are assumed to produce flows of revenue which are constant.

Required:(a) Calculate the present values of keeping one machine for one, two, three, four or five years. (b) Convert these to annual equivalent annuities and find the most economical age at which to replace the machines.

Problem No 21

S Engineering Company is considering replacing or repairing a particular machine, which has just broken down. Last year this machine cost Rs.20,000 to run and maintain. These costs have been increasing in real terms in recent years with the age of the machine. A further useful life of 5 years is expected, if immediate repair of Rs.19,000 are carried out. If the machine is not repaired it can be sold-immediately to realize about Rs.5,000 (Ignore loss / gain on such disposal).

Alternatively, the company can buy a new machine for Rs.49, 000 with an expected life of 10 years with no salvage value after providing depreciation on straight line basis. In this case, running and maintenance costs will reduce to Rs.14, 000 each year and are not expected to increase much in real terms for a few years at least. S Engineering Company regards a normal return of 10% p.a. after tax as a minimum requirement on any new investment. Considering capital budgeting techniques, which alternatively will you choose? Take corporate tax rate of 50% and assume that depreciation on straight line basis will be accepted for tax purpose also.

Problem No 22

A company is exploring the installation of a new polishing machine

Details of the two machines under consideration are:

Machine A B Initial Cost Rs.50, 000 Rs.90, 000Life-Years 4 7Salvage Value at the end of Year 4 Rs.5, 000 ---

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Year 7 --- Rs.7, 000Annual running costs Rs.10, 000 Rs.8, 000

Both machines fulfill the same function and have equal capacities. The appropriate discount rate is 10%. Taxation may be ignored.

(i) Determine which machine should be purchased. (ii) To what amount would the initial cost of machine A be required to alter in order that

the two machines were then of equal financial attractiveness?

Problem No 23

Excel operations Ltd. is proposing to replace its fully depreciated machine by a new one costing Rs.1.5 lacs. The current market value of the old machine is Rs.0.20 lacs. The salvage value after 6 years is zero. The salvage value of the new machine after 6 years is expected to be Rs.16, 000. With the use of the new machine, sales are expected to increase by Rs.20, 000 per annum and operating expenses to decrease by Rs.12, 000 per annum. If the company follows a 30% WDV depreciation policy, has a marginal cost of capital of 12% and attracts a marginal tax rate of 30%, should the company replace the old machine?

Problem No 24

Nine Gems Ltd. has just installed Machine R at a cost of Rs. 2,00,000. The machine has a five year life with no residual value. The annual volume of production is estimated at 1,50,000 units, which can be sold at Rs. 6 per unit. Annual operating costs are estimated at Rs. 2,00,000 (excluding depreciation) at this output level. Fixed costs are estimated at Rs. 3 per unit for the same level of production.

Nine Gems Ltd. has just come across another model called Machine S capable of giving the same output at an annual operating cost of Rs. 1,80,000 (exclusive of depreciation). There will be no change in fixed costs. Capital cost of this machine is Rs. 2,50,000 and the estimated life is for five years with nil residual value.

The company has an offer for sale of Machine R at Rs. 1,00,000. But the cost of dismantling and removal will amount to Rs. 30,000. As the company has not yet commenced operations, it wants to sell Machine – R and purchase Machine S.

Nine Gems Ltd. will be a zero-tax company for seven years in view of several incentives and allowances available.

The cost of capital may be assumed at 14%. P.V. factors for five years are as follows:

Year P.V. Factors1 0.8772 0.7693 0.6754 0.5925 0.519

(i) Advise whether the company should opt for the replacement.

(ii) Will there be any change, if Machine R has not been installed but the company is in the process of selecting one or the other machine?

33


Problem No 25

New Style Ltd is considering the replacement of one of its moulding machines. The existing machine is in good operating condition, but is smaller than required if the firm is to expand its operations. The old machine is 5 years old, and has remaining depreciable life of 10 years. The machine was originally purchased for Rs.1, 50,000 and is being depreciated at Rs.10, 000 per year for tax purposes.

The new machine will cost Rs.2, 20,000 or Rs.1, 70,000 if exchanged with the existing machine. It will be depreciated on a straight line basis for 10 years, with no salvage value. The management anticipates that, with the increased operations, there will be need for an additional net working capital of Rs.30, 000. The new machine will allow the company to expand current operations, thereby increasing annual revenue by Rs.60, 000 and variable operating costs from Rs.2, 00,000 to Rs.2, 20,000.

The company’s tax rate is 35% and its cost of capital is 10%.

Should the company replace its existing machine? Assume that the loss on exchange of existing machine can be claimed as short-term capital loss at Y0.

Problem No 26

A company is considering the possibility of manufacturing a particular component which at present is being bought from outside. The manufacture of the component would call for an investment of Rs.7, 50,000 in a new machine besides an additional investment of Rs.50, 000 in working capital. The life of the machine would be 10 years with a salvage value of Rs.50, 000. The estimated savings (after incremental depreciation but before tax) would be Rs.1, 80,000 per annum. The income tax rate is 50%. The company’s required rate of return is 10%. Depreciation is provided on straight-line system. Should the company make this investment? Working should part of your answer.

Problem No 27

A Cosmetic company is considering introducing a new lotion, which is useful both in winters and summers. The manufacturing equipment will cost Rs.5, 60,000. The expected life of the equipment is 8 years. The company is thinking of selling the lotion in a single standard pack of 50 grams at Rs.12 each pack. It is estimated that variable cost per pack would be Rs.6 and annual fixed cost, Rs.4, 20,000. Fixed cost includes (straight-line) depreciation of Rs.70, 000 and allocated overheads of Rs.30, 000. The company expects to sell 1 lakh packs of lotion each year. Assume that the tax paid is 45% and straight-line depreciation is allowed for tax purposes. The opportunity cost of capital is 12%. Should the company manufacture the lotion?

Problem No 28

Cadbury choco has been studying an investment project calling for the manufacture and introduction of a new candy bar called Yuppie Nougat, targeted (you guessed it) for the yuppie market. As a consequence, Cadbury Choco expects to use the finest foreign chocolate and to price the candy very high relative to its cost; otherwise no self-respecting yuppie would even

34


think of buying it. Part of the expenses will consist of a vast marketing program, complete with endorsements by yuppie heroes.

The project is expected to last eight years, after which time yuppies will be more interested in dentures than candy bars. The introduction of the candy bar requires 400 new machines costing Rs.10, 000 each. Installing each machine costs Rs.100. The machines will be depreciated on a straight-line basis over five years. The production facility will be located at a site the company already owns. The company could rent the space that the candy facility will occupy for Rs.500, 000 per year.

Cadbury choco expects to sell 2 million bars per year for the entire life of the project. The price will be Rs.2.50 per candy bar, with a production cost of Rs.0.50. The plan schedules the marketing expenses per candy bar at Rs.1.00. Outlets for the candy bar have been chosen with yuppies in mind. The firm expects to maintain an average inventory of about 500, 000 bars, and expects no other increase in working capital. The appropriate after-tax discount rate for Yuppie Nougat is 18 per cent.

Calculate NPV of the projects cash flows.

You may consider the following while doing your calculations:(a) For tax purpose, depreciate the machine, including installation cost, using straight-

line method.(b) Estimate working capital in terms of production costs, and consider the amount as

investment in the zero year.(c) Assume salvage value equal to recovery of working capital.(d) Assume tax rate of 34 per cent.

Should Cadbury Choco help sweeten the world with Yuppie Nougat?

Problem No 29

Multiplex Limited is considering a capital investment for which the following detailed information is available:

(i) Cost of the project is estimated to be Rs.435 crores which includes:

(a) Contingencies of Rs.30 crores;(b) Margin money for working capital of Rs.10.5 crores;(c) Interest during construction of Rs.31 crores and (d) capital issue expenses of Rs.13.5

crores.

(ii) Incremental investment on working capital is estimated to be:

(Rs.Crores)Year 0 1 2 3Inc.WC 10.5 32.3 7.0 5.6

(iii) Salvage value has been estimated to be Rs.80 crores.

(iv) The operational cash flows are projected as follows: ________________________________

35


Year PBIT Taxation Interest ________________________________ 1 42 8 25 2 111 6 46 3 125 9 36 4 125 14 37 5 125 33 16 6 125 39 11 7 125 44 5 8 125 47 1 9 125 48 0 10 125 48 0 __________________________________

(v) Project will be financed with a debt of Rs.268 crores and the remaining through equity capital. The overall cast of financing the project would be 13 percent. Calculate NPV of the cash flows. Is this project financially viable? Note: Extracted from the table of PV of Re.1.

Problem No 30

Aditya Mills has a number of machines that were used to make a product that the firm has phased out of its operations. An existing machine was originally purchased 6 years ago for Rs.5 lacs. It is depreciated on SLM with remaining life of 4 years. No salvage value is expected at the end of 4 years from now. However it can currently be sold for Rs.1.5 Lacs. The machine can also be modified to produce another product at a cost of Rs.2 Lacs. The modification will not affect the useful life or the salvage value. After modification SLM would continue. If the present machine is not modified, it shall buy a new machine at a cost of Rs.4.4 Lacs (no salvage value), which shall be written off during the useful life of 4 years under SLM. The production in charge estimates that the new machine would save cash operating cost by Rs.25000 per annum. The cost of capital is 15% and the corporate tax is 55%.

Advice the company whether the new machine should be bought or the old one modified?

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Risk Analysis in Capital Budgeting

Risk Adjusted Discount Rate

Problem No 1From the following particulars, ascertain the appropriate discount rate:

(a) Project A: Risk free rate is 10%. The project is to be funded with a Debt Equity Mix of 9:1, which is significantly higher than the existing Debt Equity Mix of the Company. A premium of 9% is considered appropriate for such a high risk debt equity mix. The project offers little or no risk, which is comparable to investment in Government Bonds. Such an investment commands a risk discount of 2%.

(b) Project B: Existing cost of Capital is 15%. The firm adheres to Sustainable Growth Rate model. The proposed investment is considered to riskier than the firm’s other investments. The management considers a risk premium of 5% for such projects.

(c) Project C: The cash inflows flows from the project have been estimated at the most conservative basis. Inflows have been measured based on only 80% of guaranteed orders. Risk free rate is measured at 8%. Risk premium for the class to which the firm belongs is 7%. Risk premium for the project is considered at 3%.

Problem No 2

Salvation and Solutions have been in IT business for six years and enjoy a favorable market reputation. Corporate tax is 30%. They anticipate that the demand for IT solutions would increase sizably since many foreign firms are setting up their BPO shops in India. For an expansion project, they propose to invest Rs.22 crores to be funded by new debt and equityon 50/50 basis. Enquires with merchant bankers reveal that funds can be raised as under:

Debt Rate %First Rs.5 croresNext Rs. 5 croresAll additional fundsEquityRisk gradation by company

10%12%15.72%12%2% over WMCC

(i) Compute the appropriate risk adjusted discount rate.(ii) What should be target break-even level of net annual cash flow after tax for the

company, if the life of the project is four years?

Certainty Equivalent Analysis

Problem No 3The Textile Manufacturing Company Ltd., is considering one of two mutually exclusive proposals, Projects M and N, which require cash outlays of Rs. 8,50,000 and Rs. 8,25,000

37


respectively. The certainty-equivalent (C.E) approach is used in incorporating risk in capital budgeting decisions. The current yield on government bonds is 6% and this is used as the risk free rate. The expected net cash flows and their certainty equivalents are as follows:

Project M Project N

Year-end Cash Flow Rs.

C.E. Cash Flow Rs.

C.E.

1 4,50,000 0.8 4,50,000 0.9

2 5,00,000 0.7 4,50,000 0.8

3 5,00,000 0.5 5,00,000 0.7

Present value factors of Re. 1 discounted at 6% at the end of year 1, 2 and 3 are 0.943, 0.890 and 0.840 respectively.

Required:

(i) Which project should be accepted?

(ii) If risk adjusted discount rate method is used, which project would be appraised with a higher rate and why?

Sensitivity Analysis

Problem No 4

Canned Foods Ltd. is evaluating a project whose life will not fall below 2 years, involving production and sale of 13,00,000 units of mango-pulp at a rate of Rs.10/- unit. The following cash flows have been estimated.

Amount Rs.000sYear 0 Year 1 Year 2

Initial investmentVariable costsCash in flowsNet cash flows

(14,000) (4,000) (4,000) 13,000 13,000(14,000) 9,000 9,000

Their cost of capital is 8%.

(i) Can be project be accepted?(ii) Measure the sensitivity of the project to changes in variables.

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Problem No 5

Better Ltd is considering whether to set up a division in order to manufacture a new product, the Agni the following statement has been prepared, showing the projected “profitability” per unit of the new product: _________________________________________ Rs. Rs. __________________________________________ Selling Price 22.00 Material (3kg @ Rs.1.50 per kg) 4.50 Labour (2 hours @ Rs.2.50 per hour) 5.00 Overheads 11.50 21.00 Profit per unit 1.00 ____________________________________________ A feasibility study, recently undertaken at a cost of Rs.50000, suggests that a selling price of Rs.22 per unit should be set. At this price, it is expected that 10000 units would be sold each year. Demand for the product is expected to cease after 5 years. Direct Labour and materials costs would be incurred only for the duration of the product life.

Overheads per unit have been calculated as follows: ________________________________ Rs. ________________________________ Variable overheads 2.50 Rent (see note a below) 0.80 Managers’ Salary (See note b) 0.70 Depreciation (See note c) 5.00 Head Office cost (See note d) 2.50 _________________________________ 11.50 _________________________________Notes:

a) Agni would be manufactured in a factory rented specially for the purpose. Annual rental would be Rs.8000 payable only for as long as the factory was occupied.

b) A manager would be employed to supervise production of Agni’s at a salary of Rs.7000 per annum. The manager is at present employed by the company but is due to retire in the near future on an annual pension of Rs.2000. If he continued to be employed his pension would not be paid during the period of employment. His subsequent pension rights would not be affected.

c) Manufacture of the Agni would require a specialized machine costing Rs.250000. The machine would be capable of producing Agni for an indefinite period, although due to its specialized nature it would not have any resale or scrap value when the production of Agni ceased. It is the policy of Better Ltd to provide depreciation on all fixed assets using the straight line method. The annual charge of Rs.50000 for the new machine is based on a life of 5 years, equal to the period during which Agni are expected to be produced.

d) Better Ltd allocates it head office fixed costs to all products at the rate of Rs.1.25 per direct labour hour. Total head office fixed costs would not be affected by the

39


introduction of the Agni to the company’s range of products. The required return of Better Ltd for all new projects is estimated at 5% per annum in real terms, and you may assume that all costs and prices given above will remain constant in real terms. All cash flows would arise at the end of each year; with exception of the cost of the machine would be payable of all the estimates given above, with the exception of those relating to product life, annual sales volume and material cost per Agni.

Required:

(a) Prepare NPV calculations, based on the estimates provided, to show whether Better Ltd should proceed with manufacture of Agni.

(b) Prepare a statement showing how sensitive the NPV of manufacturing Agni is to errors of estimation in each of the three factors: Product Life, annual sales volume and material cost per Agni.

Standard Deviation and Hiller’s Model

Problem No 6A company is considering two mutually exclusive Projects X and Y. Project X costs Rs.30,000 and Project Y costs Rs.36,000. The NPV probability distribution for each project is given below:

Project X Project Y

NPV Estimate (Rs.) Probability NPV Estimate (Rs.) Probability

3,000

6,000

12,000

15,000

0.1

0.4

0.4

0.1

3,000

6,000

12,000

15,000

0.2

0.3

0.3

0.2

Compute the expected Net Present Value of Projects X and Y. Compute the risk attached to each project i.e. Standard Deviation of each

probability distribution. Which project is more risky and why? Compute the probability index of each project.

Problem No 7

Investment in a four-year project is Rs.60,000, and expected CFAT carry the following probability distribution. Cash flows for each period is uncorrelated.

Probability CF (Rs.) Year 1

CF (Rs.) Year 2 to 4

0.100.250.300.250.10

18,00024,00030,00036,00042,000

12,00018,00024,00030,00036,000

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Required: (i) Compute the NPV of the Project, assuming a discount rate of 10%. (iii) Compute standard deviation.

Problem No 8Consider the data in the above problem. Assume that the cash flow streams are perfectly correlated. Compute the Standard Deviation of this project with correlated cash flow streams.

Problem No 9A project with an outlay of Rs.32,00 and a life of three years, is estimated to produce the following CFAT, having probability distribution as under:

Year 1 Year 2 Year 3

CFAT (Rs.) Probability CFAT (Rs.) Probability CFAT (Rs.) Probability9,00012,00015,00018,00021,000

0.1250.2500.2500.2500.125

6,0009,00012,00015,00018,000

0.1250.2500.2500.2500.125

6,0009,00012,00015,00018,000

0.1250.2500.2500.2500.125

Compute the NPV and Standard Deviation. The risk-adjusted cost of capital is 7%.

Normal Distribution – Z values

Problem No 10A project has an originally estimated NPV of Rs.5,864. The of the possible NPV is Rs.3,064. Assuming a normal distribution of probabilities, determine the probability that the NPV of the project will be Zero.

Problem No 11The project with an investment of Rs.22.43 lacs has shown a negative NPV of Rs.4,760/-. The Standard deviation of the probability distribution of possible NPVs is Rs.18,400/-. Determine the probability that the NPV will be greater than Rs.7,200/-.

Problem No 12A new product is being introduced by XYZ Ltd. at a cost of Rs.1,00,000/-. The following cash flows have been projected for the life of the project.

Year 1 Year 2 Year 3CFAT (Rs.) Probability CFAT (Rs.) Probability CFAT (Rs.) Probability5,15052,80059,40063,25066,000

0.10.20.40.20.1

39,32543,45048,40050,60055,000

0.10.20.40.20.1

35,75014,20015,60016,60018,000

0.10.20.40.20.1

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The company feels that flows over time are perfectly correlated. Assume a risk free rate of 8%. (i) Compute the expected value and standard deviation of the probability distribution of possible net present values. Assuming a normal distribution, what is the possibility of the project providing a net present value of (ii) Zero or less, (iii) of Rs.12,000 or more.

Problem No 13The cost of a project is Rs.54,000/-. Life of this project is 4 years. The cash flow estimates for years 1 to 5 have the following probability distribution..

12,500 13,500 16,500 17,550 18,5000.15 0.20 0.30 0.20 0.15

Required:

(i) Compute the NPV, using a discount rate of 9%(ii) Compute the Standard Deviation of the probability distribution of possible NPVs,

assuming that the cash flows are perfectly correlated.(iii) Assuming that the distribution is normal, determine the probability that the NPV of

the project will be Rs.2780/-

Scenario Analysis

Problem No 14Following are the estimates of the nest cash flows and probability of a new project of M/s X Ltd

Particulars Year P = 0.3 P = 0.5 P = 0.2

Initial investment

Estimated net after tax cash inflows per year

0

1 to 5

4,00,000

1,00,000

4,00,000

1,10,000

4,00,000

1,20,000

Estimated salvage value (after tax) 5 20,000 50,000 60,000

Required rate of return from the project is 10%. Find:

1. The expected NPV of the Project.2. The best case and the worst case NPVs.3. The probability of occurrence of the worst case, if the cash flows are –

(a) Perfectly dependent overtime(b) Independent Overtime

4. Standard deviation and coefficient of variation assuming that there are only three streams of cash flow, which are represented by each column of the table with the given probabilities.

5. Coefficient of variation of X Ltd. on its average project which is in the range of 0.95 to 1.0. If the coefficient of variation of the project is found to be less riskier than average, 100 basis points are deducted from the Company’s cost of Capital..

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Should the project be accepted by X Ltd?

Problem No 15Sanathana Ltd is evaluating a project costing Rs.20 lacs. The Project generates savings of Rs.2.95 Lakhs per annum to perpetuity. The business risk of the project warrants a rate of return of 15%.

(a) Calculate Base case NPV of the project assuming no tax.(b) Assuming tax rate of 30% with 12% cost of debt constituting 30% of the cost of the

project, determine Adjusted present value.

Problem No 16XYZ Ltd is planning to introduce a new product. The initial investment required is Rs.48 Lakhs. Total requirement of Rs.48 Lakhs will be met by, Rs.8 Lakhs from internally generated funds, Rs.15 Lakhs from a right issue and remaining from a long term loan at 12% p.a.

The ratio of loan reflects debt capacity of the company. Right issue will involve floatation cost at 3% and term loan processing cost will be 1%. Corporate taxes are payable at 40% p.a. on net operating cash flows of the particular year.

Risk free rate of interest is 9%, market return I 14% and relevant company assets beta for the investment is estimated to be 1.5

Net operating profit after tax cash flows from the project is

Year 1 Rs.15 Lakhs

Year 2 Rs. 34 Lakhs

Year 3 Rs. 12 Lakhs

Besides, these inflows include a residual value of Rs.5 Lakhs (after all taxes) which is expected at the end of third year. You are required to estimate APV (Adjusted Present Value) of the investment and decide whether the investment is worth undertaking.

Joint Probability

Problem No 17Albatross Ltd. are purchasing a machine at a cost of Rs.3,000. Life is two years. The CFAT for two years is as follows:

Year 1 Year 2Cash flow(Rs.) Initial probability Cash flow (Rs.) Conditional

probability1,500

2,500

0.4

0.6

2,2001,8001,8002,000

0.50.50.70.3

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(i) What are the various joint probabilities of occurrences of various branches?(ii) If the risk free rate is 12%, what are the mean and Standard deviation of the

probability distribution of possible NPVs?

Problem No 18Elegant IT Solutions, engaged in computer hardware development, are condidering introducing a new chip based addition that would enhance the processing speed of computers. They are seized of the fast developments in technology and expect three situations to emerge:

A) The product is a success

B) The product is a relative failure

C) The product is a disaster

The estimates of net CFAT, depending on the state of the market in both year 1 and year 2 are projected by Elegant as follows:

Year 1 (Rs. Lacs) Year 2 (Rs. Lacs)

State of the market

Net Revenue Probability State of the market

Net Revenue Probability

A 120 0.5 ABC

150.0120.030.0

0.60.30.1

B 45 0.3 ABC

120.060.015.0

0.40.40.3

C 15 0.2 ABC

105.060.07.5

0.10.40.5

Decide if the company can go ahead if (a) investment cost is Rs. 60 lacs and (b) hurdle rate is 20%

Problem No 19XY 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 Rs.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 Rs.2,000 lacs which is mainly dependent on the ability of the Company to obtain the new contract, the chance for which is

44


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 Prob. Turnover Prob.

Rs. (in lacs) Rs.(in lacs)

2,000 0.6 2,500 0.7

3,000 0.3

1,500 0.3 2,000 0.5

1,800 0.5

1,200 0.1 1,500 0.6

1,200 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%.

Decision Tree Approach

Problem No 20L & R Limited wishes to develop new virus-cleaner software. The cost of the pilot project would be Rs.2,40,000. Presently, the chances of the product being successfully launched on a commercial scale are rated at 50%. In case it does succeed, L&R can invest a sum of Rs.20 lacs to market the product. Such an effort can generate perpetually, an annual net after tax cash income of Rs.4 lacs. Even is the commercial launch fails, they can make an investment of a smaller amount of Rs.12 lacs with the hope of gaining perpetually a sum of Rs. 1 lac. Evaluate the proposal, adopting a decision tree approach. The discount rate is 10%.

Problem No 21Go-getters Ltd. are considering the production of a new consumer item with afive-year product lifetime. In order to manufacture this item, it would be necessary to build a new plant. After having considered several alternatives, the management are left with the following three possibilities:

A. Build a large plant at an estimated cost of Rs.6,00,000. This alternative carries with it two types of market conditions. High demand with a probability of 0.7, or low demand with a probability of 0.3. If the demand is high, the

45


company can expect to receive a net annual cash inflow of Rs.2,50,000 for each of the next five years. If the demand is low, there would be a net annual cash outflow of Rs.50,000/-

B. Build a small plant at an estimated cost of Rs.3,50,000/-.This alternative also faces two types of market conditions, namely high demand with 0.7 probability, and low with 0.3 probability. Net cash inflow of the five period for the small plant is Rs.25,000 if the demand is low, and Rs.1, 50,000 if it is high.

C. Do not build a plant initially.This consists of leaving the decision for one year, during which period more information will be collected. The resulting information can be positive or negative, with probabilities of 0.8 and 0.2 respectively. At the end of this time, management may decide to build either a large plant or a small plant at the same costs as at present, provided the information is positive. If the resulting information is negative, management would decide to build no plant at all. Given positive information, the probabilities of high and low demand change to 0.9 and 0.1 respectively, regardless of which plant is built. Net annual cash inflows for the remaining four year period for each type of plant are the same as those given in Alternative A, and Alternative B.

Required:

(a) Draw a decision tree to represent the alternative courses of action.(b) Determine expected return for each possible course, and recommend a decision. Ignore

time value.

Problem No 22

A firm has an investment proposal, requiring an outlay of Rs. 80,000. The investment proposal is expected to have two years economic life with no salvage value. In year 1, there is a 0.4 probability that cash inflow after tax will be Rs. 50,000 and 0.6 probability that cash inflow after tax will be Rs. 60,000. The probability assigned to cash inflow after tax for the year 2 are as follows:

The cash inflow year 1 Rs. 50,000 Rs. 60,000

The cash inflow year 2 Probability Probability

Rs. 24,000 0.2 Rs. 40,000 0.4

Rs. 32,000 0.3 Rs. 50,000 0.5

Rs. 44,000 0.5 Rs. 60,000 0.1

The firm uses a 10% discount rate for this type of investment.

Required:

(i) Construct a decision tree for the proposed investment project and calculate the expected net present value (NPV).

(ii) What net present value will the project yield, if worst outcome is realized? What is the probability of occurrence of this NPV?

(iii) What will be the best NPV and the probability of that occurrence?

46


(iv) Will the project be accepted?

Problem No 23Big Oil is wondering whether to drill for oil in Westchester Country. The prospectus are as follows:

Depth of Well Feet

Total Cost Millions of Dollars

Cumulative Probability of Finding Oil

PV of Oil (If found) Millions of Dollars

2,000 4 0.5 10

4,000 5 0.6 9

6,000 6 0.7 8

Draw a decision tree showing the successive drilling decisions to be made by Big Oil. How deep should it be prepared to drill?

Real Options

Problem No 24GMR Ltd are considering the purchase of a piece of land for limestone quarrying. The purpose is extraction of limestone and sale to cement manufacturers. The price for the property is Rs. 4.20 lacs. The property if bought, can be sold a year later for at least Rs. 3.60 lacs. Initial costs for removing overburden is Rs. 6.00 lacs. GMR anticipate that they can remove 10,000 tonnes of limestone each year. The limestone content is reported to be huge, and mining can continue to perpertuity. Presently cement manufacturers are able to buy limestone of comparable quality at Rs. 40 per ton. Allowing for mining costs, the net CFAT is estimated at Rs. 8 per ton. Required:

i) If risk adjusted rate is 10%, should GMR buy this property?

ii) What would be the decision if the following additional information is taken into account?

Ministry of Highways is considering implementation of Golden Quadrilateral that links the four metros. The decision will be known in one year. If the decision is positive, demand for Cement – and therefore raw material will rise, and the price of limestone can go up as high as Rs. 85 a tone. But the least climb will be upto Rs. 60 (CFAT will be Rs. 28 per ton) Simultaneously, a low cost alternative for cement ideally suited for paving highways is also likey to emerge. If this happens, the limestone prices will drop to Rs. 30 fully eroding the margin.

Problem No 25Option to abandon / Put Option

A company is about to invest in a project with an initial cost of Rs.80 lacs. The project cash flows structure is as follows:

47


a. CFAT of Rs.28 lacs per annum if the project is successfulb. CFAT of Rs.10 lacs per annum if it is not successful.

Life of the project is six years. The cost of capital is 12%. The probability of success of the project is 0.50. Required:

(i) Evaluate the project for its acceptance(ii) Independent of “a” above, determine whether the company can go ahead, if (i) the

project turns out to be unsuccessful and (ii) the investment is sold for Rs.50 lacs at the end of first year.

Problem No 26An investment of Rs.65,000/- in a new machine, is expected to bring in the following cash flows in years 1 and 2.

Amount / Rs.Cash flow – Year1 Cash flow – Year2 RV

Favourable (60%)Unfavourable (40%)

52,00026,000

39,00019,500

2,6001,300

Should the environment turn out to be unfavourable, the company will dispose of the machine for a value of Rs.32,500 at the end of year 1. They can nevertheless continue with the machine, if they so choose. Reckoning the cost of capital at 15%, evaluate the overall investment decision, and decide the course of action for the owner of the project.

Problem No 27Option to delay / Timing Option

Tours and Resorts Ltd. are investing in a holiday resort at a cost of Rs.200 lacs. Project life is estimated at 20 years, during which, the annual cash flows will be Rs.30 lacs each.

Indications are that, there is a probability (0.25) of government imposing a luxury tax on revenues. This will however be known only after one year from now. If imposed, net cash flows will come down to Rs.24 lacs. If the tax is not imposed, the cash flows will be Rs.32 lacs each year thereafter.

Required:

(i) Ascertain the NPV of the project if the discount rate is 12%.(ii) Determine whether Tours and Resorts can wait for one year and proceed thereafter.

Initial investment cost at that time will be Rs.200 lacs.

Problem No 28

Option to expand

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Pancea Drug Company is considering a new drug, which would be sold over the counter without any prescription. To develop the drug and to market it on a regional basis will cost Rs.120 Lacs over the next 2 years, as 60 Lacs in each year. Expected cash inflows associated with the project for the next 6 years are as follows:

__________________________ Year Cash inflow in lacs __________________________ 3 10 4 20 5 40 6 40 7 30 8 10 _________________________

If the project is successful, at the end of year 5 the company will have the option to invest an additional Rs.100 Lacs to secure a national market. The probability of success is 0.60, if not successful, the company will not invest at all. If successful, the cash inflow will be better by Rs.60 Lacs per annum in each of the years through year 10. That is the project will be elongated by 2 more yeas than scheduled. The chance of better cash inflow by Rs.60 Lacs is 0.50 with other 0.50 for a cash inflow better only by Rs.40 lacs. In both cases, the life will be elongated by 2 years. The company’s cost of capital is 14%.

D) What is the NPV of the initial project lasting for 6 years after 2 years? Is it acceptable?E) What is the worth of the project if we take account of the option to expand? Is the project

acceptable?

Problem No 29The projected cash flows and the expected net abandonment values for a project are given below:

Year Cash inflows Abandonment Value0 (1,00,000) 01 35,000 65,0002 30,000 45,0003 25,000 20,0004 20,000 0

Should the project be abandoned and if so, when? (Cost of Capital is 10%)

Problem No 30

ABCL Ltd is ordering a special purpose machinery costing Rs. 9000 with a life of 2 years, after which there is no expected salvage value. The possible incremental cash inflows are –

Year 1 Year 2Cash inflow (in Rs.) Probability Cash inflow (Rs.) Conditional

Probability

49


6000 0.3 200030004000

0.30.50.2

7000 0.4 400050006000

0.30.40.3

8000 0.3 600070008000

0.20.50.3

The required rate of return for the company for this investment is 8%

Required – (a) Calculate mean of probability distribution of possible net present values (b) Suppose now that the possibility of abandonment exists and that the abandonment value of the project at the end of year 1 is Rs. 4500. Calculate the new mean NPV, assuming that the company abandons the project if it is worthwile to do so. Compare your calculations with those in part (a). What are the implications?

Simulation Analysis

Problem No 31

For a washing powder manufacturing factory, frequency distribution of contribution (i.e Sale price – variable cost) per unit, annual demand and requirement of investment were found as follows:

Contribution p.u 3 5 7 9 10Relative frequency 0.1 0.2 0.4 0.2 0.1

Annual Demand (‘000) 20 25 30 35 40 45 50Relative frequency 0.05 0.10 0.20 0.30 0.20 0.10 0.05

Required Investment (Rs. ‘000) 1750 2000 2500Relative frequency 0.25 0.50 0.25

Consider the random numbers 93, 03, 51, 59, 59, 77, 61, 71, 62, 99, 15 for using Monte Carlo Simulation for 10 runs, to estimate the percentage of return on investment (ROI%) defined as follows:

ROI % = Cash inflow x 100 Investment

Recommend an optimum investment strategy based on model value of ROI%

Problem No 32

A project requires an outlay of Rs. 12,000 and runs for the three. The discount rate is 10% Return are independent between years and in each of the years are given by

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Probability Return 0.06 Rs. 1,500 0.17 Rs. 2,000 0.22 Rs. 4,500 0.29 Rs. 6,000 0.16 Rs. 7,500 0.10 Rs. 9,400

Given the digits 8 7 0 5 6 9 0 5 8 1 9 4 2 7 1 4 2 1 8 7 7 4 9 5 3 1 5 8 0 4

Conduct a simulation exercise (five runs) to estimate expected net present value (ENPV). Use the information obtained to estimate the coefficient of variation.

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Capital Market – Risk Return Analysis

Problem No 1

Mr. Y decides to invest Rs. 10 lakhs, out of which the investor intends to maintain 60% equity exposure. The initial portfolio will have Rs. 6 lakhs in equity and Rs. 4 lakhs in bonds.

Calculate the asset allocation between equity and bond/term deposits:

i. If the equity portfolio declines by 10 percent, ii. If the equity portfolio moves up by 10 percent

Problem No 2

Mr. Mohta has purchased 100 shares of Rs. 10 each of Thermax Ltd. in 2005 at Rs.78 per share. The company has declared a dividend @ 40% for the year 2008-09. The market price of share as at 1-4-2008 was Rs. 104 and on 31-3-2009 was Rs. 128. Calculate the annual return on the investment for the year 2008-09.

Problem No 3

The average market prices and dividend per share of Fin Corp Ltd. for the past 6 years are given below:

Year Average market price (Rs.) Dividend per share (Rs.)

2008-09 68 3.0

2007-08 61 2.6

2006-07 50 2.0

2005-06 53 2.5

2004-05 45 2.0

2003-04 38 1.8

Calculate the average rate of return of Fincorp Ltd.’s share for past 6 years.

Problem No 4

The rate of return of equity shares of Hill Top ltd. for past six years are given below:

Year 2004 2005 2006 2007 2008 2009

Rate of return (%)

12 18 -6 20 22 24

Calculate the Average rate of return, Standard deviation and Variance.

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Problem No 5

Mr. Srivastav invested in equity shares of Dry-dock Ltd. its anticipated returns and associated probabilities are given below:

Return % -15 -10 5 10 15 20 30

Probability 0.05 0.10 0.15 0.25 0.30 0.10 0.05

You are required to calculate the expected rate of return and risk in terms of standard deviation.

Problem No 6

The possible returns and associated probabilities of Securities X and Y are given below:

Security X Security Y

Probability Return % Probability Return %

0.05 6 0.10 5

0.15 10 0.20 8

0.40 15 0.30 12

0.25 18 0.25 15

0.10 20 0.10 18

0.05 24 0.05 20

i. Calculate the expected return and standard deviation of Security X and Y.ii. Calculate the co-efficient of variationiii. Which stock is less risky

Problem No 7Following is the data regarding six securities:

A B C D E F

Return %

8 8 12 4 9 8

Risk %

4 5 12 4 5 6

i. Which of the securities will be selected?ii. Assuming perfect correlation, analyze whether it is preferable to invest 75% in

security A and 25% in security C or to invest 100% in E

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Problem No 8

Mr. Amar’s Portfolio consists of six securities. The individual returns of each of the security in the portfolio is given below:

Security Proportion of investment in the portfolio

Return

A 10% 18%

B 25% 12%

C 8% 22%

X 30% 15%

Y 12% 6%

Z 15% 8%

Calculate the weighted average of return of the securities consisting the portfolio.

Problem No 9

The returns of Security A and Security B for the past six years are given below:

Year Security A Return (%) Security B Return (%)

2005 9 10

2006 5 -6

2007 3 12

2008 12 9

2009 16 15

Calculate the risk and return of portfolio consisting of 80% of A and 20% of B.

Problem No 10

The possible returns on two securities are as follows:

Find out mean, variance, standard deviation, Co-variance and correlation.

Problem No 11

A Portfolio consists of three securities P, Q and R with the following parameters:

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Probability Securities

0.2 0.5 0.3

(1) (2) In %14 1520 13 25 26


SecurityP Q R

Correlation coefficient

Expected return (%)Standard deviationCorrelation coefficient:PQQRPR

2530

2226

2024

-0.5+0.4+0.6

If the securities are equally weighted, how much is the risk and return of the portfolio of these three securities?

Problem No 12

A portfolio has 3 securities A, B and C. Proportion of investment in these 3 securities is 30:30:40. Compute the portfolio risk from following using Matrix Method

Security Variance of individual Security Co-Variance of pairsA 38.20 AB – 6.87B 6.39 BC – 7.20C 8.45 AC – 4.00

Problem No 13

Novelis owns a portfolio of two securities with the following expected return, standard deviations, and weights:

Security Expected Return Standard Deviation Weight X Y

12% 15%

15% 20%`

0.40 0.60

What are the maximum and minimum portfolio standard deviations for varying levels of correlation between two securities?

Problem No 14

A client has presented you with three alternatives shares that he is proposing to invest in. He has instructed you to analyze the possibilities if he were to invest an equal amount in any two of these shares:

Details are:

Share Expected return

next yearStandard Deviation of return

A 12.6% 7.9% B 10.3% 3.4% C 9.7% 1.9%

The correlation co-efficient of returns between share are

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A and B 0.98B and C 0.89A and C 0.79

Required:

a. Prepare calculation to identify which combination of shares is to be preferred.b. Explain how portfolio diversification can reduce risk.

Problem No 15

T Limited and A Limited have low positive correlation coefficient of 0.5. Their respective risk and return profile is made up as under:

T Ltd A LtdReturns 10.00% 15.00%Standard Deviation 20.00% 25%

Determine the proportion in which the investments should be made in T and A, in order that the total risk in the portfolio is minimum.

Problem No 16

L Ltd and M Ltd have the following risk and return estimates.

RL = 20%

RM = 22%

σL = 18%

σM = 15%

Correlation Coefficient = RLM = -1

Calculate the proportion of investment in L Ltd and M Ltd to minimize the risk of portfolio.

Problem No 17

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

Name of Co. No. of shares Cost (Rs.)

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

N Ltd. 500 (Rs.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 Rs.220 and Rs.290 per share for M Ltd. and N Ltd. respectively.

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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 case.

Problem No 18

The rate of return on the security of Company X and market portfolio for 10 period are given below:

Period Return of Security X (%) Return on Market Portfolio (%)

12345678910

2022252118-51719-720

22201816208-65611

What is the beta of Security X?

Problem No 19Given below is information of market returns and data from two companies A and B (%)

Year 2007 Year 2008 Year 2009

Market Company ACompany B

12.013.011.0

11.011.510.5

9.09.89.5

Required: Determine the beta coefficients of the shares of Company A and B Company B.

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Problem No 20The distribution of return of security ‘F’ and the market portfolio ‘P’ is given below:

Return %Probability F P

0.30 30 -100.40 20 200.30 0 30

You are required to calculate the expected return of security ‘F’ and the market portfolio ‘P’, the covariance between the market portfolio and security and beta for the security.

Problem No 21

Stock A has a beta of 1.6 and stock B has a beta of 1.2. They make up the portfolio in the ratio of 70:30. Find the beta of the portfolio.

Problem No 22

The beta coefficient of security ‘A’ is 1.6. The risk free rate returns is 12% and the required rate of return is 18% on the market portfolio. If the dividend expected during the coming year is Rs. 2.50 and the growth rate of dividend and earnings is 8%. At what price should security ‘A’ be sold based on the CAPM?

Problem No 23

An investor is seeking the price to pay for a security, whose standard deviation is 4%. The correlation coefficient for the security with the market is 0.9 and the market standard deviation is 3.2%. The return from government securities is 6.2% and from the market portfolio is 10.8%. The investor knows that, by calculating the required return he can then determine the price to pay for the security. What is the required return on the security?

Problem No 24

Investor’s Weekly, a news magazine on the happenings at Dalal Street, publishes the following information in its July edition for Security A – Equilibrium Return = 15%, Market Portfolio Return = 15%, 6% Treasury Bills (Rs.100) are traded at Rs.120. Covariance of the Security with the market portfolio is 225% and correlation is 0.75. Determine market risk (σ of Market Portfolio) and security risk.

Problem No 25

The Beta Coefficient of Target Ltd is 1.4. The company has been maintaining 8% rate of growth in dividends and earnings. The last dividend paid was Rs.4 per share. Return on Government securities is 10%. Return on market portfolio is 15%. The current market price of one share of Target Ltd is Rs.36.

(i) What will be the equilibrium price per share of Target Ltd?(ii) Would you advise purchasing the share?

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Problem No 26

You are analyzing two alternative portfolios. Each consists of 4 securities. Data are

Portfolio 1:

Security

Beta of security

Expected Return (%)

Amount invested Million Rs.

A B C D

1.4 00.71.1

16 6 10 13

3.8 5.2 6.1 2.9

Portfolio 2:

Security

Beta of security

Expected Return (%)

Amount invested Million Rs.

E F G H

1.20.80.21.5

14 11 7 17

7.1 2.7 5.4 2.8

The market return is expected to be 12.5% and the risk free rate is 5.5%

Required:

a) Calculate the beta of each portfolio and the required return on each portfolio.b) Explain whether the individual shares in portfolio 1 appear to be over or under

valued and what action this would imply for the portfolio manager?c) A colleague has commented that the actual return on each security has often been

quite different to that predicted by its beta value. Explain why that is not unusual.

Problem No 27

P Ltd has an expected return of 22% and Standard deviation of 40%. Q Ltd. has an expected return of 24% and standard deviation of 38%. P has a beta of 0.86 and Q 1.24. The correlation between the returns of P and Q is 0.72. The standard Deviation of the market return is 20%. (a) Is investing in Q better than investing in P? (b) if you invest 30% in Q and 70% in P, what is your expected rate of return and the portfolio standard deviation? (c) What is the market portfolios expected rate of return and how much is the risk-free rate? (d) What is the beta of portfolio if P’s weight is 70% and Q is 30%?

Problem No 28

The market portfolio has a historically based expected return of 0.095 and a standard deviation of 0.035 during a period when risk free assets yielded 0.025. The 0.06 risk premium is thought to be constant through time. Riskless investments may now be purchased to yield 0.08.

A security has a standard deviation of 0.07 and 0.75 correlation with the market portfolio. The market portfolio is now expected to have a standard deviation of 0.035.

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Find out the following: (i) Market’s return-risk trade-off, (ii) Security beta, (iii) Equilibrium required expected return of the security.

Problem No 29 As an Investment Manager you are given the following information:

Particulars Initial Price (Rs)

Dividends (Rs) Market Price year end (Rs)

Beta (Risk factor)

Investment in equity shares of:A. Cement Ltd. Steel Ltd Liquor Ltd.

B. Govt. of India bonds

253545

1,000

222

140

5060135

1,005

0.80.70.5

0.99

Risk –free return may be taken at 14%.

Your are required to calculate: (i) Expected rate of returns of portfolio in each using capital asset pricing model (CAPM) (ii) Average return of portfolio.

Problem No 30

Expected returns on two stocks for particular market returns are give the following table:

Market Return Aggressive Defensive7% 4% 9%25% 40% 18%

You are required to calculate: The Betas of the two stocks. Expected return of each stock, if the market return is equally likely to be 7% or 25%. The Security Market Line (SML), if the risk free rate is 7.5% and market return is equally

likely to be 7% or 25%. The Alphas of the two stocks.

Problem No 31

XYZ Ltd. pays no taxes and is entirely financed by equity shares has β of 0.6, a PE ratio of 5 and is priced to offer an expected return of 20%. XYZ Ltd now decides to buy back, half of the equity shares by borrowing an equal amount. If the debt yields a risk free return of 10%, calculate

(i) The β of the equity shares, after the buy back.(ii) Required return and the risk premium on the equity shares before the buyback.(iii) The required return and risk premium of the equity shares after buyback.(iv) The required return on debt.(v) The % increase in EPS

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(vi) The new price earning multiple.

Assume that operating profit of the firm is expected to remain constant in perpetuity.

Problem No 32

XYZ is at present engaged in production of sport shoes and has a debt equity ratio of 0.80. Its present cost of debt funds is 14% and it has a marginal tax rate of 40 percent. The company is proposing to diversify to a new field of adhesives which is considerably different from the present line of operations. XYZ Ltd. is not well conversant with the new field. The company is not aware of risks involved in area of adhesives but there exists another company PQR, which is a representative company in adhesives. PQR is also a public limited company whose shares are traded in the market. PQR has a debt to equity ratio of .25, a beta of 1.15 and an effective tax rate of 40 percent.

(a) Calculate what systematic risk is involved for XYZ Ltd. if the company enters into the business of adhesives. You may assume CAPM holds and XYZ employs same amount of leverage.

(b) In case risk free rate at present is 10 percent and expected return on market portfolio is 15% what return XYZ Ltd. should require for the new business if it uses a CAPM approach.

Problem No 33

Excellent Ltd. is a frozen food packaging company and is looking to diversify its activities into the electronics business. The project it is considering has a return of 18% and Excellent Ltd. is trying to decide whether the project should be accepted or not. To help it decide it is going to use the CAPM. The company has to find a proxy beta for the project and has the following information on three companies in the electronics business:

a) Superior Ltd.

Equity beta of 1.33. Financed by 50% debt and 50% equity.

b) Admirable Ltd.

Admirable Ltd. has an equity beta of 1.30, but it has just taken on a totally unrelated project, accounting for 20% of the company’s value, that has an asset beta of 1.4. The company is financed by 40% debt and 60% equity.

c) Meritorious Ltd.

Equity beta of 1.05 Financed by 35% debt and 65% equity.

Assume that all the debt is risk-free and that corporation tax is at a rate of35 percent. Excellent Ltd. is financed by 30 percent debt and 70 percent equity. The return of risk-free securities stands at 10 percent and the return on the market portfolio is 14 per cent. Should the company accept the project?

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Problem No 34

Two companies are identical in all respects except capital structure. One company AB Ltd. has a debt equity ratio of 1:4 and its equity has a (beta) value of 1.1. The other company XY Ltd. has a debt equity ratio of 3:4. Income Tax is 30%. Estimate (beta) value of XY Ltd given the above.

Problem No 35

M/s V Steel Ltd is planning for a diversification project in Automobile Sector. Its current equity beta is 1.2, whereas the automobile sector has 1.6. Gearing of automobile sector is 30% debts, 70% equity. If expected market return is 25%, risk free debt is 10% and taxation rate is taken as 30% and also that corporate debt is assumed to be risk free, compute suitable discount rate under the following situations.

(i) Project financed by equity only.(ii) By 30% debt and 70% equity.(iii) By 40% debt and 60% equity.

Problem No 36

Vinay Company’s WACC is 10 percent and its tax rate is 35 percent. Vinay Company’s pre-tax cost of debt is 10 percent and its debt-equity ratio is 1:1. The risk-free rate is 8 percent and the market risk premium is 7 percent. What is the beta of Vinay Company’s equity?

Problem No 37

Company D has a beta value of 1.2. It is thinking of undertaking a project with a beta value of 1.7. If, when accepted, the project will comprise 10% of the firm’s total worth, what will be the subsequent beta value of the company?

Problem No 38

An investor is holding 1000 shares of a company. Presently the rate of dividend being paid by the company is Rs.2 per share and the share is being sold at Rs.25 per share in the market. However, several factors are likely to change during the course of the year as indicated below.

Particulars Existing RevisedRisk free % 12 10Market risk premium % 6 4Beta value 1.4 1.25Expected growth rate % 5 9

In view of the above factors whether the investors should buy, hold or sell the shares? And why?

Problem No 39

Young Limited last paid a dividend of Rs.2 per share. Its earnings and dividends are expected to grow @ 8% p.a. The beta of the company is 1.3. It risk free-return is 6% p.a. and the return on market portfolio is 10% p.a. what is the price per share of the equity stock?

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What will be the effect on the price per share of Young limited if the following changes take place together?

There is a decrease in the inflation premium by 2% p.a. The expected growth rate increases by 1 p.a.

Problem No 40

XYZ Ltd is a consumer goods company which earns expected return of 12% on its existing operations subject to standard deviation of 20%. The company is owned by a family and the family has no other investment.

New project is under consideration and the new project is expected to give a return of 16% subject to standard deviation of 32%. The new project has a correlation of 0.25 with XYZ’s existing operations.

The new project is likely to account for 25% of XYZ’s operation.

XYZ has identified a utility function to appraise risk project. The function is as under:-

Shareholder’s utility = 100R - σ² Where R = Expected return (in %) σ² = Standard deviation of return (in %)

The project can be accepted only if total utility goes up. Evaluate the project.

Problem No 41

If the risk free return is 10% and the expected return on NSE index is 18% (and risk measurement by standard deviation is 5%),

(a) Construct a portfolio to produce a 16% expected return and what would be its risk?(b) An investor has Rs.100000 to invest, how would you advise him to invest for an expected

return of 20%? What is the risk of the portfolio?

Problem No 42

Risk free rate is 8% and the return of the market is given by 12%.

Portfolio BetaA 0.6B 1.0C 1.4

a. Calculate the expected return of each portfolio using CAPMb. Show graphically (SML) the expected return in (a) abovec. What would happen to SML if the expected return on market portfolio were 10%

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MUTUAL FUNDS

Problem No 1

You can earn a return of 15 percent by investing in equity shares on your own. You are considering a recently announced equity mutual fund scheme where the initial issue expenses are 5 percent and the recurring annual expenses are expected to be 2 percent. How much should he mutual fund scheme earn to provide a return of 15 percent to you?

Problem No 2

You can earn a return of 13 percent by investing in equity shares on your own. You are considering a recently announced equity mutual fund scheme where the initial issue expenses are 5 percent. You believe that the mutual fund scheme will earn 16.5 percent. At what recurring expense (in percentage terms) will you be indifferent between investing on your own and investing through the mutual fund.

Problem No 3

The following particulars are available for a scheme of a mutual fund. Calculate current net asset value (NAV) of each unit of the scheme.

Problem No 4

A has invested in three mutual fund schemes as per details below:

Name of the scheme MFA MFB MFCDate of investment 01.12.04 01.01.05 01.03.05Amount of Investment Rs.50000 Rs.1 Lac Rs.50000Entry date NAV Rs.10.50 Rs.10 Rs.10Closing date NAV (31.3.05) Rs.10.40 Rs.10.10 Rs.9.80Dividend Received till 31.3.05

Rs.950 Rs.1500 Nil

Required:

What is the effective yield per annum in respect of each of the three schemes up to 31 st

March, 2005?

Problem No 5

Following is the content of an open end scheme of a Mutual Fund, which contains 15000 units as on Day 1.

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Scheme sizeFace Value of a unitInvestmentsMarket value of shares

Rs.1000 LacsRs.10In sharesRs.2500 Lacs


Company No. of shares Day 1 price J 10,000 49.93 K 2000 38.23 L 4500 44.07

Calculate Day 1’s NAV.

Supposing 1000 additional units were purchased by investor by Day 2 at day 1’s NAV price and the portfolio manager utilizes entirely for L Ltd. Find out NAV of Day 2 if J, K & L are 51.23, 40.93, & 45.97. There is no load in the above scheme.

Problem No 6

Grow more firm is trying to decide between two investments funds. From past performance they were able to calculate the following average returns and standard deviations for these funds. The current risk-free rate is 8 percent and the firm will use this as a measure of the risk-free rate.

ABC Fund XYZ FundAverage return (r) (percent)Standard deviation, s (percent)

18 1620 15

Risk-free rate, Rf = 8.0%

Problem No 7

With a risk-free rate of 10%, and with the market portfolio having an expected return of 20% and 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?

Problem No 8

Six portfolios experienced the following results during at 7-year period:

Portfolio Average Annual Return

Standard Deviation

Correlation with market

A 18.6 27.0 0.81 B 14.8 18.0 0.65 C 15.1 8.0 0.98 D 22.0 21.2 0.75 E -9.0 4.0 0.45 F 26.5 19.3 0.63Market Risk 13.0 12.0Free Rate 9.0

(a) Rank these portfolios using (i) Sharpe’s method, and (ii) Treynor’s method.(b) Compare the ranking in part (a) and explain the reasons behind the differences.

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Problem No 9

Consider the following performance information on three portfolios:

Treynor Tp Sharpe Sp Jensen JpPortfolio A -4.0 -5 -5.0Portfolio B 8.0 1.2 3.0Portfolio C 4.0 .3 0XYZ Index 5.0 .6 0

a) Rank each of the portfolios using each of the performance measures. Are the rankings consistent for the three techniques?

b) Compare each portfolio’s performance to the market’s performance. Are the comparisons consistent for the three techniques?

Problem No 10

The following are the data on five mutual funds:

Fund Return Standard Deviation BetaDhan RakshaDhan VarshaDhan VredhiDhan MitraDhan Laheri

16 8 1.50 12 6 0.90 14 5 1.40 18 10 0.75 15 7 1.25

What is the reward-to-variability ratio and reward to volatility and ranking if the risk-free rate is 7 percent?

Problem No 11

Consider the following information for three mutual funds, X, Y and Z, and the market.

Mean return (%) Standard deviation (%) Beta X Y ZMarket index

12 18 1.1 10 15 0.9 13 20 1.2 11 17 1.00

The mean risk-free was 5 percent. Calculate the Treynor measure, Sharpe measure, and Jensen measure for the three mutual funds and the market index.

Problem No 12

Find NAV of the following Scheme:

Name of the scheme : DSP Blackrock Mining FundSize of the scheme : Rs.100 CroreFace Value of the Share : Rs.10Number of the outstanding shares : 10 Crore

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Market value of the fund’s investments : Rs.180 CroreReceivables : Rs.1 CroreAccrued Income : Rs.1 CroreLiabilities : Rs.0.5 CroreAccrued expenses : Rs.0.5 Crore

Problem No 13

Sun moon mutual fund (Approved mutual fund) sponsored open-ended equity oriented scheme “Chanakya Opportunity fund”. There are three plans viz. ‘A-Dividend Reinvestment plan, B-Bonus plan and C-Growth plan.

At the time of initial offer on 1.4.1995, Mr. Anand, Mr. Bachchan and Ms. Charu, three investors invested Rs.1 Lac each and chosen plans B, C and A respectively. The history of the fund is as follows:

Date Dividend % Bonus ratio NAV per unit (FV Rs.10)28.07.1999 20 30.70 31.05 70.0531.03.2000 70 5:4 58.42 31.05 70.0531.10.2003 40 42.18 25.20 56.1515.03.2004 25 46.45 29.10 64.2831.03.2004 1:3 42.18 20.05 60.1224.03.2005 40 1:4 48.10 19.95 72.4031.07.2005 53.75 22.98 82.07

On 31st July all 3 investors redeemed all the balance units. Calculate annual rate of return to each of the investors. Consider the following:

1. Long term capital gain is exempt from Income-tax2. Short term capital gain is taxed at 10%.3. Security transaction tax @ 0.2% only on sale / redemption of units.4. Ignore education cess.

Problem No 14

A fund is quoted today at stock market at Rs. 15. It just paid a dividend of Rs. 2 per unit (i) If a year later the unit was to quote at Rs. 16 and if you had bought the unit cum-dividend, what is the normal return? (ii) What is the return taking into account actual cash flows.

Problem No 15

A Portfolio Manager earned 25%, while the market rose by 18%. The risk free rate was 5%. The portfolio beta was 0.8; its standard deviation was 9% while the market standard deviation was 6%. Find Fama.

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DERIVATIVES

Continuous Compounding

Problem No 1

Mr. Brave gave a loan to Mr. Y amounting to Rs.1,00,000 with continuous compounding interest rate p.a. of 12% for 3 months. What is the Maturity Value?

Problem No 2

Trina has two investment opportunities, A and B, carrying a yield of 15% p.a. The tenor of both these investments is 3 years. A offers continuous compounding facility whereas B offers yield on the basis of monthly compounding. Which offer will Trina opt for?

If continuous compounding facility comes at a price of Rs. 180 p.a. per lakh of deposit (chargeable at the end of the period), what will be the position?

At what price Trina be indifferent to continuous compounding and monthly compounding?

Problem No 3

Mr. Hari is going to receive Rs.8000/- on Bharti stock in 3 months time from now. He would like to know the present value of dividend if risk free continuous compounding rate p.a. is 16%.

Problem No 4An interest rate is quoted @ 18% per annum with half yearly compounding. What is the equivalent continuous compounding rate?

Problem No 5

Mr. D gives a loan which he quotes the interest rate as 24% p.a. with continuous compounding. Calculate the equivalent rate if compounding was done quarterly.

Theoretical Forward Price

Problem No 6

Compute the theoretical forward price of A Ltd for 1 month, 3 month and 6 months. A Ltd is currently quoting at a price of Rs. 140. Assume the risk free interest rate of 9% p.a

Problem No 7

X Ltd. a company that historically has not paid any dividend and has no plans to do so in the future, is currently being quoted at the Bombay Stock Exchange at Rs.60/-. You wish to enter into a futures contract on this stock maturing in 3 months time. If the risk free rate of return is 8% per annum continuously compounded what do you expect the futures price to be? If the futures contract were priced at Rs.64, what action would you take? In case it is priced at Rs.61 will your decision change?

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Problem No 8

ABC Ltd is quoted in the market at Rs.40. A 6-month futures contract on 100 shares of ABC Ltd can be bought. The risk free rate of interest is 12% per annum continuously compounded. ABC Ltd is certain to pay a dividend of Rs.2.5 per share 3 months from now. What should be value of the futures contract? If the futures contract is priced at Rs.4100 what action would follow? If it is priced at Rs.3800 what would you do?

Problem No 9

The price of Infosys Stock of a face value of Rs.10 on 31st December, 2007 was Rs.350 and the futures price on the same stock on the same date i.e. 31st December, 2007 for March, 2008 was Rs.370.

Other features of the contract and the related information are as follows.

Time to expiration 3 months (0.25 year)

Annual dividend on the stock of 30% payable before 31.3.2008.

Borrowing Rate is 20% p.a.

Based on the above information, calculate future price for Infosys stock on 31st December, 2007. Please also explain whether any arbitrage opportunity exists.

Problem No 10

If Learning Point Ltd provided a dividend yield of 4% per annum, the current value of the stock is Rs.500 and that the continuously compounded risk free rate of interest is 8% per annum, what would be the value of a 3-month futures contract? If the futures price is Rs.510 what action would follow? Will the position change if the price is Rs.490?

Problem No 11

Consider a 6-month gold futures contract 0f 100 gm. If the spot price is Rs. 600 per gram and that it costs Rs. 3 per gram for the 6-monthly period to store gold and that the cost is incurred at the end of 2 months. If the risk free rate of interest is 12% per annum continuously compounded, compute the futures price? If the futures were available at Rs. 620, what action would follow? Would the position change if the futures were available at Rs. 660?

Convenience Yield

Problem No 12The spot price of steel scrap is Rs. 5000 per ton. The one-year futures price is Rs. 5802. The interest rate is 15%. The present value of storage cost is Rs. 250 per ton. Compute the convenience yield assuming that the futures are fairly priced.

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Problem No 13

APL manufactures and supplies printed polyfilms and sachets to its clients. The spot price of 50 Microns Polyfilm Rolls is Rs.120 per kg. The 6-month futures price is Rs.133500 per tonne. If the bimonthly storage cost is Rs.2,500 per tonne, payable in advance and the relevant interest rate is 12%, ascertain return (savings as a percentage) earned by APL by carrying inventory of 1 tonne.

What will be the answer if the storage cost is Rs.6000 payable in advance? Assume Futures Price is fairly priced.

Index Futures

Problem No 14

A 3-month futures contract on NIFTY is available at a time when the NIFTY is quoting 1800 points. Continuously compounded risk free rate is 10%. Continuously compounded yield on the Nifty stocks is 2% per annum. One futures contract equals 200 Nifty. How much will you pay for Nifty futures? If the Nifty forward trades at 1825 what action would follow?

Hedging with Futures Contract

Problem No 15

Consider the following data relating to KM stock. KM has a beta of 0.7 with NIFTY. Each Nifty contract is equal to 200 units. KM now quotes at Rs.150 and the Nifty future is 1400 Index points. You are long on 1200 shares of KM in the spot market.

(i) How many futures contracts will you have to take?(ii) Suppose the price in the spot market drops by 10%, how are you protected?(iii) Suppose the price in the spot market jumps up by 5%, what happens?

Problem No 16

Identify the action to be taken in respect of the following situations?

Stock beta Stock position Stock Value (Rs. lakh)

Hedge needed

0.81.20.91.01.3

LongLongShortLongShort

25124

FullFullFull50%110%

Problem No 17

Which position on the index future gives a speculator, a complete hedge against the following transactions:

(a) The share of Right Limited is going to rise. He has a long position on the cash market of Rs.50 Lakhs on the Right Limited. The beta of the Right Limited is 1.25.

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(b) The share of Wrong Limited is going to depreciate. He has a short position on the cash market of Rs.25 Lakhs on the Wrong Limited. The beta of the Wrong Limited is 0.90.

(c) The share of Fair Limited is going to stagnant. He has a short position on the cash market of Rs.20 Lakhs of the Fair Limited. The beta of the Fair Limited is 0.75.

Problem No 18A portfolio manager owns 3 stocks

Stock Shares owned Stock price (Rs.) Beta

1 1 lakh 400 1.1

2 2 lakhs 300 1.2

3 3 lakhs 100 1.3

The spot Nifty Index is at 1350 and futures price is 1352. Use stock index futures to (a) decrease the portfolio beta to 0.8 and (b) increase the portfolio beta to 1.5. Assume the index factor is Rs.100.

Find out the number of contracts to be bought or sold of stock index futures.

Problem No 19

The Fund Manager of Premier Multicap Fund, which has a portfolio beta of 1.25 with the NIFTY, expects the market to go on a bullis binge over the next 3 months. Fearing erosion in Net Asset Value, he wants to lower his Fund Beta to reduce the impact of downfall.

He is contemplating replacing a part of his fund with risk free assets or using NIFTY Futures to reducing the beta levels to 1.

Advise the fund manager on the alternatives if –

The portfolio value is Rs.5 Crores.

NIFTY is quoted at Rs.5,000 per unit with a contract size of 100 units.

The Fund Manager cannot load more than 10% of the Fund Value with risk free assets.

OPTIONS

Problem No 20

The Infosys stock is selling at Rs.5000. Mr. X has a negative view about the stock. He decides to go through the option route to take advantage of the situation. He buys an option from Mr. A which will entitle him to sell 100 shares on or before 30th December at Rs.4500 per share for which has to pay Rs.200 per share today. Identify type of option, exercise price, expiry date,

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option premium, buyer of the option, writer of the option, underlying asset and current market price.

Problem No 21

From the following, find whether the holder of Call Option would exercise his right on the expiry, comment thereon.

S.NO Strike Price Future spot price Compare Action Describe1 120 1402 400 5003 700 5004 175 1605 190 2406 450 450

Problem No 22

From the following find whether the holder of Put Option would exercise his right on the expiry date, comment thereon.

S.NO Strike Price Future spot price Compare Action Describe1 120 1402 400 5003 700 5004 175 1605 190 2406 450 450

Problem No 23

What option would you choose on the following Strike Price and Expected Future Spot? Will you exercise the option if the Actual Future Spot are as follows?

S.NO Strike price

Expectation of Future Price

Choice of Option Actual Future Spot

1 100 120 ? 1202 180 160 ? 1603 100 120 ? 1304 135 120 ? 1375 140 175 ? 135

Problem No 24

From the following find out the payoff for a holder of a call.

S.NO Strike Price Future spot price Premium 1 106 140 12 2 120 170 10 3 150 130 22

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4 900 780 30 5 600 790 42 6 250 160 190

Problem No 25

From the following, find out the pay off for a holder of put.

S.NO Strike Price Future spot price Premium 1 106 140 12 2 120 170 10 3 150 130 22 4 900 780 30 5 600 790 42 6 250 160 190

Problem No 26

From the following find out the payoff for a writer of a call

S.NO Strike Price Future spot price Premium 1 140 170 12 2 120 120 15 3 240 290 20 4 290 200 25 5 600 900 1006 320 400 31

Problem No 27

An investor purchases one option of a stock currently trading at Rs 39.2. The strike price is Rs 40 and the option premium Rs.3 (per share).

Future Spot Price Strike Price3839404142434445

4040404040404040

From the following find out the value of call, payoff, maximum profit, maximum loss and break-even for holder as well as writer

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Problem No 28

Stock of Indra Air Cargo Ltd is currently quoted at Rs.112. Ascertain the Time Value and Intrinsic Value of Option from the following particulars available in relation to derivatives market –

Put Options Call OptionsSituation Exercise Price Premium Situation Exercise Price Premium

A Rs.100 Rs.10 A Rs.124 Rs.9B Rs.104 Rs.11 B Rs.121 Rs.10C Rs.108 Rs.11 C Rs.118 Rs.10D Rs.112 Rs.11 D Rs.115 Rs.11E Rs.116 Rs.12 E Rs.112 Rs.11F Rs.120 Rs.12 F Rs.109 Rs.12G Rs.124 Rs.13 G Rs.106 Rs.12H Rs.128 Rs.13 H Rs.103 Rs.12

Problem No 29

Narendra Modi holds 50 share of Xerox Company. He is intending to write calls on Xerox’s shares. If he writers a call contract for 50 shares with an exercise price of Rs 60 each share determine the value of his portfolio when the option expires if (a) the current share price of Rs 45 rises to Rs 65, or (b) the share price falls to Rs 40.

Problem No 30

The market received rumour about ABC corporation’s tie-up with a multinational company. This has induced the market price to move up. If the rumour is false, the ABC corporation stock price will probably fall dramatically. To protect from this an investor has bought the call and put options.

He purchased one 3 months call with a striking price of Rs.42 for Rs.2 premium, and paid Re.1 per share premium for a 3 months put with a striking price of Rs.40.

(i) Determine the Investor’s position if the tie up offer bids the price of ABC Corporation’s stock up to Rs.43 in 3 months.

(ii) Determine the Investor’s ending position, if the tie up programme fails and the price of the stocks falls to Rs.36 in 3 months.

Problem No 31

The September option on AB Corp stock at a strike price of Rs.130 is available at a call option price of Rs.10. The contract size is 100 shares. The price of the stock today in 15 June is Rs.140. A range of prices beginning from 110 and ending with 160 with intervals of 10 is possible as at the expiry date.

(i) What is the payoff for the call holder on expiration?(ii) Draw the pay off graph.(iii) What is the call writer’s pay off on expiration?(iv) Draw the pay off table and the pay off graph.

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Problem No 32

The September put option on JB Ltd stock at a strike price of Rs.110 is available at a price of Rs.10. The contract size is 100 shares. The price of the stock today on 15 June is Rs.115. A range of prices beginning from 90 and ending with 140 with intervals of 10 is possible as at the expiry date.

(i) What is the payoff for the put holder on expiration?(ii) Draw the pay off graph.(iii) What is the put writer’s pay off on expiration?(iv) Draw the pay off table and the pay off graph.

Problem No 33

An investor buys a put option with an exercise price of Rs.200 for Rs.15. What is the maximum loss that he could incur? What is the maximum profit, which could accrue to him? Also determine break even stock price? What is the position for the put writer?

Problem No 34

An investor buys a call option with an exercise price of Rs.100 for Rs.10. What is the maximum loss that he could incur? What is the maximum profit, which could accrue to him? Determine break-even stock price what is the maximum position for the call writer.

Arbitrage

Problem No 35A call option has an exercise price of Rs.100. On the expiry date the market price of the stock is Rs.110. (i) if on that date the call is priced Rs.8 what would happen? (ii) If it is priced Rs.12 what action would follow?

Problem No 36

A put option has an exercise price of Rs.200. On the expiry date the market price of the stock is Rs.180. (i) if on that date the call is priced Rs.14 what would happen? (ii) If it is priced Rs.23 what action would follow?

Put Call Parity

Problem No 37In June 08 a six-month call on I Ltd’s stock with an exercise price of Rs.25 sold for Rs.2. The stock price was Rs.20. The risk free interest rate was 5% per annum. How much would you be willing to pay for a put on I Ltd’s stock with the same maturity and exercise price? What happens if the actual price is different from what you are willing to pay?

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Problem No 38

Amjad is furnished with the following information about securities of two Companies – Indra Ltd and Chandra Ltd.

1. Indra Ltd: Call option is traded is at Rs.85 for an exercise price of Rs.700. Presently stock of Indra Ltd is traded for Rs.650. Put options is available for Rs.110.

2. Chandra Ltd: Put option is traded at Rs.40 at an eexercise price of Rs.200. Presently stock of Chandra are traded at Rs.180. Call options are available for rs.20.

If Amjad has sufficient money and also holds stock in both these companies, wants to make only ascertained profit and no loss, advice him on the course of action and the resultant gain / loss.

Risk Free Interest rate may be assumed at 10% and expiry date for option is 3 months away.

Binomial Model

Problem No 39

The current share price is Rs.60. In one month it could either be 65 or 50. What will a European call with an exercise price of Rs.62 be worth if the risk free rate is 12% per annum.

Problem No 40

A stock is currently priced at Rs.50. It is known that in the first 6 months of current year from now prices will either rise by 20% or go down by 20%, further in the later half of the year prices may again go up by 20% or go down by 205 in the second step.

Suppose risk free interest rate is 5% continuous compounded, and strike rate is Rs.52.

Calculate value of European Put Option.

Black Scholes Model

Problem No 41

Consider the following information with regard to a call option on the stock of AB Corp

Details PriceCurrent share price Rs.120Exercise Price Rs.115Time Period 3Standard deviation of CCRFI 0.6CCRFI 10%

Compute the value of the call using Black-Scholes model. What would be the value of the put?

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a. If the value of the call is Rs.16 in the market what action would follow?

b. If the value of the put is Rs. 18 in the market what action would follow?

Problem No 42

The shares of TIC Ltd, are currently price at Rs.415 and call option exercisable in three month’s time has an exercise rate of Rs.400. Risk free interest rate is 5% p.a. and standard deviation (volatility) of share price is 22%.

Based on the assumption that TIC Ltd is not going to declare any dividend over the next three months, is the option worth buying for Rs.25?

(a) Calculate value of aforesaid call option based on Black Scholes valuation model if the current price is considered as Rs.380.

(b) What would be the worth of put option if current price is considered Rs. 380.

(c) If TIC Ltd, share price at present is taken as Rs.408 and a dividend of Rs.10 is expected to be paid in the two months time, then, calculate value of the call option.

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International Finance

Problem No 1

Following are the quotes given by Forex dealer at Mumbai. Identify the quote as Direct or Indirect quote. Also compute the Direct for indirect Quote and Vice-versa.

Particulars1$ =Rs.43.181£ =Rs.78.681 INR =Euro 0.0184100 Indo Rupiah =Rs.0.531 HK$ =Rs.5.54

Problem No 2

Following are the quotes in India for foreign currencies

(a) INR/$48.72-48.94(b) INR/Euro 44.44-44.67(c) INR/100¥38.01-38.14(d) INR/£71.00-71.12(e) INR/HK$6.17-6.32(f) INR/SFr4.52-4.78(g) INR /Aus$26.41-26.72(h) INR /100SKw3.71-3.83

Find out Bid-Rate, Ask-rate, Spread, Spread in % and corresponding indirect quote

Problem No 3

INR 47.10 – 47.25 per USD is a direct quote. Another direct quote is ¥/₤ 179-180. Find (i) the country where the quote is made and (b) The bid, ask and the spread.

Problem No 4

The following INR/SGD direct quote of ICICI Mumbai is available: 26.50 – 26.75 (a) What is the cost of buying Rs. 55,000(b) How much would you receive by selling Rs. 92,000(c) What is the cost of buying SGD 7,450(d) What is your receipt if you sell SGD 18,340

Problem No 5

Following quotes are available - SGD/INR = 0.045; Euro/INR = 0.02a. Find the quote for SGD in terms of Eurob. Find the quote for Euro in terms of SGD

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Problem No 6

Consider the following and determine the cross rates, as indicated1. INR/NOK = 6.44 2. USD/AUD = 0.6051 3. INR/GBP = 74.5 – 75.00 INR/GBP = 47.10 INR/AUD = 28.97 $/GBP – 1.62 – 1.63 NOK/GBP = ? USD/INR = ? INR/$ = Bid – Ask - ?

Problem No 7

The spot rate for INR/AUD is 29.36 and the 3-month forward rate is 29.45. Which currency is appreciating and which is depreciating? Which currency is trading at a discount and which is at a premium? Which currency is more expensive? Compute the annual percentage premium or discount?

Problem No 8

The spot rate for Euro is Rs 50-52. The forward rate is 53-56. Compute swap points, spot and forward spread.

Problem No 9

Consider the following rates and suggest which currency is quoting at premium and which is at a discount

(a) Spot Rs./HKD is 6.02. 1 month forward = Rs 6.04(b) Spot Rs./SGD is 26.83. 3-months forward = Rs. 26.73

Forward Rates – Swap Points

Problem No 10

Following quotes are available at Kualalumpur for Spot and Forward –

Spot 1 - Month Forward 3 Month ForwardUSD 1 = MYR 3.30 – 3.50 0.15 – 0.10 0.25 – 0.20MYR 1 = HKD 2.25 – 2.40 0.10 – 0.15 0.20 – 0.30GBP 1 = MYR 6.75 – 7.00 0.20 – 0.25 0.35 – 0.50

MYR 1 = Euro 0.2150 – 0.2190 0.020 – 0.015 0.040 – 0.035

Required – (a) Ascertain the Forward Rates.(b) Ascertain cost of buying USD 50,000 1-Month forward(c) Cost of buying Euro 1,00,000 3-Months forward(d) GBPs that can be bought 1-Month forward for MYR 500,000(e) HKD required to be sold to obtain MYR 100,000 3-Months forward

Impact of Currency appreciation / depreciation

Problem No 11

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Suppose that 1 € could be purchased in the foreign exchange market for 50 US cents today. If the € appreciated 10 percent tomorrow against the dollar, how many € would a dollar buy tomorrow?

Problem No 12

Forever Products, a French Co., 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 French francs 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?

Interest rate parity Theory (IRPT) and Purchasing Power Parity Theory (PPP)

Problem No 13

Risk free rate in Japan is 6% p.a., while that in India is 3% p.a. Spot Rupee yen is 0.04002 and the 12 month yen rate is 0.388874. You wish to invest Rs. 1,00,000 in risk free investments for one year. Will you invest the sum of Rs. 1,00,000 in India or convert in into yen and invest in Japan, assuming that the IRPT holds?

Problem No 14

Yen/ $ is quoted at 120.10. 12 –month forwaed rate is 117.00. Interest rate for one-year deposit in Tokyo is 2.03% and the corresponding $ deposit rate in Chicago is 7.03%. What action would follow?

Problem No 15

You are in New York. The spot $/₤ rate is 1.5865 – 84. The 12 month forward rate is 1.5443 – 1.5463. The T-Bill rate in US is 5%, while that in UK is 8%. If you invest ₤25,000 in UK, by simultaneously taking a 12 month forward contract how much will you gain or lose?

Problem No 16

The US$ is selling in India at Rs. 45.50. If the interest rate for a 6-months borrowing in India is 8% per annum and the corresponding rate in USA is 2%.

(i) Do you expect US$ to be at a premium or at discount in the Indian forward market(ii) What is the expected 6-months forward rate for United States Dollar in India; and (iii) What is the rate of forward premium or discount?

Problem No 17

Interest rates in Luxembourg and in India stand at 3.50% p.a. and 6.00% p.a. respectively. If the spot Rupee/Euro rate is 51.75, what is your estimate of future spot rate if the interest rate parity theory holds good? If the forward rate is 52 what action would follow? If the forward rate is 54 will there be a change in action?

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Problem No 18

In 2000 a Transistor cost $22.84 in New York S$69 in Singapore, and 3240 rubles in Moscow.(i) If the law of one price held, what was the exchange rate between US dollars and Singapore dollar and between US dollars and rubles?(ii) The actual exchange rates in 2007 were S$6.13= US$1 and 250 rubles= US$1. Where would you prefer to buy your Transistor?

Problem No 19

In London, Dollar is quoted at GBP 0.0510. The estimated inflation rates over the next four years for UK and US are as follows:

Years 1 2 3 4UK 5% 7% 6% 7.5%US 8% 6% 6.5% 7%

Determine estimated future spot rate at the end of four years.

Problem No 20

An investor in India can invest Rs. 1,00,000 and earn 8%. Alternatively, he can convert funds into Singapore Dollars at Rs. 28, and earn 10% on Singapore Dollar. If the expected inflation rate in India is 5%, what is the expectation in Singapore, if the real rates were the same?

Problem No 21

Ansh Infotech Ltd., a company in Delhi is trying to recover from difficult times. They have begun trade with two foreign countries, Algeria and Bermuda. From Algeria, they have purchased recently, competitively priced components at a cost of Dinars 45,00,000/- This payment is due in three months. The Company has also supplied quality goods to Atrie Pvt. Ltd in Bermuda, and the sale price of Bermuda $35,00,000 is receivable in Bermuda $. As per credit terms agreed up on, Atrie will release payments in six months from now. Ansh Infotech is facing cash crunch, and the outcome of discussions with banker is that there cannot be any further increase in overdraft limit.

MD of Ansh Infotech, after discussions with his Sales Manager, has stated that there would be substantial foreign exchange risk in the case of Algeria, while there is little risk in the case of Bermuda, since that currency is linked to US Dollars. US Dollar has been stable relative to Rupee recently. Exchange rates are:

SPOT 3 m Forward 6 m forward

Rupee/Dinars 0.0270 – 0.0285 No market No market

Rupee/Dollar 47.50 – 75 47.25 – 50 47.00 – 25

Rupee/Bermuda $ 0.04348 – 0.04545 No market No market

Other details are:

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Annual Inflation Investing rate Borrowing rate

India

US

Algeria

Bermuda

3%

6%

12%

20%

4.50%

6.00%

12.50%

15.00%

10%

12%

NA

NA

Explain briefly whether MD is correct? State your own concerns about the payments and receipts to be made in foreign exchange involving the two currencies.

Problem No 22

Transaction RiskOn 1st February, a business entity in Mumbai purchases materials from France. The invoice amount of 5,00,000 Euro is payable at the end of April. The Spot rate on 1 st February was Rs.49.00 – 50.00. The entity incurs a conversion expenditure of Rs.50 lacs. Finished goods were sold to a company in USA on 15th March. Invoice value of Finished goods was US $ 12,50,000/-. Terms of sale included payment at the end of April. Spot rate on 15 th March was Rs.45-46. Other selling expenses amounted to Rs.10 lacs. At the end of April, the spot rates stood at, (a) Rupee / Euro: Rs.51.00 – 52.00 and (b) Rupee/$: Rs.44-45

Required:(a) Compute and show the actual cash profit.(b) Comment on exchange rate movements.

Problem No 23

Home Currency InvoicingAtlanta Systems Ltd. in India exports software for an invoice value $ 100 Million. Spot rate is Rs.45. Forward is Rs.46. (a) If the forward rate is an indicator of future spot rate, in which currency should Atlanta Ltd invoice? (b) What will be its approach, if the forward rate were to Rs.44? (c) Will the position change if it were importing, and not exporting, software for a value of $ 100 Million?

Problem No 24

Leading and LaggingBPL Ltd. (BPL) had already received the invoice for HKD 2,10,000/-. Spot rate Rs/HKD is 6.50 and 60-day forward rate is 6.60. Determine whether BPL should avail of the full credit period of 60 days, or lead the payment – if interest rate in India is (a) 11% p.a. (b) 6.5% p.a.

Netting

Problem No 25

Fortune International has Head Office in USA. This group has subsidiaries in UK, France and Japan. As on 31st March, inter-company indebtedness stood as under:

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Debtor Creditor Amount (in Million)UKUKJPFCFC

FCJPFCUKJP

€ 240¥ 120,00€ 120Sterling 75¥ 120,00

US Headquarters follow the multi-lateral netting policy, and adopts the following exchange rates: US $ 1 = € 0.90; Sterling 0.70; ¥ 120Compute and show net payments to be made by subsidiaries, after netting off.

Problem No 26

CISCO Ltd (MNC Co.) has subsidiaries whose cash positions for the month of September, 2007 are given below:

Swiss subsidiary Cash surplus of SF 1, 50,000Canadian subsidiary Cash deficit of Can $ 2, 50, 00,000UK subsidiary Cash deficit of 30, 00,000(UK pound)

What are the cash requirements, if:(i) Decentralized cash management is adopted?(ii) Centralized cash management is adopted?

Exchange rate: SF 1.48/$ Can $ 1.58/$, $1.5/£)

Hedging through Forward Contracts

Problem No 27

Copper Connections Ltd (CCL), an Indian importer is aware on 1st January that he must pay the foreign seller 32,400 Swiss Francs in three months’ time on 1st April. Spot rate is Rs.34.25. CCL can arrange a forward exchange contract with his bank on 1 st January. Under such a contract, the bank undertakes to sell the importer SFr 32,400 at a fixed rate of Rs.34.93. State what would happen if on 1st April the S Fr quotes (i) 34.63 (ii) 35.25

Problem No 28

Exporter of Defense equipments in New Delhi expects the next remittance 3 months later. The amount involved is € 1,15,000/-. The exporter fears that rupee may gain against € in the next three months. He enters into a three-month forward exchange contract with his banker so that he can be assured of the quantum of rupee-funds that he would receive at the designated date. The Bank provides him a contract with a Rupee / € forward rate of 51.10. Explain. State what would happen if on 1st April the € quotes (i) 52.10 (ii) 50.10?

Problem No 29

A company is considering hedging its foreign exchange risk. It has made a purchase on 1st. January, 2008 for which it has to make a payment of US $ 50,000 on September 30, 2008.

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The present exchange rate is 1 US $ = Rs. 40. It can purchase forward 1 US $ at Rs. 39. The company will have to make a upfront premium of 2% of the forward amount purchased. The cost of funds to the company is 10% per annum and the rate of Corporate tax is 50%. Ignore taxation. Consider the following situations and compute the Profit/Loss the company will make if it hedges its foreign exchange risk:

(i) If the exchange rate on September 30, 2008 is Rs. 42 per US $.

(ii) If the exchange rate on September 30, 2008 is Rs. 38 per US $.

Problem No 30

NTT DoCoMo, a company is operating in Japan has today effected sales to an Indian company, the payment being due three months from the date of invoice. The invoice amount is Yen 108 lacs. At today’s spot rate, it is equivalent to Rs.30 lacs. It is anticipated that the exchange rate will decline by 10% over the three months period, and in order to protect the yen payments, the importer proposes to take appropriate action in the foreign exchange market. The three-month forward rate is presently quoted at 3.3 yen per Rupee.

You are required to calculate the expected loss, and to show how it can be hedged by a forward contract.

Problem No 31

Shoe Company sells to a wholesaler in Germany. The purchase price of a shipment is 50,000 deutsche marks with term of 90 days. Upon payment, Shoe Company will convert the DM to dollars. The present spot rate for DM per dollar is 1.71, whereas the 90-day forward rate is 1.70.

You are required to calculate and explain:

(i) If Shoe Company were to hedge its foreign-exchange risk, what would it do? What transactions are necessary?

(ii) Is the deutsche mark at a forward premium or at a forward discount?

(iii)What is the implied differential in interest rates between the two countries?

(Use interest-rate parity assumption).

Problem No 32

Link Tele-systems has to make a payment of 10 lac ¥ three months from today. Current spot rate is Rs/Y 0.3900-0.4000. The forward rate is Rs/Y 0.3925-50. You expect the spot rate to be Rs/Y 0.3930-40 three months hence. What action would you take?

Problem No 33

Lucent Technologies Ltd is to receive 5 million USD 6 months hence. Current spot rate is Rs/$ 45.50-75. The 6-month forward rate is Rs./$ 46.00-46.500. Lucent expects the spot rate to be Rs/$ 45.75-46.75 six months hence. What action would Lucent take?

Forward Contracts : Honor, Rollover or Cancel

Problem No 34

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On 1st Jan 04 Sixth Sense Ltd entered into a 3 month forward contract in respect of an import obligation of $ 1,00,000. The INR/$ rates on various dates are given below:

1st Jan 28th Feb 31st MarchSpotForward MonthsForward RateForward MonthsForward Rate

46.50 – 46.753

46.60 – 46.90-

46.70 – 47.002

47.10 – 47.501

47.25 – 47.40

46.90 – 48.102

47.00 – 48.25

Explain the further course of action if Sixth Sense –(a) Honors the contract on

31st March 28th February

(b) Cancel the contract on 28th February 31st March

(c) Roll over the contract For 2 months on 28th February For 2 months on 31st March

Problem No 35

On 1st Jan 04 Learning Curve Ltd entered into a 3 month forward contract in respect of an export obligation of $ 1,00,000. The INR/$ rates on various dates are given below:

1st Jan 28th Feb 31st MarchSpotForward MonthsForward RateForward MonthsForward Rate

46.50 – 46.753

46.60 – 46.90-

46.70 – 47.002

47.10 – 47.501

47.25 – 47.40

46.90 – 48.102

47.00 – 48.25

Explain the further course of action if Learning Curve –(d) Honors the contract on

31st March 28th February

(e) Cancel the contract on 28th February 31st March

(f) Roll over the contract For 2 months on 28th February For 2 months on 31st March

Problem No 36

A customer with whom the Bank had entered into 3 months’ forward purchase contract for Swiss Francs 10,000 at the rate of Rs. 27.25 comes to the bank after 2 months and requests

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cancellation of the contract. On this date, the rates, prevailing, are:

Spot CHF 1 = Rs. 27.30 27.35

One month forward Rs. 27.45 27.52

What is the loss/gain to the customer on cancellation?

Money Market Hedge

Problem No 37

AE Morgan is a UK based exporter. Invoice amount is $3,50,000/-. Credit period three months. Exchange rates in London

$/₤ Spot 1.5865-1.5905

3 months Forward 1.6100-1.6140

(i) Show how a money-market hedge can be put in place.(ii) Determine whether it would have been advantageous to take forward cover?

Problem No 38

JC Stanley is a UK based importer. Invoice amount is $3,50,000/-. Credit period six months. Exchange rates in London:

$/₤ Spot 1.5865-1.5905

6 month Forward 1.5505-1.5545

(i) Show how a money-market hedge can be put in place.(ii) Determine whether it would have been advantageous to take forward cover?

Currency Futures

Problem No 39

Accentia Plc is a UK based export oriented Company. It is now April. Accentia is due to receive in June, a sum of US $ 1,40,000 from its customer in Los Angeles USA. Spot rate in April is $/₤ 1.5865-85. Contract size for ₤s is ₤25,000. The contract price is $ 1.59. Delivery dates are June, September and December. Spot rate in June is $/₤ 1.6120-40. FX Futures Sterling sale contracts are priced in June at 1.6100.

Show how Accentia can use Futures as a hedging tool

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Money market rates

Deposit Loan

$

₤

7%

5%

9%

8%


Currency Options

Problem No 40

Veratronix has put in a bid for securing a contract in USA. In order to hedge the FX risk exposure, they have bought an Over the counter put option for $3,40,000/- , settlement six months, with an exercise price of $ 1.60 per unit of Domestic Currency (DC).

Required: Advise whether the company should cancel the Put option, and go for a call option.

Indicate the actions by the bidder in the following circumstances:(a) If the bidder wins the contract, and the spot selling moves to (i) Either 1.75 or (ii) 1.45(b) If the bidder losed the contract, and the spot purchase moves to (i) Either 1.80 or (ii) 1.40

Problem No 41

Zephyr Group of UK will need to make a payment of $2,50,000 in six month’s time. Following market information is available

Forex (indirect quote) FX OptionsSpotSix months forwardExercise priceSix months CallSix months PutContract size

US $UK Pounds

$ 1.5617 – 1.5773$ 1.5455 – 1.5609

Money Market RatesDeposit4.505.50

1.70$ 0.037 c per Pound$ 0.096 c per PoundAssume: Pound 12,500

Borrow67

Zephyr is considering, forward rates, money market hedge and Options. Give your recommendations on the best alternative with reasons.

Interest Rate Swaps

Problem No 42

Steve Ltd. enjoys a high credit rating, and is capable of raising term funds either at a fixed rate of 10% p.a. or at a floating rate of 40 basis points over MIBOR. Somappa Ltd. enjoys a relatively lower credit rating, and is able to borrow either at 80 basis points over MIBOR, or at a fixed rate of 11%. Somappa wants to borrow at fixed rate whereas Steve would like to enjoy a floating rate. Structure a swap arrangement such that Steve gains 2/3rd of the total gain. Assume that there are no intermediaries involved.

Problem No 43

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Consider data in Problem 18. Assume that the interest rates applicable to Steve and Somappa are as under:

Steve SomappaFixed interestFloating rate

10.00%MIBOR

10.5%MIBOR + 0.8%

What action will follow if Steve apprehends that interest rates will harden while Somappa believes that interest rates will soften?

Currency Swap

Problem No 44

A leading company in USA wishes to lend $ 500000 to its subsidiary in Japan. There is also another company in Japan that desires funding for its subsidiary in USA for an amount that is approximately equal to half a million US $. An intermediary brings these parties together and lines up a currency swap arrangement, with the following terms:

US Company will lend $ 500,000 to Japanese subsidiary in USA for 4 years an interest rate of 13%. Principal and interest are payable only at the end of the 4 th year, with interest compounding annually.

Japanese company, in turn will lend to the subsidiary of US Company a sum of Yen 70 million for four years at 10%. Here again, the principal amount, and interest compounded annually for four years, together payable at the end of the loan period.

Current exchange rate is $ 1 = Yen 140. However, the $ is expected to decline by Yen 5 per dollar, per annum over the next four years.

Required: If this swap arrangement is concluded and expectations of exchange rate movement also prove to be correct.

Additional Questions:

Problem No 45

A dealer sold HK$ 10 Million value spot to the customer at Rs.5.70 and covered in London market on the same day, when the exchange rates were $ =HK$ 7.5880-7.5920.

Local interbank market rates for US$ were Spot $= Rs.42.70-42.85Calculate cover rate and ascertain the dealers Profit or Loss in the transaction.

Problem No 46

Followings are the spot exchange rates quoted at three different forex markets :

USD/INR 48.30 in MumbaiGBP/INR 77.52 in London

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GBP/USD 1.6231 in New York

The arbitrageur has USD1,00,00,000. Assuming that there are no transaction costs, explain whether there is any arbitrage gain possible from the quoted spot exchange rates.

Problem No 47

Alert Ltd. is planning to import a multi-purpose machine from Japan at a cost of 3,400 lakhs yen. The company can avail loans at 18% interest per annum with quarterly rests with which it can import the machine. However, there is an offer from Tokyo branch of an India based bank extending credit of 180 days at 2% per annum against opening of an irrevocable letter of credit.

Other Information:

Present exchange rate Rs. 100 = 340 yen.

180 days’ forward rate Rs. 100 = 345 yen.

Commission charges for letter of credit at 2% per 12 months.

Advise whether the offer from the foreign branch should be accepted?

Problem No 48

X Ltd. an Indian company has an export exposure of 10 million (100 lakhs) yen, value September end. Yen is not directly quoted against Rupee. The current spot rates are USD/INR = 41.79 and USD/JPY = 129.75.

It is estimated that Yen will depreciate to 144 level and Rupee to depreciate against dollar to 43.

Forward rate for September 1998 USD/Yen = 137.35 and USD/INR = 42.89.

You are required to:

(i) to calculate the expected loss if hedging is not done. How the position will change with company taking forward cover?

(ii) If the spot rate on 30th September, 1998 was eventually USD/Yen = 137.85 and USD/INR = 42.78, is the decision to take forward cover justified?

Problem No 49

In March, 2003, the Multinational Industries makes the following assessment of dollar rates per British pound to prevail as on 1.9.2003:

$/Pound Probability1.60 0.151.70 0.201.80 0.251.90 0.202.00 0.20

(i) What is the expected spot rate for 1.9.2003?

(ii) If, as of March, 2003, the 6-month forward rate is $ 1.80, should the firm sell forward its

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pound receivables due in September, 2003?

Problem No 50

On January 28, 2005 an importer customer requested a bank to remit Singapore Dollar (SGD) 25,00,000 under an irrevocable LC. However, due to bank strikes, the bank could effect the remittance only on February 4, 2005. The interbank market rates were as follows:

January, 28 February 4

Bombay US$1 = Rs. 45.85/45.90 45.91/45.97

London Pound 1 = US$ 1.7840/1.7850 1.7765/1.7775

Pound 1 = SGD 3.1575/3.1590 3.1380/3.1390

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? (Calculate rate in multiples of .0001)

Problem No 51

L.B, Inc., is considering a new plant in the Netherlands the plant will cost 26 Million Guilders. Incremental cash flows are expected to be 3 Million Guilders per year for the first 3 years, 4 Million Guilders the next three, 5 Million Guilders in year 7 through 9, and 6 Million Guilders in years 10 through 19, after which the project will terminate with no residual value. The present exchange rate is 1.90 Guilders per $. The required rate of return on repatriated $ is 16%.

a. If the exchange rate stays at 1.90, what is the project net present value?

b. If the guilder appreciates to 1.84 for years 1-3, to 1.78 for years 4-6, to 1.72 for years 7-9, and to 1.65 for years 10-19, what happens to the net present value?

Problem No 52

A dealer in foreign exchange has the following position in Swiss Francs on 31st October, 2004:

Swiss Francs

Balance in the Nostro A/c Credit 1,00,000

Opening Position Overbought 50,000

Purchased a bill on Zurich 80,000

Sold forward TT 60,000

Forward purchase contract cancelled 30,000

Remitted by TT 75,000

Draft on Zurich cancelled 30,000

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What steps would you take, if you are required to maintain a credit Balance of Swiss Francs 30,000 in the Nostro A/c and keep as overbought position on Swiss Francs 10,000?

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BOND VALUATION

Problem No 1

The face value of a Bond is Rs. 1,000 with 8% coupon and a current yield of 9%

a) What is the price of the bond?i) If it is a perpetual bondii) It has 5 years to maturity

b) What changes would you make in (a) above if the current yield changes to 11% instead of 9%?

Problem No 2

Rs. 1000 per value bond bearing a coupon rate of 11% will mature after 5 years. What is the price of the bond if the yield is 15%?

Problem No 3

A Rs. 1000 per value bond, bears a coupon rate of 12% will mature after 6 years. Coupon interest payable semi annually. Compute the value of the bond if required rate of return 16% p.a.

Problem No 4

What is the value of 5 year 5.8% coupon bond if the appropriate discount rate for discounting each cash flow is as follows?

Year 1 2 3 4 5Discount Rate in% 5.9 6.4 6.6 6.9 7.3

Problem No 5

M/s. Agfa industries are planning to issue a debenture series on the following terms.

Face value Rs.100 Term of maturity 10 Years ______________________________ Yearly coupon rate ______________________________ Years

1-4 9%5-8 10%

_______________________________9-10 14%

The currently market rate on similar debentures is 15% per annum. The company proposes to price the issue in such a manner that it can yield 16% compounded rate of return to the investors.

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The company also proposes to redeem the debentures at 5% premium on maturity. Determine the issue price of the debentures.

Problem No 6

A company had a bond at Yo having a face value of Rs 1000. Coupon rate is 14% Redemption value Rs.1200 at any time of maturity during 5 years. If the investor desired to get 17% return what is the issue price during each of the beginning of 5 years?

Problem No 7

Face value of bond is Rs 1000 Coupon rate is 10% p.a. payable annually as the outstanding bond amount. Redemption shall be carried out @ Rs.500 each at the end of Y4 and Y5. Find out the price of the bond if the investor expects 12%p.a. return

Problem No 8

Suppose 10%, 15 year bond has the call structure

Not Callable for the next 5 years First callable in 5 years at Rs.105 First par callable date is in 10 years. The price of the bond is Rs.127.59

(a) Is the yield to maturity 7%, 7.4%, or 7.8%(b) Is the yield to first call 4.55%, 4.65% or 4.85%(c) Is the yield to par call 6.25% 6.55% or 6.7

Note: Semi annual payment of coupon envisaged.

Problem No 9

Suppose a year 9% coupon bond is selling for Rs.112 with an par value of Rs.100. what is the current yield of the bond?

Problem No 10

The market value of Rs.1,000 par value bond carrying coupon rate of 12% and maturing after 7 years is RS.750 What is YTM?

Problem No 11

Mr. A paid Rs. 1036 for a bond having a maturity period of 3 years. Coupon is paid @ 9% as the face value of Rs.1000.

(a) What is the YTM if redemption value is Rs.1,100(b) If bond were callable at the 2nd year @ Rs.1,150 what is yield Coupon? (YTC)

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Problem No 12

There is a 9% year bond issue in the market. The issue price is Rs.90 and the redemption price is Rs.105. For an investor with marginal income tax rate of 30% and capital gains tax rate of 10% what is the post tax yield maturity? No indexation permitted.

Problem No 13

A Company had issued a bond at Yo having a face value of Rs.1,000. coupon rate is 14% and redemption @20% premium.

Find out the issue and YTM when the investor expects 17% p.a. return if the bond period were to be

(a) One year to maturity(b) Two years to maturity(c) 3 years to maturity (d) 4 years to maturity(e) 5 years to maturity

Problem No 14

You are considering investing in one of the Bond Coupon rate Maturity Price (FV Rs.1,000) A 12 % 10 years 700 B 10% 6 years 600

Tax rate is 30% and capital gain tax is 10%, what is post tax yield to maturity?

Problem No 15

Mr. X purchased bond at Rs.950 for a 15% coupon interest (face value Rs.1000). the time of maturity is one year.( in case of maturity period <2 this formula to be used for YTM)

What is the yield to maturity for the investor?

Problem No 16

An Rs.1000 par value bond carries a coupon rate of 10% payable annually and has a remaining maturity of 4 years. The bond is presently selling for Rs.1020. the reinvestment rate applicable for the future cash flow of the bond is 9% per annum. What will the realized to maturity?

Problem No 17

Consider a Bond P Bond PFace value Rs.100Coupon (interest rate) 8% pa payable semi-annuallyYears to maturity 4Redemption Value Rs.1000

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Current market price Rs.935.36

What are the yields to maturity durations, and volatilities of these bonds?

Problem No 18

Consider two bonds P and Q

Bond P Bond QFace value 1,000 1,000Coupon (interest rate) 16 per cent payable annually 12 percent payable annuallyYears to maturity 8 5Redemption value 1,000 1,000Current market price Rs.918.5 Rs.761

What are the yields to maturity, durations, and volatilities of these bonds?

Problem No 19

A 12% coupon bond has a maturity of 5 years. It pays interest semi-annually. Its yield to maturity is 5% per half-year period. What is its duration?

Problem No 20

A zero Coupon bond of Rs.10000 has a term to maturity of 8 years. Market yield at the time of issue is 10%.

a. What is the issue price of the bond?b. What is the duration of the bond?c. What is the modified duration of the bond?d. If 100% basic points were changed in the yield, find its impact in the price of the bond. Prove.

Problem No 21

What is the price of zero coupon bonds, having a face value of Rs.1000, redeemable after 3 years with 14% yield p.a. compounded semi annually? In case the yield is 14% compounded annually. What is the price?

Problem No 22

You receive a cash inflow of Rs.15 Lacs The funds deployed and duration details are provides as follows:Bond %of founds Duration (years) A 10 10.35 B 22 4.25 C 19 7.50 D 7 9.50 E 17 12.67 F 6 5.82 G 11 8.50

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H 8 6.71

All the bonds have a face value of Rs 1000 and YTM of 9% What is the duration of the portfolio?

Problem No 23

Find the current market price of a bond having a face value of Rs.12 redeemable after 6 years with YTM @16% payable annually and duration of 4.3202 years. Problem No 24

A company had issued 11.5% convertible bond maturity in 10 years time. 3 years after the issue bond holder can convert 1 bond for shares of Rs.10 each. Price of similar bond without conversion is trade at Rs.870.

The price of the convertible bond is Rs.970 and each share is traded at Rs. 18.50 To latest dividend is declared @21.2% you are required to find out on the 1st day of conversion.

(a) Premium over conversion(b) Premium over investment(c) Equilibrium price of equity share(d) Option period of conversion

Problem No 25

A company has 500 bonds waiting for conversion It is 13% convertible bond traded at Rs.1,060 1 bond is eligible for 10 equity shares. The present PE ratio of 20 is likely to move up upon conversion to 25 times. Number of Equity Shares before conversion was 10,000. operating profit before tax was 2,10,000. the company pays 33.33% tax. Should conversion be declared?

Problem No 26

Smith Corporation has a Rs40 million 14% bond issue outstanding with 15 years remaining. The call premium is 8% of face value. the new 15-year bond issue for Rs.40 million can be issued at a 10% interest rate. Floatation costs applicable to the new issue are Rs. 350,000. Should Smith Corporation call the original bond issue?

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Leasing Decisions

Problem No 1

Ambience Ltd wants to lease out an asset costing Rs.720,000 for a five-year period. It has fixed a rental of Rs. 2,10,000 per annum payable annually in arrears. The company enjoys a nil tax status. Its cost of capital is 12%. Is this agreement favorable to it?

Problem No 2

JLL Ltd. wants to lease out an asset worth 100 lacs for a 4 year period. The asset is to be written off at 25% under the Companies Act and qualifies for 30% depreciation under the Income Tax Act. At the end of the lease period it can be sold at whatever is its Tax WDV. Cost of capital after tax is 10% and the tax rate is 25%.

a) Determine whether a lease rental of Rs.30 lacs per annum payable in arrears advantageous to JLL Ltd.

b) If the lease rental is Rs.180,000 per annum payable annually in advance. Is the arrangement favorable?

Problem No 3

Xstrata Ltd buys an asset for Rs.424,000. At the end of its useful life of 5 years it will have no realizable value. The asset is leased out to Penguin Ltd. First payment is made on the date contract is signed. What is the implied rate if the lease rentals are fixed at Rs.100,000 payable annually in advance?

Problem No 4

ABC Finance Ltd. is a hire purchase and leasing company. It has been approached by a small business firm interested in a acquiring a machine through leasing. The quoted price of the machine is Rs.5,00,000. 10% sale tax is extra. The lease will be for a primary lease period of 5 years.

The finance company wants 8% post-tax return on the outlay. Its effective tax rate is 35%. The income tax rate of depreciation on the machine is 25% (WDV). Lease rents payable in arrear at the end of each year.

Calculate the annual rent to be charged by ABC Finance Ltd.

Problem No 5

ABC Leasing Ltd. has been approached by a client to write a five years lease on an asset costing Rs.10,00,000 and having estimated salvage value of Rs.1,00,000 thereafter. The company has a after tax required rate of return of 10% and its tax rate is 50%. It provides depreciation @33 % on written down value of the asset. What lease rental will provide the company its after tax required rate of return?

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Equated Annual Lease Rent

Problem No 6

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 Rs.10 lakhs and the primary period of lease to be 10 years. Kuber Leasing is able to give you the following additional information:

(a) The machine can be depreciated fully over the 10 years on straight line basis

(b) The current effective tax rate for Kuber Leasing is 40% and they expect to go down to 30% from the beginning of the 6th year of the lease.

(c) It is the normal objective of Kuber to make to make a 10% post-tax return in its lease pricing.

(d) Lease management fee of 1% of the value of the asset is usually collected from the lessees upon signing of the contract of lease, to cover the overhead costs related to processing of the proposal.

(e) Annual lease rents are collected at the beginning of every year.

You are required to determine the equated annual rent to be charged for the proposal.

Problem No 7

Axis Ltd wants to lease an asset costing Rs.420,000. The useful life of the asset is 4 years. Rentals are payable annually in arrears. The estimated RV is 20,000. Lease rentals are fixed at Rs.128,000. Axis is subject to corporate tax of 40%. Asset is depreciated at 25% SLM after taking into account the RV and this is allowed under tax. Compute the implied post tax rate of return.

Problem No 8

Armada Leasing Company is considering a proposal to lease out a school bus. The bus can be purchased for Rs. 5,00,000 and, in turn, be leased out at Rs. 1,25,000 per year for 8 years with payments occurring at the end of each year:

(i) Estimate the internal rate of return for the company assuming tax is ignored.

(ii) What should be the yearly lease payment charged by the company in order to earn 20 per cent annual compounded rate of return before expenses and taxes?

(iii) Calculate the annual lease rent to be charged so as to amount to 20% after tax annual compound rate of return, based on the following assumptions:

(i) Tax rate is 40%;(ii) Straight line depreciation;(iii) Annual expenses of Rs. 50,000; and(iv) Resale value Rs. 1,00,000 after the turn.

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Evaluation of Lease – Lessee’s Perspective

Problem No 9

Engineers Ltd. is in the business of manufacturing nut bolts. Some more product lines are being planned to be added to the existing system. The machinery required may be bought or may be taken on lease. The cost of machine is Rs. 20,00,000 having a useful life of 5 years with the salvage value of Rs. 4,00,000 (consider short term capital loss/gain for the Income tax). The full purchase value of machine can be financed by bank loan at the rate of 20% interest repayable in five equal instalments falling due at the end of each year. Alternatively, the machine can be procured on a 5 years lease, year-end lease rentals being Rs. 6,00,000 per annum. The Company follows the written down value method of depreciation at the rate of 25 per cent. Company’s tax rate is 35 per cent and cost of capital is 14%

(i) Advise the company which option it should choose – lease or borrow.

(ii) Assess the proposal from the lessor’s point of view examining whether leasing the machine is financially viable at 14 per cent cost of capital.

Problem No 10

The FFM Ltd. is in the tax bracket of 35% and discounts its cash flows at 16%. In the acquisition of an asset worth Rs.10,00,000, it is given two offers – either to acquire the asset by taking a bank loan @ 15% p.a. repayable in five yearly instalments of Rs.2,00,000 each plus interest or to lease-in-the asset at yearly rentals of Rs.3,24,000 for five years. In both cases, the instalment is payable at the end of the year. Applicable rate of depreciation is 15% using ‘written down value’ (WDV) method.

You are required to suggest the better alternative.

Year 1 2 3 4 5P.V. factor @ 16% 0.862 0.743 0.641 0.552 0.476

Problem No 11

Hypothetical Ltd. is planning to have an access to a machine for a period of 5 years. The company can either have an access through the leasing arrangement or it can borrow money at 14% to buy the machine. The company is in 50% tax bracket.In case of leasing, the company will be required to pay annual year-end lease rent of Rs.1,20,000 for 5 years. All maintenance, insurance and other costs are to be borne by the lessee.

In case of purchasing the machine (which costs Rs.3,43,300), the company would have to repay 14% five year loan in 5 equal annual instalments, each installment becoming due at the end of

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each year. Machine would be depreciated on a straight line basis, with no salvage value. Advise the company which option it should go for, assuming lease rents are paid at the end of the year.

Problem No 12

ABC Limited is considering acquiring an additional sophisticated computer to augment its time-share computer services to its clients. It has two options:Either, (a) to purchase the computer at a cost of Rs.44,00,000

Or, (b) to take the computer on lease for 3 years from a leasing company at an annual lease rental of Rs.10 lakhs plus 10% of the gross time-share service revenue. The agreement also requires an additional payment of Rs.12 lakhs at the end of the third year. Lease rentals are payable at the year end and the computer reverts back to lessor after period of contract.

The company estimates that the computer will be worth Rs.20 lakhs at the end of the third year.

The gross revenue to be earned are as follows:

Year 1 2 3Rs. in lakhs 45 50 55

Annual operating costs (excluding depreciation / lease rental) are estimated at Rs.18 lakhs with an additional cost of Rs.2 lakhs for start up and training at the beginning of the first year. These costs are to be borne by the lessee in case of lease arrangement also. The company proposes to borrow @ 16% interest to finance the purchase of the computer and the repayments are to be made as per the following schedule:

Year end

Repayment of principal Interest for year Total

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10,00,00017,00,00017,00,000

7,04,0005,24,0002,72,000

17,04,00022,44,00019,72,000

For the purpose of this computation assume that the company uses the straight line method of depreciation on assets and pays 50% tax on its income.

You are required to analyze and recommend to the company which of the two options is better.

Year 1 2 3P.V. factor @ 8% 0.926 0.857 0.794P.V. factor @ 16% 0.862 0.743 0.641

Problem No 13

Ambit Ltd. is considering a proposal to acquire an equipment costing Rs.5,00,000. The expected effective life of the equipment is 5 years. The company has two options-either to acquire it by

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obtaining a loan of Rs.5 lakhs at 12% interest p.a. or by lease. The following additional information are available:

(i) The principal amount of loan will be repaid in 5 equal yearly instalments.(ii) The full cost of the equipment will be written off over a period of 5 years on straight

line basis and it is to be assumed that such deprecition charge will be allowed for tax purpose.

(iii) The effective tax rate for the company is 40% and the after tax cost of capital is 10%.(iv) The interest charge, repayment of principal and the lease rentals are to be paid on the

last day of each year.You are required to work out the amount of lease rental to be paid annually, which will match the loan option. The discount factors at 10% are as follows:

Year 1 2 3 4 5Discount factor 0.909 0.826 0.751 0.683 0.621

Problem No 14

A Company is planning to acquire a machine costing Rs.5,00,000. Effective life of the machine is 5 years. The Company is considering two options. One is to purchase the machine by lease and the other is to borrow Rs.5,00,000 from its bankers at 10% interest p.a. The Principal amount of loan will be paid in 5 equal instalments to be paid annually. The machine will be sold at Rs.50,000 at the end of 5th year. Following further informations are given:

(a) Principal, interest, lease rentals are payable on the last day of each year.

(b) The machine will be fully depreciated over its effective life.

(c) Tax rate is 30% and after tax. Cost of Capital is 8%.

Compute the lease rentals payable which will make the firm indifferent to the loan option.

Problem No 15

Welsh Limited is faced with a decision to purchase or acquire on lease a mini car. The cost of the mini car is Rs. 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 instalments, 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 the annual lease rental to be charged by the leasing company to match the loan option?

For your exercise use the following discount factors:

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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

Problem No 16

A factory needs equipment for use. It has the option of outright purchase or leasing the equipment. Data are given below. Recommend the best option that the factory should choose.

Option 1

Purchase outright for a cost of Rs.80 lakhs. It is to be entirely financed by a term loan @ 18% p.a. interest on outstanding payable on a yearly basis. The term loan to be repaid in eight equal instalments of Rs.10 lakhs each, beginning from second year-end. The economic life of the equipment is assessed to be ten year. The equipment will be depreciated @ 10% p.a. on straight line basis, with insignificant salvage value at the end of the economic life? The estimated maintenance expenses would be as detailed below:

Year 1 2 3 4 5 6 7 8 9 10MC* 4.00 4.40 4.88 5.47 6.18 7.05 8.11 9.41 11.01 13.00

(*) MC – Maintenance cost in Rs. lakhs

Option 2

The equipment may be leased for a ten-year period. The maintenance of the equipment will be done by the lessor. The lessee has to pay Rs.18 lakhs annual rental at the beginning of each year over the lease period.

Note: Assume that the lessee is in a tax bracket of 50% and average cost of capital of the lessee firm as 14% p.a.

Present value factors for discounting at 14% p.a. given below may be used for ready reference:

1 2 3 4 5 6 7 8 9 100.877 0.769 0.675 0.592 0.519 0.465 0.400 0.351 0.308 0.270

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Net advantage of Leasing (NAL) Method

Problem No 17

A leasing company is planning to install a machine which becomes scrap in 3 years. It requires an investment of Rs.120 lakhs and scrap realizes Rs.25.92 lakhs. The company has following options:

(1) Take a 3 year loan @ 15% and buy that machine; Quantum to be determined, such that annual repayment of principal will be equal to the annual lease payment(2) Take it on lease @ 434/000 payable annually for 3 years in arrears Depreciation is 40% (WDV). Tax rate is 40%. Opportunity Cost of Capital is 11%.

Determine which option is better.

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