PARIS GRADUATE SCHOOL OF MANAGEMENT

INTERNATIONAL EXECUTIVE PROFESSIONAL MBA

COURSE: CORPORATE FINANCE

STUDENT NAME: NASARA ABUOSI FRANCIS

STUDENT ID: WA 10295

MARCH, 2011

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22ND BATCH TAKE HOME EXAMINATION

Q1. What are the theoretical justifications for the NPV decision rules?

Net Present Value (NPV)

A project’s NPV equals to the sum of its cash inflows and outflows, discounted at a rate that is consistent with the project’s risk.

In fact, if you receive cash you are quite likely to save it and put it in the bank. So what a business sacrifices by having to wait for the cash inflows is the interest lost on the sum that would have been saved.

Looked at another way, it is likely that the business will have borrowed the capital to invest in the project. So, what it foregoes by having to wait for the revenues arising from the investment is the interest paid on the borrowed capital.

NPV is a technique where cash inflows expected in future years are discounted back to their present value. This is calculated by using a discount rate equivalent to the interest that would have been received on the sums, had the inflows been saved, or the interest that has to be paid by the firm on funds borrowed.

To make sensible investment decisions, a good financial analyst should use a method that considers all of the costs and benefits of each investment opportunity, and makes a logical allowance for the timing of those costs and benefits. The net present value (NPV) method provides for these investment assessment criteria. The NPV is a financial valuation concept that is essential to all financial modeling projects.

The NPV of an investment is the present value of its cash inflows minus the present value of the cash outflows. Why would $100 to be received in a years time be as unequal in value to $ 100 to be paid immediately?

The 3 major reasons are:

Interest Lost Risk Effects of inflation

The steps involved in computing NPV are:

1. Identify all cash flows2. Determine, r, the discount rate

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3. Using discount rate, find PV4. Sum all PVs5. Apply NPV rule. If NPV is positive, investor should undertake it else not undertake

This simplified formula illustrates the NPV method:

PV of the cash flow of year n = Actual cash flow of year n / (1+r) ^ n

The basic rule for NPV is that if the project shows a positive NPV, we need to accept the project. This is because the underlying rule is that if a project has a positive NPV it increases the shareholder wealth because all money goes to investors.

The NPV decision rules are:

Projects with positive NPV should be accepted Projects with negative NPV should be rejected In case of mutually exclusive projects, the one with higher NPV should be selected

When the project NPV is zero, the rate at that point of time is considered to be its Internal Rate of Returns (IRR).

The NPV method is used for evaluating the desirability of investments or projects.

where:

Ct = the net cash receipt at the end of year tIo = the initial investment outlayr = the discount rate/the required minimum rate of return on investmentn = the project/investment's duration in years.

The discount factor r can be calculated using:

Justification of the NPV rule

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The NPV rule makes intuitive sense, is easy to use, and can be justified as the appropriate evaluation technique since it leads to the maximization of shareholder wealth. To prove that this is the case, consider the simple economy described below. We assume that:

all cash flows are perpetuities, all earnings after interest and taxes are paid out as dividends, the firm is financed with only two types of securities; common stock and perpetual

bonds.

We use the following notation:

E00

Market value of old shareholders common stock before investment.

E10 Market value of old shareholders common stock after

investment.

D00 Market value of old bondholders bonds before

investment.

D10 Market value of old bondholders bonds after investment.

V0 Total market value of the firm before investment.

V1 Total market value of the firm after investment.

p0 Price per share of common stock before investment.

p1 Price per share of common stock after investment.

n0 Number of shares of common stock before investment.

n1 Number of shares of common stock after investment.

X0 Firm’s net cash flow before investment.

X1 Firm’s net cash flow after investment.

E1n Market value of new common stock issued to finance the

investment.

D1n Market value of new bonds issued to finance the

investment.

C Coupon payment on perpetual bonds.

Note that since all new investments are financed with either new common stock (equity) or new bonds (debt),

(a)

Now suppose the firm undertakes the proposed investment projected. The total market value of the firm after the investment is:

(b)

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where the value of the firm before the investment is

(c)

Subtracting Equation (c) from Equation (b), therefore, gives us the incremental value of the firm as a result of undertaking the investment project,

(d) V1 - V0 = (E10 - E0

0) + (D10 - D0

0) +1

where the identity in Equation (a) was applied to Equation (d) for simplification.

Since we are interested in identifying whether the shareholders existing before the investment (i.e., the old shareholders) benefit from the firm undertaking the investment project, we rearrange Equation (d) to yield:

(e) E10 - E0

0 = (V1 - V0) - (D10 - D0

0) - 1

The second term on the right-hand-side of Equation (e) is the change in the value of the old bonds as a result of undertaking the investment. As long as the investment does not affect the probability of default, the market value of the old bonds before the investment,

(f)

is the same as the value of the old bonds after the investment,

(g)

Since D00 = D1

0, Equation (e) simplifies to:

(h) E10 - E0

0 = (V1 - V0) - 1

Focusing on the term V1-V0, first recognize that the firm’s value may be expressed as the present value of the firm’s cash flows both before and after the investment

(i)

and

(j)

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Subtracting Equation (i) from Equation (j) yields:

Substituting Equation (k) into Equation (h), we find that the NPV of the project may be interpreted as the increment to shareholder wealth,

Conclusion

The decision rule of NPV is very important to the life of any project yet to undertaken. A zero

NPV represents a break-even point , a positive NPV means a firm is creating wealth for its

shareholders and a negative NPV indicates that the firm is destroying wealth by undertaken such

a project. It is however worthy of note that, a zero NPV means an investment will increase the

book value of the firm’s assets but will neither create nor destroy wealth. Under this

circumstance however, shareholders becomes indifferent to whether accept or reject a project.

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Q2. Explain what is meant by conventional and unconventional cash flows and what problems

they might cause in investment appraisal.

Introduction

Although financial managers are interested in the information in the firm’s accrual-based

financial statement, their primary focus is on cash flows. Without adequate cash to pay

obligations when the fall due, to fund operations and growth, and to compensate owners, the firm

will fail.

The process of evaluating a firm’s cash flows involves analyzing cash and marketable securities

as perfect substitutes. They both represents a reservoir of liquidity that increases with cash

inflows and decreases with cash outflows.

A firm’s cash flows can be divided into;

1. operating flows which involves cash inflows and outflows directly related to the

production and sale of products or services.

2. Investment flows which includes cash flows associated with the purchase or sale

of fixed assets and business equity. Purchases generates outflows whiles sales

generates inflows.

3. Financing flows which results from debt and equity financing transactions.

Taking on a new debt (short term or long term) results in cash inflows whiles

repaying debts requires cash outflow.

Measurement of cash flow can be used for calculating other parameters that give information on a company's value and situation. Cash flow can e.g. be used for calculating parameters:

to determine a project's rate of return or value. The time of cash flows into and out of projects are used as inputs in financial models such as internal rate of return and net present value.

to determine problems with a business's liquidity. Being profitable does not necessarily mean being liquid. A company can fail because of a shortage of cash even while profitable.

as an alternate measure of a business's profits when it is believed that accrual accounting concepts do not represent economic realities. For example, a company may be notionally profitable but generating little operational cash (as may be the case for a company that barters its products rather than selling for cash). In such a case, the company may be deriving additional operating cash by issuing shares or raising additional debt finance.

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cash flow can be used to evaluate the 'quality' of income generated by accrual accounting. When net income is composed of large non-cash items it is considered low quality.

to evaluate the risks within a financial product, e.g. matching cash requirements, evaluating default risk, re-investment requirements.

Conventional Cash FlowA conventional cash flow pattern is a time series of outgoing and incoming cash flows that has only one change in direction or sign. For example, a project might have an initial outlay of $200,000 and then future cash inflows of $60,000 each year for the next five years. This would result in a cash flow pattern of -, +, +, +, +, +, which is only one change in sign.

Unconventional Cash FlowAn unconventional cash flow pattern is a series of cash flows that has more than one change of sign. For example, the pattern of -, +, -, +, +, + represents an unconventional cash flow pattern.

Investment Appraisal

One of the key areas of long-term decision-making that firms must tackle is that of investment - the need to commit funds by purchasing land, buildings, machinery and so on, in anticipation of being able to earn an income greater than the funds committed. In order to handle these decisions, firms have to make an assessment of the size of the outflows and inflows of funds, the lifespan of the investment, the degree of risk attached and the cost of obtaining funds.

The main stages in the capital budgeting cycle can be summarised as follows:

1. Forecasting investment needs.2. Identifying project(s) to meet needs.3. Appraising the alternatives.4. Selecting the best alternatives.5. Making the expenditure.6. Monitoring project(s).

Looking at the above, investment appraisal is involved in stage 3 and 4 of this cycle.

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Q3. RAILCAM (A Supplier to the Railway Industry)

i. We first compute the debtors schedule

Debtors Schedue for the Period 20X1 to 20X5

YEAR 20X1 20X2 20X3 20X4 20X5 20X6

Sales (£) 20m 22m 24m 21m 25m -

ii. We also compute for raw materials. It is however stated in the question that, raw

materials cost one-half of sales (sales figure divided by two)

Raw Materials schedule for the Period 20X1 to 20X5

Year 20X1 20X2 20X3 20X4 20X5 20X6

Workings 20m÷2 22m÷2 24m÷2 21m÷2 25m÷2 -

Raw materials

(£)

10m 11m 12m 10.5m 12.5 -

iii. Cash Flow Statement for the Period 20X2 to 20X4

Years 20X2 20X3 20X4

Receipts: Sales (£) 22m 24m 21m

LESS Payments: Raw materials

(£)

11m 12m 10.5m

Direct overheads

(£)

5m 5m 5m

Wages (£) 6m 6m 6m

Total Payments

(£)

22m 23m 21.5m

Receipts Less

Payments

Net Cash Flows

(£)

0 1m (0.5m)

Explanations to Net cash flows realized from the various years

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20X2: the Net cash flow of zero indicates that the company has broken even. This means that

sales is equal to operating costs. This is acceptable especially for a new product lunch whiles

they expect to generate future profits.

20X3: this year’s results of one million pounds sterling indicates a gain or profit to the

organization. It could be assumed that the product is gaining grounds and more promotional

strategies such as advertising and sales needs to be more aggressive in order to boost profit

levels.

20X4: a negative return of half a million is made in this year. This may be as a result of high cost

of raw materials which is 50% of total sales. Strategies aimed at purchasing raw materials from a

relatively low price should be looked at whiles taking keen interest in quality. A number of

suppliers should be sampled to arrive at this strategy. If all these fails to produce a positive net

cash flow, it may not be financially wise to embark on this kind of business.

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Q4. PINE LIMITEDa. Computation of NPV for the purpose of project appraisal

Periods 0 20X1 20X2 20X3 20X4 20X5 20X6Sales (£) - - 400 400 400 320 200LESS other costs:MaterialsVariable costsFixed Overheads (40% of total)

24040

8

24040

8

24040

9.6

19232

9.6

12020

9.6

--

-Totals 288 288 289.6 233.6 149.6 -Net Trading Inflows (Sales Less other costs)

- (288) 112 110.4 166.4 170.4 -

ADD:Initial investmentScrap

(240) --

--

--

--

-40

--

Capital Inflows:MaterialsOther variable cost

--

(30)(20)

--

--

--

3020

--

(Net trading + other inflows)

(240) (338) 112 110.4 166.4 260.4 200

Discounted Factor (12%) 1 0.893 0.797 0.712 0.636 0.567 0.507Present Values (240) (301.8) 89.3 78.6 105.8 147.7 101.4NET PRESENT VALUE (240)+(301.8)+89.3+78.6+105.8+147.7+101.4 = (19)The decision rule is that, reject projects with negative NPV. A negative NPV of £19m indicates that Pine Ltd should not go on with the project.

b. Explain to a management team unfamiliar with discounted cash flow appraisal techniques the significance and value of the NPV method. The NPV method is very important in any management decision. To make sensible investment decisions, a good financial analyst should use a method that considers all of the costs and benefits of each investment opportunity, and makes a logical allowance for the timing of those costs and benefits. The net present value (NPV) method provides for these investment assessment criteria. The NPV is a financial valuation concept that is essential to all financial modeling projects.

The decision rule of NPV is very important to the life of any project yet to undertaken. A

zero NPV represents a break-even point , a positive NPV means a firm is creating wealth

for its shareholders and a negative NPV indicates that the firm is destroying wealth by

undertaken such a project. It is however worthy of note that, a zero NPV means an

investment will increase the book value of the firm’s assets but will neither create nor

destroy wealth. Under this circumstance however, shareholders becomes indifferent to

whether accept or reject a project.

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Q5.

a. Payback Method : It refers to the length of time it will take a project to start yielding profits. It is computed as: Total of periods before complete recover PLUS (unrecovered investment DIVIDED by Cash flow during the period of complete recovery)

Investment Initial Investment (£)

Computation (£) Payback period

A 3,000 P1+P2+P3+P4+P5+P6= 3,000500+500+500+500+500+500=3,000

6 years

B 10,000 P1+P2+P3=10,0002000+5000+3000= 10,000

3 years

C 15,000 P1+P2+P3=15,000But 5000+4000+4000=13,000, and next value of 5000 will add up to make it 18,000 so we apply the formular3years + (15000-13000)/5000=3years + 0.4

3.4 years

D 4,000 P1+P2+P3+P4=40001000+1000+1000+1000 = 4000

4 Years

E 8,000 PI+P2+P3+P4=8000But 500+500+500+2000=3500 and next period value will add up to 8500, therefore we apply formular4years + (8000-3500)/5000=4years + 0.9

4.9 years

The decision rule of the payback method is that, we should accept projects with a shorter payback period. From the above therefore, it will be wise and financially prudent to invest in B since it has the shortest payback period of 3.

b. With the discounted cash flows, cash inflows are discounted to their present values, where present Value (PV) = Future cashflow ÷ (1+cost of capital(r))*period (t).

Therefore we first compute the PVs of each investment using 12% as cost of capitalPeriods A PV.A B PV.B C PV.C D PV. D E PV.E0 (3000) - (10000) (15000) (4000) (8000)1 500 446.5 2000 1786 5000 4465 1000 893 500 446.52 500 398.5 5000 3985 4000 3188 1000 797 500 398.53 500 356 3000 2136 4000 2848 1000 712 500 3564 500 318 2000 1272 5000 3180 1000 636 2000 12725 500 283.5 - - 10000 5670 7000 3969 5000 28356 500 253.5 - - - - 7000 3549 10000 50707 500 226 - - - - 7000 3164 -From the above calculations, the payback method is now used to compute the payback periods for each investment.

Investment Initial Computation (£) Payback

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Investment (£)

period

A 3,000 P1+P2+P3+P4+P5+P6+P7= 3,000446.5+398.5+356+318+283.5+253.5+226=2,281The value is not even up to the initial cashflow

More than 7 years

B 10,000 P1+P2+P3+P4=10,0001786+3985+2136+1272= 9,179The sum of the PVs of this project is inefficient

More than 4years

C 15,000 P1+P2+P3+P4=15,000But 4465+3188+2848+3180=13,681, and next value of 5670 will add up to make it 19,351 so we apply the formular4years + (15000-13681)/5670=4years + 0.2 4.2 years

D 4,000 P1+P2+P3+P4=4000But 893+797+712+636+ = 3038 and the next PV is 3969 so we apply the formular4years + (4000-3038)/39694+0.2

4.2 Years

E 8,000 PI+P2+P3+P4+P5=8000But 446.5+398.5+356+1272+2835=5308 and next period value will be 5070, therefore we apply formular5years + (8000-5308)/5070=5years + 0.5

5.5 years

The decision rule of the payback method is that, we should accept projects with a shorter payback period. From the above therefore, it will be wise and financially prudent to invest in C or D because they both have a payback period of 4.2 which are also the least among the projects.

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Q6. WASHER DIVISION OF PLUMBER PLCi. Computation of NPVs for various projects using a cost of capital of 12%

Years A PV.A B PV.B C PV.C D PV.D E PV.E(£)m (£)m (£)m (£)m (£)m (£)m (£)m (£)m (£)m (£)m

0 (1.5) (2.0) (1.8) (3.0) (0.5)1 0.5 0.45 0 0 0 0 1.2 1.07 0.3 0.272 0.5 0.40 0 0 1.2 0.96 1.2 0.96 0.3 0.243 1.0 0.71 0 0 1.2 0.85 1.2 0.85 0.3 0.214 1.0 0.64 4.2 2.67 1.2 0.76 1.2 0.76 0.3 0.19Total PVs

2.20 2.67 2.57 3.64 0.90

NPVs= PV-y0

0.7 0.67 0.87 0.64 0.40

a. The decision rule states that, choose a project with a positive NPV. According to the computation above, the profitability or viability of the projects can be arranged from most viable to less viable as follows; Project C, Project A, Project B, Project D and Project E. However, since the projects are not mutually exclusive and they all also have positive NPVs, they can all be undertaken.

b. If all projects are undertaken, the level of NPV that will be achieved will be the sum of the individual NPVs. i.e. 0.87+0.70+0.67+0.64+0.4 = £ 3.26. Averagely each project will be 3.26/5= £ 0.65m of NPV.

c. Assuming that these projects are mutually exclusive, the following will be the decisionProjects ranked from best

NPVS Initial Investments of each project

Allocation of £5m

C 0.87 1.80 5m-1.80m=3.20A 0.70 1.5 3.20-1.50 = 1.70B 0.67 2.00 The remainder of 1.70m is

not enough to invest in this next viable project.

D 0.64 3.00E 0.4 0.50

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Q7. Computation of IRRa. Calculations to determine cashflow or Gross profit

Sales revenue per annumLess: Variable costs per annum

£21 x22000 units

£16 x 22000 units

£462,000

£352,000Sales Less Variable cost(Cashflow)

£110,000

Investment in Machinery £400,000

Since cost of capital is not known, we assume 10% and 20% as cost of capital for determining their NPVs.Year

Cashflows( £)10% Discount Factor

PV (£) 20% Discount Factor

PV (£)

0 400,000 (400,000) (400,000)1 110,000 0.909 99,990 0.833 91,6302 110,000 0.826 90,860 0.694 76,3403 110,000 0.751 82,610 0.579 63,6904 110,000 0.683 75,130 0.482 53,0205 110,000 0.621 68,310 0.402 44,2206 110,000 0.564 62,040 0.335 36,8507 110,000 0.513 56,430 0.279 30,6908 110,000 0.467 51,370 0.233 25,6309 110,000 0.424 46,640 0.194 21,34010 110,000 0.386 42,460 0.162 17,820NPVs 275,840 61,230

However, IRR = (NPV of lowest discount rate ÷ Range of the 2 NPVs)(High discount rate – lowest discount rate) + lowest discount rate.

= [275,840 ÷ (275,840-61230)] [0.2-0.1] + 0.1 =1.285(0.1) + 0.1 =0.1285+0.1 = 0.2285 or 22.85%This means that management should accept any required return that is lower than 22.85%

b. Recalculation of IRR with the assumption that there is an adverse change of 5%

Sales revenue per annumLess: Variable costs per annum

(95% of £21)(95% of 22000 units)

(95%£16)(95% 0f 22000

£416,955

£317,680

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units)Sales Less Variable cost (Cashflow)

£99,275

Investment in Machinery £400,000

Using the same discounting factors of 10% and 20%, Year

Cashflows( £)10% Discount Factor

PV (£) 20% Discount Factor

PV (£)

0 400,000 (400,000) (400,000)1 99,275 0.909 90,241 0.833 82,6962 99,275 0.826 82,001 0.694 68,8973 99,275 0.751 74,556 0.579 57,4804 99,275 0.683 67,805 0.482 47,8515 99,275 0.621 61,650 0.402 39,9096 99,275 0.564 55,991 0.335 33,2577 99,275 0.513 50,928 0.279 27,6988 99,275 0.467 46,361 0.233 23,1319 99,275 0.424 42,093 0.194 19,25910 99,275 0.386 38,320 0.162 16,083NPVs 209,946 16,261Using the formula IRR = (NPV of lowest discount rate ÷ Range of the 2 NPVs)(High discount rate – lowest discount rate) + lowest discount rate.

= [209946 ÷(209946-16261)] [0.2-0.1] + 0.1= 1.083(0.1) + 01= 0.2083 or 20.83%Therefore any required rate of return lower than 20.83% should be accepted.

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Q8. RJW PLC

a. Calculation of the expected net present value and the standard of deviationPlease find the attached excel sheet the complete computation of the NPV

From the above computation, the expected value of NPV is (£776.22M) is a negative and very unattractive and therefore RJV Plc should not buy the English Lignite Mines.

EXPECTED PRESENT VALUE OF CASH FLOWS (£M) 123.78

LESS: INITIAL INVESTMENT ( £M) ( 900.00)

EXPECTED VALUE OF NPV ( £M) (776.22)

b. Already the NPV of negative 776.22m Euros is worse than the expected worse situation of 550m Euros will produce a probability of zero. This means that if RJW Plc goes ahead with this investment under this situation, it will be liquidated.

c. Considering this high negative NPV expected, it is just not prudent for RJW to go ahead with this kind of investment. An NPV of more than 100m Euros will still be insufficient to produce a rising share price considering the high investment involved in this project.

Q9. PENGIUN PLCs

a. We can consider the following to arrive at an economically wise decisioni. Savings as a result of discount is 2% of (0.8x12) = £0.19mii. This is financed by overdraft extra = 70days – 7days = 63days

Cost = 15% of (63÷365)(9.6) = £0.25miii. Net Savings is therefore £0.19m - £0.25m = -£0.06m.

The above analysis indicates that it is not worthwhile accepting the discount but the current arrangements should be maintained. Penguin can even further negotiate for a better deal.

ALTERNATIVELYi. Discount as a percentage of amount paid = 0.19÷(98% of 9.6) X 100= 2.04%ii. Savings in 63 days = 365÷63 = 5.79 or 6daysiii. Average cost = (1+0.0204)*6 – 1 = 0.1288 Or 12.88%. However overdraft is 15%

b. 1. Steps to improve balance sheet. I will answer this by computing some few ratios

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i. Current ratio = current assets ÷ current liabilities, = 4.5÷9 = 0.5 : 1. An ideal ratio is 1.5 : 1. This indicates that the company is overtrading and therefore needs more liquid assets.

ii. Equity gearing = Debt÷Equity, = (4+4+5)÷5 = 2.60 or 260%. Considering the capital structure of Penguin, an equity gearing of 260% makes the company highly geared. It will therefore be prudent for Penguin to improve its capital structure by issuing more equity shares. This could take the form of rights issue or a new issue of equity shares. The proceeds from this could be used to improve the liquidity position of Penguin to meet its short term obligation when they fall due.

2. Steps to improve the Profit and Loss i. The company has to improve its cost of sales and overheads since that alone constitutes 90.5% of annual sales. ii. More materials should be acquired at high quality and moderate prices and the company should beef up its promotional activities.

iii. Budgets should also be drawn to help monitor transactions

3. Steps to help improve cash flow i. Steps should be taken to reduce debtors collection period as well as negotiate for an extension of creditors payment periods.

Q10. WHITBORROW PLC

i. Debtors ScheduleSept (£) Oct (£) Nov (£) Dec (£) Jan. (£) Feb (£)

Sales 400,000 450,000 550,000 700,000 - -Cash (20%) 55,000 90,000 110,000 140,000 - -September receipts

- 165000 180,000 -

1 month after (70%)

- - 315,000 385,000 490,000 -

2 months after (10%)

- - - 45,000 55,000 70,000

Cash Receipts

55,000 255,000 605,000 570,000 545,000 70,000

ii. Creditors ScheduleSept (£) Oct (£) Nov (£) Dec (£) Jan. (£) Feb (£)

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Sales 400,000 450,000 550,000 700,000 - -Variable cost 100÷140

286,000 321,000 393,000 500,000 - -

Labour & other costs

(40,000) (45,000) (55,000) (70,000) - -

Materials 246,000 276,000 338,000 430,000 - -

Cashflow statement for the period for October to DecemberOct. Nov. Dec. Total

Receipts:Sales (workings i) 255,000 605,000 570,000 1,430,000

Payments: Materials(workings ii)Labour & other expense

276,00045,000

338,00055,000

430,00070,000

1,044,000170,000

Total Payments 321,000 393,000 500,000 1,214,00NET CASH FLOW (receipts – payments)

(66,000) 212,000 70,000 216,000

Opening Balances (70,000) (136,000) 76,000 130,000Closing Balances (136,000) 76,000 146,000 86,000

Management concerns are valid as cash available in December is £146m. However, other means of raising funds could help top up to buy the equipment especially through overdraft.

REFERENCES1. Megginson, Smart and Graham (2010), Financial Management, third edition,

international edition

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