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M.Sc. Finance (A4) 1 of 7 To Be Completed (please write clearly)
Department of Accounting and Finance
M.Sc. Finance
And
M.Sc. International Accounting and Financial Studies
Finance I
Class Test A & B
Tuesday 7
th
November 2006 11.00am – 12.00pm (1 hour)
Instructions for Candidates
Answer ALL Questions (in the spaces provided) [Failure
to comply will result in papers not being marked]
Calculators must not be used to store text and/or formulae nor be capable of communication. Invigilators may require calculators to be reset. All answers are to be written in the spaces provided in ink. Please write clearly as illegible writing cannot be marked. If more space is required the answer can be continued on the back of the page where the question appears. Failure to follow these requirements will lead to a deduction of marks.
To Be Issued: Discount Tables
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M.Sc. Finance M.Sc. IAFS
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SOLUTIONS
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Q1. a) Determine the approximate value of the internal rate of return on an investment of £6,000 that is expected to produce a single cash inflow of £11,550 in year 5. (5 marks) NPV = 0 = -6,000 + 11,550 1/(1 + i) 5 (1 + i) 5 = 11,550/6,000 = 1. (1 + i) = 5 √1.925 = 1. i = 0. b) Determine the approximate value of the internal rate of return on an investment of £20,000 that is expected to produce a constant net cash flow of £6,580 for the next four years. (5 marks) NPV = 0 = -2,000 + 6,580 PVAF4/i PVAF4/i = 20,000/6,580 = 3. PVAF4/0. 12 = 3. i ≈ 12 per cent c) An investment of £30,000 is expected to produce a constant net cash flow in perpetuity and offers a yield of 12 per cent whereas the required rate of return is 10 per cent. Determine its net present value and briefly interpret your answer. (5 marks) NPV = 30,000 = [(0.12 – 0.10)/.10] = 6, C = i I = 0.12 x 30,000 = 3, NPV = -30,000 + 3,600 1/0.10 = 6, As the investment is a perpetuity the net cash flow can be determine as the rate of return times the capital outlay. The NPV can then be derived, treating the next cash flow as a perpetuity. d) A loan of £10,00 0 is to be paid off in four equal annual payments and the rate of interest on the balance of the loan is 6 per cent (the payments cover the repayment of capital plus interest). Determine the annual payment. ( 5 marks) Loan = PV (Repayments at the contractual rate of interest) 10,000 = X · PVAF4/. 06 = X · 3. X = 10,000/3.4651 = 2,
Q3. Determine the approximate value of the modified rate of return on the following investment in a natural resource project if outlays are required at the end of its life. The company’s cost of capital is 12 per cent. 0 -40, 1 14, 2 14, 3 14, 4 16, 5 -2, Value in year 4 of the net cash flow in year 5 -2,575 1/1.2 = 2,229 ≈ 2, (10 marks) Adjust value in year 4 16,600 – 2,300 = 14, The discounted rate of return on the adjusted net cash flows = modified rate of return NPV = 0 = -4,000 + 14,300 PVAF4/i PVAF4/i = 40,000/14,300 = 2. PVAF4/0. 16 = 2.7982 use tables (for 4 years!) Modified rate of return ≈ 16% Q4. Demonstrate how you can choose between the following investments to maximise wealth using the discounted rate of return (not the net present value approach). The company’s required rate of return is 8 per cent. Explain briefly the basis of your analysis 0 1 2 3 4 IRR A -10,000 3,292 3,292 3,292 3,292 12 per cent B -16,000 5,157 5,157 5,157 5,157 11 per cent (10 marks) incremental 0 1 – 4 investment -6,000 +1, NPV = 0 = -6,000 + 1,865 PVAF4/i PVAF4/i = 6,000/1,865 = 3. PVAF4/0. 09 = 3. i
≈ 9 per cent > 8 per cent As investment B can be thought of as being made up of investment A and an incremental investment NPV(B) = NPV(A) ± NPV (Incremental Investment) If the NPV (Incremental Investment) is positive then NPV(B) > NPV(A) And the NPV of the incremental investment is positive if its yield is greater than the required rate of return. In this case as the incremental rate of return is 9 per cent and higher than 8 per cent required rate of return the adoption of the larger project will maximise the firm’s NPV.
Q5. Rhoda McTaggart’s runs her own consultancy company. Her estimated net wealth is £150,000, and she intends to retire in ten years and her annual salary after tax is £80,00 0 and current expenditure is £50,000, allowing her to save £30,00 0 per annum. Her pension fund advisor tells her, on the basis of actuarial evidence, that she should plan on an expected life of 16 years following retirement. She wonders how much she will be able to spend on an annual basis during retirement if the rate of interest she can expect to earn on invested funds is 8 per cent, while also maintaining a minimum wealth position of £150,00 0 after the expected 16 years of retirement. (1 0 marks) Q6. Analysis can be done in various ways – though there is only one correct answer! Calculate the funds available at the start of retirement. V 10 = 150,000 (1 + 0.08) 10
- 30,000 1/.08 ((1 + .08) 10
= 150,000 x 2.1589 + 30,000 x 14. = 323,835 + 434, = 758, Resources free for pension – total funds available less present value of the sum required at the end of the 16 year period. V 10
= 758,431 – PV (150,000) = 758,431 – 150,000 1/(1.08) 16 = 758,431 – 43, = 714,
- 714,647 = X · PVAF16/. 08 714,647 = X · 8. X = 714,647/8. = 80, Fallin plc is expected to produce earnings of £36 million next year and to pay out 50 per cent in the form of dividends. Dividends are expected to grow at 6 per cent indefinitely into the future. Investors require a rate of return of 12 per cent on investments in companies such as Fallin. The value of the company can be determined by using the constant rate of growth of dividends model. a) Determine a value for the company. (5 marks) V 0 = 36(1 – 0.5) 1/ 0.12 – 0.016 = 300 b) What rate of return is the company expected to produce on its reinvested earnings? (5 marks) Growth rate = retention rate x rate of retrun 0.06 = 0.50 x i i = 0.06/0.50 = 0. c) If the company’s rate of return on new investments increased to 15 per cent while retentions remain at 50 per cent determine the increase in the value of the company and comment on your results. (5 marks) V 0
= 36(1 – 0.5) 1/(0.12 – 0.075) = 400 The increment in value comes from the present value of growth opportunities. This is based on the assumption that 50 per cent of earnings can be re-invested annually to earn 15 per cent. The PVGO is equal to £100m.
Q7. The price earnings ratios reported in the Financial Times for Stirling Electronics and Resolven Electronics are 16/1and 24/ 1 respectively. Both companies operate in the same industrial sector and are about the same size. Identify factors that might account for the differences in their price-earnings ratios. The price-earnings raio can be derived from the valuation models. ( 5 marks) P 0 =
PVGO
= ( 1 − b )^
E 1 r E 1 r − bi The P/E ratio will be higher
- The lower the value of r.
- The greater the PVGO or the higher the value of i, and if i, is greater than r, the higher the value of b (the retention ratio). Difference in r between the two companies are not likely to be significant if they are drawn from the same industry unless they have difference levels of gearing. (This observation could not be expected on the basis the Finance I material!) The primary differences are most likely to arise because of the differences in growth opportunities – with Resolven having more opportunities than Stirling. The differences could arise in part from differences in accounting policies, eg. Resolven might be writing off its assets (higher depreciation charges) more rapidly than Stirling, thereby decreasing earnings and increasing the price-earnings ratio. (Accounting differences are unlikely to explain all of such a wide gap in the price earnings ratio). Another possibility is the earnings of Resolven may be temporarily low. If the low level earnings is not expected to be maintained the price will fall less than earnings, thereby pushing up the price-earnings ratio.
Q8. Friction plc is considering replacing some stacking equipment. The existing equipment was bought six years ago for £400,000 and is still in good working order. While it could be used for another ten years it is being depreciated for tax purposes on a straight line basis over an assumed working life of ten years. If it is replaced now it could be sold for scrap for £30,000, but if it is used for another ten years it would have little or no value. The new equipment is much more efficient and would reduce operating costs by £120,000 per annum. It would cost £600,000, has an estimated working life of ten years and would be depreciated for tax over this time period on a straight line basis. A residual value of £50,000 is anticipated. Is this a profitable investment if the required rate of return is 8 per cent and the tax rate is 40 per cent? (Set out all your calculations!) (10 marks) Profit and Loss 0 1 – 4 5 – 10 10 Capital Loss (OM) - Capital Gain (NM) 50 Cost Savings 120 120 Change in Depreciation (20) (60) Change in Profit -130 100 60 50 Change in Tax 52 (40) (24) (20) Net Cash Flow 0 1 – 4 5 – 10 10 Recovery Value (OM) 30 Investment (600) Recovery Value 50 Cost Savings 120 120 Change in Tax 52 (40) (24) (20)
