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Department of Accounting and Finance
M.Sc. Finance
And
M.Sc. International Accounting and Financial Studies
Finance I and II
Tuesday 9th January 2007 10.00am – 1.00pm (3 hours)
Instructions for Candidates
Answer ALL Questions from Section A (in the spaces provided),
ONE Question from Section B (in the answer book)
and ONE Question from Section C (in the answer book)
[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
To Be Completed (please write clearly)
Family Name:
Other Name:
Course (please indicate by ticking appropriate box)
M.Sc. Finance M.Sc. IAFS
For Examiners Use Only
SOLUTIONS
SECTI
ON A
TOTAL
MARKS
you
I
(3 marks)
Project Net Cash Flows IRR
0 1 → 6
1 (20,000) 4,865 12%
2 (30,000) 6,888 10%
ncremental (10,000) 2,023 5.8%
Q3. Determine the approximate value of the modified rate of return on the following
investment in a strip mining operation which requires an expenditure at the end of its life to restore the land to its original state, if its current borrowing rate is 8 per cent.
(3 marks)
Period
0
NCF
Adjusted NCF
-10, 1 2,572 2, 2 2,572 2, 3 2,572 2, 4 2,572 2, 5 2,572 2, 6 3,500 926 2,572* 7 -1, NPV = 0 = -10,000 + 2,572 x PVAF6/i
PVAF6/i = 10,000/2,572 = 3.
PVAF6/0.4 = 3.
i ≈ 14 per cent
Q4. Gwyn Ltd plc is considering replacing one of its machines that has become expensive to maintain and repair. The new machine is more efficient and will produce manufacturing cost savings of £80,000 per annum, as well as eliminating the maintenance and repair costs that amount to £30,000 per annum. The new machine costs £220,000 and will be used for the next five years after which it would be sold. Its sale can be expected to realise £20,000. The expenditure on the machine can be written off for tax purposes on a straight line basis over five years. The machine to be replaced could be kept in operation for another five years as long as the company continues to cover the annual expenditure on maintenance and repairs. The existing machine’s accounting value for tax purposes is zero, but could be sold today for scrap to realise £10,000. The greater reliability of the new machine implies that Gwyn Ltd. plc could cut its holdings of stocks from £120, to £60,000. Is this a profitable investment if the required rate of return is 14 per cent and the tax rate is 30 per cent?
(4 marks)
b) How much does the expected rate of growth contribute to the share price?
(2 marks)
No growth
P 0 = E11/r = 60 1/0.15 = 400
PVGO = -
IRR = growth rate/retention rate = 0.07/.6 = 0.1167. 11.67 per cent is less than the required rate of return of 15 per cent.
Q7. Hunter plc has achieved a rate of growth of 35 per cent over the last five years by reinvesting a relatively high proportion of its earnings and maintaining a high rate of return on its new assets. The company has followed a policy of financing all investment from retentions. The company has been reinvesting 80 per cent of earnings and plans to do so again next year. The following year it is anticipated that the retentions will be limited to 70 per cent of earnings as the scope for profitable investments is reduced. Three years from now investment and retentions will be restricted to 40 per cent of earnings, its anticipated long term level of retentions. The investment to be undertaken next year is expected to produce an internal rate of return of 45 per cent. This return is expected to fall to 30 per cent on the investment undertaken in year two and to fall to 15 per cent on investments undertaken from year three onwards. The minimum rate of return acceptable to shareholders, the return available on similar risk investments available in the capital market, is also
15 per cent. Next year the company is expected to produce earnings of £40m. Determine a value for the company today, and indicate the proportion of the value accounted for by its growth prospects.
(4 marks)
YEAR 1 2 3 4 5
INITIAL EARNINGS 40
RETENTION RATE 0.80 0.70 0.40 0.
RATE OF RETURN
ON INVESTMENT 0.45 0.30 0.15 0.
DISCOUNT RATE 0.
GROWTH RATE 0.36 0.21 0.06 0.
Yea Next
r Earnings Retention Dividend Retentions Rate of NPV Incremental Period Ratio Investment Return Earnings Earnings
1
40.00 0.80 8.00 32.00 0.45 64.00 14.40 54.
2 54.40 0.70 16.32 38.08 0.3 38.08 11.42 65. 3 65.82 0.40 39.49 26.33 0.15 0.00 3.95 69. 4 69.77 0.40 41.86 27.91 0.15 0.00 4.19 73. 5 73.96 0.40 44.38 29.58 0.15 0.00 4.44 78. 6 78.40 0.40 47.04 31.36 0.15 0.00 4.70 83.
DIVIDEND MODEL
YEAR Dividends
Terminal
Value (^) PVF
Present
Value 1 8.00 0.8696 6. 2 16.32 0.7561 12. 3 39.49 0.6575 25. 4 41.86 0.5718 23. 5 44.38 0.4972 22. 5 522.65 0.4972 259. 2 351. 8
EARNINGS MODEL
YEAR Earnings NPVs PVF
Present
Value 1 1.00 6.6667 266. 7 1 64.00 0.8696 55. 2 38.08 0.7561 28. 3 0.00 0.6575 0. 4 0.00 0.5718 0. 5 0.00 0.4972 0.
Q8. a) Determine the expected return and risk on a portfolio made up of 70 per cent
of A and 30 per cent of B, if the expected return on A is 20 per cent with a standard deviation of 15 per cent, the expected rate of return on B is 25 per cent with a standard deviation of 20 per cent, and the correlation coefficient for the returns on A and B is +0.40.
E(Rp) = w A E(RA ) + w B E(R B)
= 0.7 x 20 + 0.3 x 25
= 21.
(2 marks)
VAR
(R p) = w 2
VAR(R A )+wB2 VAR(R B)+2 w A wB ρ AB SD(R A) SD(R B)
= 0.7 2 x 152 + 0.3 2 x 202 + 2(0.3)(0.7)(0.4)(25)(20)
= 196.
SD(Rp) = 14.
b) Given the following information on securities X and Y determine the zero risk portfolio and the rate of return on this portfolio if the returns on these securities are perfectly negatively correlated.
Security X Security Y Expected Return 21% 30% Standard Deviation 12% 24%
w x = SD(Ry)/SD(Rx) + SD(Ry)
w y = 1/
E(Rp) = 2/3 x 21 + 1/3 x 30 = 24 per cent
(2 marks)
Q9. The risk free rate of interest is 6 per cent and the expected return on the market is 15 per cent, with a standard deviation of 18 per cent.
a) What is the risk and return of a portfolio made up of 40 per cent of the risk free asset and 60 per cent of the market portfolio?
E(Rp) = (1 – wm)R F
= 0.40 x 6 + 0.60 x 15
= 11.4 per cent
SD(Rp)^ = wmSD(R^ m)
= 0.6 x 18 = 10.4 per cent
b) Determine the beta of this portfolio.
βp = (1 – w)βF
= wβm
= 0.6 x 1. = 0.
(1 mark)
(1 mark)
c) How should a portfolio, consisting of the risk free asset and the market portfolio, be structured to produce a risk (standard deviation) of 6 per cent?
(2 marks)
Q10. a) The expected return on security X is 23 per cent and the expected return on security Y is 17 per cent. The beta of security X is 1.3 and that of security Y is 0.70. Determine the expected rate of return on the market portfolio and the risk free rate of interest. (2 marks) E(Rx) = 23 = RF + 1.30 R p (1) E(Ry)
R p
= 17 = RF + 0.70 R p
= 6 = 0.6 Rp
= 10
Substitute into the return equation for X
E(Rx) = 23 = RF + 1.30 x 10
R F = 10
E(Rm) = 20
b) The standard deviation of the return on X is 21 per cent while the standard deviation of the return on the market portfolio is 12 per cent. Given the beta of security X of 1.3 determine the correlation of its returns with those of the market.
βx = 1.3 = ρxmS D(R x)/ SD(Rm) = ρ xm 21/
ρ xm^ = 1.3 x 12/21 = 0.
(2 marks)
Q11. The beta for the shares of Strade plc has been estimated at 1.5. The risk free rate of
interest is 6 per cent and the expected rate of return on the market is 15 per cent. The return on Strade’s shares last year was 18 per cent, whilst the return on the market was only 12 per cent. Determine the abnormal return on Strade’s shares during this period and draw a diagram to illustrate your answer.
E(Rs) = RF + β s [E(Rm) –
R F]
= 6 + 1.50 [15 – 6] = 19.
E(Rst^ /Rmt)^ = 6 + 1.50 [12 – 6] = 15.
AR st^ = Rst^ – E(Rst/R^ mt)
= 18.0 – 15.
= 3 per cent
(2 marks)
R st
AR
Characteristic Line
12 15 R mt
b) A runs test. (2 marks)
Q14. a) A call with an exercise price of 230p has been written on a share that is
currently trading at 220p. The interest rate for the nine month period to the expiry of the call is 8 per cent. Determine the minimum value for the call if it is traded in a perfect market. Comment briefly on why you would expect the market price to exceed this minimum value.
C 0 ≥ S 0 – PV(X)
C MIN^ = 270 – 230
(2 marks)
b) Draw a diagram to illustrate a covered call for the shares of Dorian plc if the current share price is 118p, the exercise price on a call is 130p and the market price of the call is 9p.
(2 marks)
(TOTAL 50 MARKS)
[Please Turn Over]
For Examiners Use Only
Page
Total
Cumulative
Mark
Section C Answer ONE Question
Q1. Explain how diversification can reduce risk and what is meant by the efficient set of portfolios. (25 MARKS)
Q2. Explain what is meant by the capital market line, show how it is derived, and consider its implications. (25 MARKS)
Q3. Discuss the determinants of the beta of a company's shares and explain how the capital asset pricing model can be employed to determine the cost of capital to be used in the evaluation of a company’s proposed investments. (25 MARKS)
Q4. Explain what is meant by an efficient market and discuss the three forms of the efficient market hypothesis proposed by Fama. (25 MARKS)
End of Paper
