Examiners' commentaries 2011

Examiners’ commentaries 2011 

92 Corporate finance – Zone B 

Important note 

This commentary reflects the examination and assessment arrangements 

for this course in the academic year 2010–11. The format and structure 

of the examination may change in future years, and any such changes 

will be publicised on the virtual learning environment (VLE). 

Format of the examination paper 

Candidates should answer FOUR of the following EIGHT 

questions: ONE from Section A, ONE from Section B and TWO 

further questions from either section. All questions carry equal 

marks. 

A list of formulas, extracts from Present Value and Annuity Discount 

tables, are given at the end of the paper. 

A calculator may be used when answering questions on this paper 

and it must comply in all respects with the specification given with 

your Admission Notice. The make and type of machine must be 

clearly stated on the front cover of the answer book. 

Comments on specific questions 

Answer one question from this section and not more than a further 

two questions. (You are reminded that four questions in total are to be 

attempted with at least one from Section B.) 

Section A 

Question 1 

a. Derive the Capital Asset Pricing Model (CAPM). 

Reading for the question 

Subject guide, pp.34–35. 

Approaching the question 

(10 marks) 

This question focuses on the derivation of CAPM. Students should refer to 

the mathematical derivation in the subject guide. 

Suppose an investor holds a portfolio which combines a% of an asset i and 

(1-a)% of the market portfolio. The expected return and variance of the 

portfolio p are: 

E ( Rpt) 

= aE ( Rit) 

+ ( 1 − a ) E ( Rmt) 

(1.1) 

and 

( ) [ ( ) ( ) ] 2 / 1 

2 2 

2 2 

σ Rpt = a σ i + 1– 

a σ m + 2a 1 – a σim 

(1.2) 

where is the variance of the return on a risky asset i; 2 is the variance 

i m 

of the return on the market portfolio; and is the covariance of returns 

im 

between asset i and the market portfolio. The marginal rate of substitution 

(MRS) between the expected return and risk of the market portfolio is 


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92 Corporate finance 

2 

defined as the ratio of the partial differentiation of its expected return over 

the partial differentiation of its expected risk of the portfolio with respect to 

a. In equilibrium, all marketable assets are included in the market portfolio 

and there is no excess demand or supply for any individual asset. This 

implies that 

∂ E ( R ) / ∂a 

pt E( 

R ) – E ( R ) 

(1.3) 

it 

mt 

= 

2 

∂E 

( σ ) / ∂a 

( σ – σ ) / σ 

pt 

im m m 

a = 0 

Also note that the MRS at the market portfolio is the same as the slope 

of the capital market line (CML) at the point of tangency to the efficient 

frontier. It can be shown that 

E ( R ) E ( R ) E ( R ) E( 

R ) 

MRS = 

it − mt 

it − mt 

= 

2 

( σ − σ ) σ 

σ 

im 

m 

Rearranging the equation (1.4), we have 

E( R ) = R + β E ( R ) − R 

it 

ft 

i 

m 

[ ] 

mt 

ft 

m 

= Slope of the CML 

(1.4) 

(1.5) 

where = / . Equation (1.5) shows that there is an exact linear 

i im m 

relationship between an asset’s return and its beta. 

Students may approach this question differently from the suggested 

guide here. An alternative approach is to discuss how the portfolio 

theory, two fund separation theorem and other related theories may 

lead to the CAPM. 

b. ‘The CAPM is untestable.’ How far do you agree and disagree with this 

statement? Critically evaluate this statement. (15 marks) 


Subject guide, pp.37–39; BMA, Chapter 8, pp.223–27. 


The key points are: 

i. The validity of CAPM depends on whether the market portfolio is 

mean-variance efficient. 

ii. But the true market portfolio is not observable. 

iii. Proxies for the market portfolio are often taken from broad-based 

equity indices which do not contain all the tradable securities or 

non-financial assets such as real estates, durable goods and even 

human capital. 

iv. This renders CAPM untestable. 

A good answer should cover the above points with emphasis on 

the emboldened words or phrases. As this question specifically asks 

students to evaluate the statement critically, high marks would only 

be given if such critical analysis is provided in the answer.

Question 2 

a. Explain clearly how an efficient takeover may occur. (15 marks) 




It should be noted that this question asks for the second part of Grossman 

and Hart (1980). Some students discuss the impossibility of an efficient 

takeover instead. Many students regurgitate the materials from the subject 

guide. 

Some key points worth noting are: 

i. The free-rising problem can be solved by the dilution effect. 

a. The raider can extract the value from the target if the takeover is 

completed. 

b. As long as the value that can be extracted by the raider exceeds 

the cost of the acquisition, shareholders are willing to tender their 

shares for the takeover (as free-riding is no long optional to them) 

ii. Existence of large shareholders may facilitate a takeover. 

a. Shareholders will tender their shares if p > z (where p is the 

premium paid by the raider and z is the value improvement after 

the takeover) 

b. Large shareholders will tender their shares if z > (1-a)p + c where 

a is the proportion of shares held by the large shareholders and c is 

the cost of acquisition. 

c. To satisfy both conditions a and b, az > c. So large shareholders will 

ensure the success of a takeover if the value improvement accrued 

to their shareholders exceeds the cost of acquisition. 

b. Outline the arguments for the agency cost on equity. Explain how the use of 

short term bonds might mitigate the agency conflict between equity-holders 

and debt-holders in financially distressed firms with high debt to equity 

ratios. (10 marks) 




This question centres on the agency cost of outside equity. It should 

be explained clearly including the following key points: 

i. Consider the rewards and costs facing a manager/equity-holder. 

ii. More equity held by outsiders, less effort spent by the managers/ 

equity-holder. 

iii. Issuing debt to replace the outside equity will then increase the 

leverage and the % of outstanding equity held by manager/equityholder. 

As his/her share of the residual value of the firm increases, 

he/she will choose to supply more effort, leading to increased firm 

value. 

iv. Conflicts between shareholders and debt-holders: 

a. The problem of asset substitution and risk shifting may arise. 

b. Using short-term debt gives debt-holders an early opportunity to 

review the firm’s managerial effect. 


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c. Managers may need to supply their effort to maximise the firm’s 

value and look after both the equity and debt-holders at the same 

time. Arguably reducing the possible conflicts between the two 

different types of stakeholders. 

Many candidates regurgitated the materials from the subject guide and 

some provided answers on the agency cost on debt instead. 

Question 3 

a. Explain clearly the 3 main conditions for dividends to work effectively as a 

signal of a firm’s value. (9 marks) 


Subject guide, pp.132 and 119–120. 


This question tests students’ ability to understand how the Ross (1977) 

model may be used to analyse the signalling effect of dividends. We are 

not expecting candidates to develop a set of equations such as those 

included on pp.119 and 120 of the subject guide. Instead the focus 

should be on the necessary conditions which enable dividends to act as an 

efficient signal. 

The three key conditions are: 

i. The market is adhering to the semi-strong form efficiency but not 

strong form. A firm’s true value is therefore not observable. 

ii. Managers (according to Lintner’s stylised fact) would not change 

dividend unless it is sustainable in the future. 

iii. Therefore good quality firm will pay high dividend to signal its 

strength and commitment. 

b. Critically assess the empirical evidence for the weak form market efficiency. 

(10 marks) 




Candidates should discuss how the weak form efficiency is tested in 

empirical studies and in particular, focus on the implications of the 

findings from the random walk tests, return autocorrelation tests, calendar 

effects and trading rules. 

c. Explain why Net Present Value is a better investment appraisal technique 

than Internal Rate of Return. (6 marks) 


Subject guide, pp.18 and 19; BMA, Chapter 5, pp.137–43. 

This part was generally quite well answered. The key points that should 

be discussed are: 

i. IRR does not account for the size and magnitude of the project. It is 

not a good tool to rank projects. 

ii. Costs of capital may vary over time but the IRR assumes that any spare 

cash can be re-invested at the same rate. 

iii. IRR is not additive and therefore the total IRR of all projects needs 

to be re-computed. NPV has an additive property and therefore the 

combined effect can be determined easily.

Question 4 

a. Explain Modigliani and Miller’s argument on the irrelevancy of debt and 

dividend policies. (10 marks) 


Subject guide, pp.91–93 and 128. 


Candidates should place equal importance to the two parts of this question. 

Many candidates simply focus on the irrelevance of capital structure and 

ignore dividend policy. 

First, we should note that the combined cash return to all stakeholders 

is the same regardless of the firm’s capital structure. This can be easily 

illustrated in a simple example such as Table 6.1 on p.92 of the subject 

guide. 

Second, regarding the irrelevancy of dividend policies, candidates should 

point out that in the world with no tax, shareholders are indifferent 

between capital gain and dividend income. They can replicate any dividend 

policy through appropriate purchases and sales of shares. 

b. Using the arguments for the signalling and tax effects of debts, to what extent 

would you conclude that debt policy is relevant to corporate value? 

(15 marks) 


Subject guide, pp.94–97 and 119–120. 


There are two parts in this question. To deal with the tax effect of debt, 

candidates should discuss the following key points: 

• Interest on debt is tax deductible and therefore creates a tax shield 

effect. 

• The higher the debt, the more interest is paid and hence the higher the 

tax shield benefits. 

• The firm’s value increases as a result of the higher level of debt. 

• However, more debt will increase the potential cost of financial distress. 

The value of the firm may not increase as much as the absolute tax 

shield. 

The second part requires candidates to discuss the main conditions 

for debt to work as an effective signal. You should explain why the 

following three conditions need to be met and what implications they 

have in terms of debt policy: 

• Market – must be adhering to the semi-strong (but not strong form 

otherwise the firm’s value can be observed). 

• Good firms with optimistic future cash flows can afford to issue more 

debt and pay more interest. Therefore those firms with high levels of 

debt signal their strength and their value will be improved. 

• The penalty of using incorrect signals is more costly than the short 

term gain. 


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6 

Section B 

Answer one question from this section and not more than a further 

two questions. (You are reminded that four questions in total are to be 

attempted with at least one from Section A.) 

Question 5 

a. Leopard plc is considering purchasing a new machine in its manufacturing 

plant. The machine is required on a going concern basis. The company has the 

following two options: 

Machines Year 0 Year 1 Year 2 Year 3 Year 4 

A –100,000 90,000 80,000 50,000 

B –150,000 35,000 45,000 55,000 65,000 

All figures are quoted in $. The cost of capital for Leopard plc is 10% per 

annum. In which machine should Leopard plc invest? 


BMA, Chapter 6, pp.169–73. 


(6 marks) 

Machine A 

Year CF’s DF PV AEV 

0 –100 1 –100 

1 90 0.909 81.81 

2 80 0.826 66.08 

3 50 0.751 37.55 

2.486 85.44 34.368 

Machine B 

Year CF’s DF PV AEV 

0 –150 1 –150 

1 35 0.909 31.815 

2 45 0.826 37.17 

3 55 0.751 41.305 

4 65 0.683 44.395 

3.169 4.685 1.478 

Given that Machine A has the higher NPV and AEV (annual equivalent 

value), we should invest in it. 

b. GQ Ltd has been presented with the following project: 

A new machine for $250,000 is required at the beginning of the first year. The 

machine will last for 4 years and thereafter can be disposed of for $25,000. 

The company’s policy is to depreciate this type of machine over its economic 

life on a straight-line basis. 

The demand for the product MH depends on the future states of the 

economy. In the good state, GQ Ltd expects to sell 15,000 units per year for 

the next 4 years. If the economy is bad, sales will fall to 5,000 units per year. 

Each state of the economy has an equal probability to materialise. Each unit 

of product MH will be priced at $40. Total variable costs are expected to be 

$30 per unit in the first year and thereafter rise at 10% per year. 

[For the full question, please refer to the Examination paper.]


BMA Chapter 6, pp.156–69. 



0 1 

Year 

2 3 4 

Machine (250,000) 25,000 

Revenue 400,000 400,000 400,000 400,000 

Costs (300,000) (330,000) (363,000) (399,300) 

NCF before tax (250,000) 100,000 70,000 37,000 25,700 

Tax (11,250) (6,938) (553) 23,931 

NCF after tax (250,000) 88,750 63,063 36,447 49,631 

DF 1 0.909 0.826 0.751 0.683 

PV (250,000) 80,674 52,090 27,372 33,898 

NPV (55,967) 

NCF = Taxable profit 100,000 70,000 37,000 25,700 

Capital allowances (62,500) (46,875) (35,156) (105,469) 

Taxable profit after CA 37,500 23,125 1,844 (79,769) 

Tax 11,250 6,938 553 (23,931) 

i. Given that the NPV of the project is negative, it is not advisable to 

invest in it. 

Would we accept this project if the cost of capital is reduced? To 

answer this question, we recomputed the NPV using a lower discount 

rate. For illustration purposes, we use 5% as a new reduced cost of 

capital. The NPV of the project can be recomputed as follows: 

NCF after tax (250,000) 88,750 63,063 36,447 49,631 

DF (5%) 1 0.952 0.907 0.864 0.823 

PV (250,000) 84,490 57,198 31,490 40,846 

NPV (35,976) 

IRR = 5% – 35,976/(–35976 + 55967) × 5% = –4% 

ii. The cost of capital needs to drop by 14% to wipe out the NPV entirely. 

This implies that this project will never break even. 

Question 6 

a. The last 5 years returns on Fly-away plc and Stay-at-home plc are as follows: 

Year Fly-away, % Stay-at-home, % 

2010 0 14 

2009 –4 –2 

2008 8 0 

2007 10 –5 

2006 6 18 

Calculate the return and risk of a portfolio which consists of 50% Fly-away 

and 50% Stay-at-home. 


(10 marks) 

BMA, Chapter 7, pp.202–05 (especially Table 7.7). 

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I II III IV IV VI VII 

Year Fly-away, % Stay-athome, 

% 

I - mean II - mean III x III IV x IV III x IV 

2010 0 14 –4 9 16 81 –36 

2009 –4 –2 –8 –7 64 49 56 

2008 8 0 4 –5 16 25 –20 

2007 10 –5 6 –10 36 100 –60 

2006 6 18 2 13 4 169 26 

Sum 20 25 136 424 –34 

Mean 4 5 

Variance 34 106 

Covariance –8.5 

Stdev 5.83 10.30 

Portfolio variance = 0.5 0.5 34 + 0.5 0.5 106 0.5 0.5 –8.5 = 30.75 

Portfolio risk = square root of the variance = 5.55 

Note that the above figures are adjusted for the small sample error. 

b. Suppose the returns on Stock x, y and z are determined by the following twofactor 

model: 

r 

r 

r 

x 

y 

z 

= 

= 

= 

0. 

2 

0. 

16 

0. 

5 

+ 2 F − F 

1 

1 

+ 1. 

2 F 

1 

+ F + F 

2 

2 

+ 

= 

= 10% 

0. 

5 

F 

6% 

2 

= 

8% 

i. Determine the portfolio weights you need to place on x, y and z in order 

to replicate the portfolio returns on F and F respectively. 1 2 (10 marks) 

ii. The return on Stock M is known to follow the following factor model 

r = 0.2 + 1.6F + 1.8F m 1 2 

It is currently traded with a return of 10%. Explain if any arbitrage 

opportunity arises in this case. 




(5 marks) 

Let x, y and z as the weight in X, Y and Z. 

For 

( 1) 

( 2) 

( 3) 

( 2) 

( 2) 

F 

1 

x + y + z = 1 

2 x + 

− x + 

− 

− 

( 1) 

( 3) 

1. 

2 

⇒ y = 10 

⇒ z = −7 

0. 

5 

⇒ x = −2 

y + z = 1 

y + z = 0 

⇒ x + 0. 

2 y = 0 

⇒ 3 x + 

0. 

7 

y = 1

For F2 

( 1) 

( 2) 

( 3) 

( 2) 

( 2) 

x + y + z = 1 

2 x + 

− x + 

− 

− 

( 1) 

( 3) 

1. 

2 

⇒ y = 20 

0. 

5 

⇒ x = −5 

⇒ z = −14 

y + z = 0 

y + z = 1 

⇒ x + 0. 

2 y = −1 

⇒ 3 x + 0. 

7y 

= −1 

The expected returns on x, y and z are given in the question as 10%, 8% 

and 6% respectively. Therefore the expected return on: 

F1 = –2 10% + 10 8% – 7 6% = 18 

F2 = -5 20% + 20 16% – 14 5% = 26 

Expected return on M = 0.2 + 1.6 F1 1.8 F2 = 75.8. 

The expected return is higher than the observed return. It seems to 

suggest that M is overpriced and an arbitrage opportunity exists. 

Consequently, we can sell M and buy the replicated portfolio using F1 and 

F2. 

However, the return figures are grossly inconsistent with the factor model, 

it might suggest that the multi-factor model is not a correct pricing 

equation. Therefore the expected return cannot be estimated correctly. It 

is therefore hard to determine if arbitrage exists. 

Question 7 

Red Apple plc, a quoted company in Hong Kong, is considering to takeover 

Green Papaya Ltd. Both companies are 100% equity financed. The following 

information is available for these two companies: 

Red Apple Green Papaya 

Number of shares 100,000,000 2,000,000 

Share price £10 Not available 

Dividend per share (latest) $1 $0.8 

You discover the following additional information: 

i. Green Papaya Ltd. has been paying dividends at a constant growth rate of 

5% per annum for the last 5 years to its shareholders. 

ii. The Directors of Green Papaya have been using a discount rate of 10% per 

annum to appraise its projects. 

iii. It is believed that the cost of capital for Green Papaya will reduce to 

8% per annum once it is taken over by Red Apple. 

[For the full question, please refer to the Examination paper.] 


BMA, Chapter 31, pp.829–33. 


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10 


Part A 

Suppose Green Papaya’s dividend grows at 5% p.a. in the foreseeable 

future before the takeover. 

Share price, S = $0.8(1.05)/0.1 – 0.05 = $16.80 

Value, V = $16.80 2,000,000 = $33,600,000 

Part B 

New share price after the merger, S = 0.8 1.05 /(0.08 – 0.1) = $28.00 

New value after the merger, V = $28 2,000,000 = $56,000,000 

Part C 

Equity issue, raising cash 

Cost of acquisition = $8 5m = $40,000,000 

Net cost = 40,000,000 – 33,600,000 = $6,400,000 

Gain = $56,000,000 – $33,600,000 = $22,400,000 

Net gain = $22,400,000 – $6,400,000 = $16,000,000 

Share exchange 

Value of the combined company = $1,000,000,000 + $56,000,000 = 

$1,056,000,000 

New share price = $1,056m/104m = $10.15 

Cost of acquisition = $10.15 4m = $40,615,385 

Net cost = $40,615,385 – $33,600,000 = $7,015,385 

Gain =$56,000,000 – $33,600,000 = $22,400,000 (same as in the cash 

offer) 

Net gain = $22,400,000 – $7,015,385 = $15,384,615 

The advantages and disadvantages of cash and share exchange in M&A 

can be summarised as follows: 

Cash Acquired Acquiring 

Advantages Shareholders will receive a Acquiring firm’s shareholders 

certain cash flow when they sell will have full control over the 

their shares to the acquiring combined operation. 

firm. It implies that they will 

obtain a certain return on their 

investment. 

Disadvantages The receipt of cash is deemed 

to a disposal of shares which 

will attract capital gains tax 

and shareholders will lose 

ownership. 

Share exchange 

Advantages The acquired firm’s shareholders 

will maintain some form of 

ownership in the combined 

operation. 

Disadvantages The return on investment from 

the combined operation might 

be uncertain. 

There is a liquidity implication. 

Acquiring firm needs to raise 

sufficient cash flows for the 

acquisition. 

There is no cash outflow in this 

type of acquisition. 

Acquired firm’s shareholders 

need to share ownership with 

the shareholders from the 

acquiring firm.

Question 8 

a. Orchard plc’s share price, S, can either go up to S or down to S in the next 

H L 

period. Derive the price of a put option written on S in terms of a position in 

the stock and a risk free asset. (7 marks) 

b. Orchard plc’s shares are currently traded at $20 each. Its share price will 

go up to $22 or down to $17 in three months’ time. The effective interest 

rate for the next three months is 3%. What is the price of a put option on 

Orchard’s share with an exercise price of $20.5? (5 marks) 

c. Explain clearly why the price of a put option does not depend on the 

investor’s risk preference and the probabilities of the future states of the 

economy. Determine the risk neutral probabilities of the two states of the 

economy in (b). (13 marks) 




a. Derive the option price 

Form a portfolio with a% in S and b in risk-free asset. This portfolio 

mimicks the payoff of a put option: 

P = aP + b(1 + r ) 

H H f 

P = aP + b(1 + r ) 

L L f 

Solving the two equations we have: 

a = P – P / S – S H L H L 

b = S P – S P / (1 + r )(S – S ) 

L H H L f L H 

The value of a put, P = aS + b 

b. Given the information in the question, we can determine that: 

P = 0 H 

P = 3.5 L 

S = 22 H 

S = 17 L 

Substituting into the two equations in (a) we have: 

a = (0 – 3.5)/(22 – 17) = –3.5/5 = –0.7 

b = (17 0 – 22 3.5) / (1.03 –5) = 14.951 

The value of the put, P = –0.6 20 + 14.951 = 0.9515 

c. If S = uS (u percentage of S) and S = dS (d percentage of S), then 

H L 

a = (P – P )/(u – d)S 

H L 

b = (uP – dP )/(u – d)R 

L H 

and 

P = aS + b 

= (P – P )/(u – d)+ (uP – dP )/(u – d)R 

H L L H 

= [qP + (1 – q)P ]/R where q=(R – d)/(u – d), the risk neutral probability 

H L 

Using the information in (b), R = 1.03; d = 0.85; u = 1.1 

q = 1.03 – 0.85 / 1.1 – 0.85 = 0.72 

Information about the probability and risk are already priced in the 

underlying asset. Therefore the option prices which derived their values 

from the underlying asset will reflect these two pieces of information. 


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To see this, we can express the current stock price as the probability 

weighted average of future prices of the two states: 

S = qSH – (1 – q)SL / 1 + rf 

q = R – d / u – d

Examiners' commentaries 2011

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