ACCA P4 Advanced Financial Management - 2010 - Study text

Answers

40 Imperfect hedge and basis 507

41 Currency hedge 508

42 Hedging with STIRs 509

43 More hedging with STIRs 510

44 FRAs and futures 511

Options and hedging with options

45 Traded equity options 512

46 Currency options 513

47 Interest rate hedge 514

Option pricing and delta hedging

48 Black-Scholes 515

49 Put-call parity 516

50 Delta hedge 516

51 Bonus scheme 517

52 Delta neutral 518

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1 Corporate social responsibility

(a) (i) Ethics and behaving in an ethical manner in business (and in some cases,

bribery and corruption)

(ii) Concern for employees

(iii) Concern for the community

(iv) Concern for human rights

(v) Concern for the environment: protecting the environment, creating a

sustainable business.

(b) CSR issues vary between different types of company. Companies most likely

to be affected include:

(i) companies that enjoy some form of monopoly, such as energy supply

companies

(ii) companies that deal directly with consumers, such as banks and retail

organisations

(iii) companies manufacturing food, drink and medicines

(iv) companies that extract resources from the environment: manufacturing

companies whose products or manufacturing systems pollute the

environment

(v) companies with a supply chain in developing countries (such as clothing

manufacturers and oil exploration and extraction companies).

(c) CSR risk is the risk that a CSR issue might affect a company in any of the

following ways:

(i) The company might suffer a loss of reputation (reputation risk). This

could lead to a loss of customers who switch to the products of rival

companies. A poor reputation could also lead to the threat of legislation.

(ii) The company might be exposed to the risk of legal action by customers

and others (litigation risk). A notable example has been the litigation

faced by tobacco companies, particularly in the US.

(iii) Another aspect of litigation risk is the possibility that a government will

introduce legislation against a company’s products (e.g. tobacco

products, food products, medicines and drugs) or its production

methods (e.g. anti-pollution laws).

(iv) Some investors choose to invest only in ‘ethical companies’. A company

with a poor CSR record might therefore attract fewer investors.

(v) Research appears to show that companies with positive CSR policies

benefit financially, in terms of profits and share price.

2 Corporate governance

(a) The main aim of a code of corporate governance should be to ensure that the

directors or managers of a company should run the company in the interests

of its shareholders.

(b) The main issues in corporate governance, for both statutory and voluntary

codes, are likely to be:

Answers

(i) the composition of the board of directors: achieving a balance of skills

and experience, preventing the board from being dominated by one

individual or a small group of individuals, the role of non-executive

directors (and in particular independent non-executive director)

(ii) the decision-making responsibilities of the board (and how much

decision-making responsibility should be delegated to management)

(iii) the process of nominating new directors for appointment to the board

(iv) the process of deciding the remuneration of directors, and trying to

ensure that remuneration systems reward directors for success and do

not reward them for failure

(v) the reliability of financial reporting, the independence of the external

auditors, and the role of the audit committee

(vi) communications between a company and its shareholders

(vii) risk management and internal control, and the review of internal control

and risk management systems

(viii) restricting the scope for insider trading or market abuse.

Corporate social responsibility and protection for whistle-blowers could also

be added to this list.

3 Dividends and retentions

The dividend growth model will be used to estimate what share price might be

expected.

It is assumed that the growth rate in earnings and dividends will be br, where b is

the proportion of earnings that is retained and r is the return on new investment.

(a) Dividends are 25% of earnings and 75% of earnings are retained:

Growth rate = 0.75% × 0.09 = 0.0675.

Expected share price = 0.50 (1.0675) = $23.72

(0.09 – 0.0675)

(b) Dividends are 50% of earnings and 50% of earnings are retained:

Growth rate = 0.50% × 0.09 = 0.045.

Expected share price = 1.00 (1.045) = $23.22

(0.09 – 0.045)

(c) Dividends are 70% of earnings and 30% of earnings are retained:

Growth rate = 0.30% × 0.09 = 0.027.

Expected share price = 1.40 (1.027) = $22.82

(0.09 – 0.027)

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4 Financial plan

Tutorial note. Many of the figures for the financial plan can be calculated by

increasing the amount by 8% each year, in line with sales growth. The bank

overdraft interest each year is calculated by taking the bank overdraft at the end of

the previous year. The bank overdraft is a balancing figure in the balance sheet, that

makes the equity and liabilities add up to the total assets.

Income statements

Year 5

Year 6

Year 7 Year 8

$m

$m $m

EBITDA (+ 8% per year)

583

630

680 735

Depreciation (+ 8% per year)

(173)

(187)

(202) (218)

Earnings before interest 410

443

478 517

Interest (see workings)

(86)

(95)

(106) (118)

Profit before tax

324

348

372 399

Tax (30%) (97)

(104)

(112) (120)

Profit after tax

227

244

260 279

Dividends (64%)

(145)

(159)

(166) (179)

Retained earnings

82

85

94 100

Balance sheets

Year 5

Year 6

Year 7 Year 8

$m

$m $m

Plant and equipment (+ 8% per

year) 2,182

2,356

2,545 2,748

Inventory + receivables –

trade payables

(+ 8% per

year) 767

828

894 966

Cash (+ 8% per

year) 32

35

38 41

2,981

3,219

3,477 3,755

Share capital 450

450

450 450

Reserves (add retained

profit) 1,283

1,368

1,462 1,562

1,733

1,818

1,912 2,012

Long-term loan

800

800 800

2,533

2,618

2,712 2,812

Bank overdraft

(balancing

figure) 448

601

765 943

2,981

3,219

3,477 3,755

Workings

(1) At the end of year 4, inventory + receivables – trade payables = 710 (in $

million). This amount will increase by 8% each year.

(2) Interest charges

Year 5

Year 6

Year 7 Year 8

$m

$m $m

Long-term loan

(8% × 800)

64

64 64

Bank overdraft

(7% × previous year)

22

31

42 54

86

95

106 118

Answers

(b)

There are several definitions of free cash flow. Other definitions are acceptable for

your answer.

Year 5

Year 6

Year 7 Year 8

$m

$m $m

EBIT (1 – t) Earnings before interest

less tax at 30%

287

310

335 362

Depreciation 173

187

202 218

Increase in plant and equipment

(162)

(174)

(189) (203)

Increase in inventory + receivables -

payables

(57)

(61)

(66) (72)

Free cash flow

241

262

282 305

(c)

A feature of the financial plan that might need review is the cash position of the

company. The bank overdraft is forecast to increase from $310,000 to $943,000,

although the company expects to make a profit each year. The free cash flow each

year, as measured, is not much more than the interest payments and dividend

payments.

This suggests that the company might need to reconsider its dividend policy, and

pay lower dividends. In addition, the company might possible consider alternative

sources of finance, so that it does not have to rely so much on an overdraft facility.

More long-term debt might be appropriate, if this can be obtained at a suitable

interest rate.

(d)

A possible value of the company’s shares at the end of the financial planning period

can be estimated using the dividend growth model, assuming that dividends will

grow by about 8% per year (in line with sales growth) and the cost of equity will

remain at 12%.

Expected equity value in $ millions = 179 (1.08)

(0.12 – 0.08)

= $4,833 million.

There are 9,000,000 shares of $0.05 each . This gives a valuation of $537 per share.

5 DCF exercises

(a)

Annuity factor at 8%, years 1

–

8

5.747

Annuity factor at 8%, years 1

–

4

3.312

Annuity factor at 8%, years 5

–

8

2.435

Annuity factor at 8%, years 1

–

10

6.710

Annuity factor at 8%, years 1

–

8

5.747

Annuity factor at 8%, years 9

–

10

0.963

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The Year 10 value of a perpetuity of $100,000 each year in perpetuity from

Year 11 onwards:

= $100,000 × 1/0.08

= $1,250,000

Years Annual cash flow Discount factor at 8% PV

$ $

0 (3,000,000)

1.000

(3,000,000)

1

–

4 500,000

3.312

1,656,000

5

–

8 400,000

2.435

974,000

9

–

10 300,000

0.963

288,900

10 1,250,000

0.463

578,750

NPV

+ 497,650

(b) (i) Ignoring inflation

Year Annual cash flow Discount factor at 12% PV

$ $

0 (900,000)

1.000

(900,000)

1 400,000

0.893

357,200

2 400,000

0.797

318,800

3 250,000

0.636

159,000

4 300,000

0.567

170,100

+ 105,100

(ii) Allowing for inflation

Year 0 1 2 3 4

$ $ $ $ $

Equipment (900,000)

243,101

Revenue

824,000

848,720

655,636 450,204

Running costs

(420,000)

(441,000)

(405,169) (364,652)

Net cash flow (900,000)

404,000

407,720

250,467 328,653

Discount factor

at 12%

1.000

0.893

0.797

0.636 0.567

Present value (900,000)

360,772

324,953

159,297 186,346

NPV = + 131,368

6 DCF and tax

Annual depreciation = $(800,000 – 200,000)/4 years = $150,000 per year.

Annual cash profits = Accounting profit + Deprecation = $250,000 + $150,000 =

$400,000.

Tax depreciation allowances (capital allowances)

Year of

claim

Written down

value

Tax saved at

30%

Year of

cash flow

$ $

800,000

0 Allowance (25%) (200,000)

60,000

1

600,000

1 Allowance (25%) (150,000)

45,000

2

450,000

2 Allowance (25%) (112,500)

33,750

3

337,500

Answers

3 Allowance (25%) (84,375)

25,313

4

253,125

4 Disposal value (200,000)

4 Balancing allowance 53,125

15,938

5

Year 0 1 2 3 4 5

$ $ $ $ $ $

Equipment (800,000)

200,000

Capital

allowance

60,000

45,000

33,750

25,313 15,938

Cash profit 400,000

400,000

Tax on cash

profit

(120,000)

(120,000) (120,000)

Net cash flow (800,000) 460,000 325,000 313,750 505,313 (104,062)

Discount

factor, 15%

1.000 0.870

0.756

0.658

0.572 0.497

Present value (800,000) 400,200

245,700

206,448

289,039 (51,719)

NPV = + $289,668

7 Free cash flow

$ million

Profit before interest and tax 3.00

Interest (0.40)

Taxation (0.60)

Depreciation charges 0.55

Essential capital expenditure (1.00)

Free cash flow

1.55

8 Two-asset portfolio

(a) Security X

EV of return (

x

)

= (0.25 x 15) + (0.60 x 10) + (0.15 x 2) = 10.05.

Probability Return

x –

x

p(x –

x

)

2

p x

0.25 15 4.95

6.1256

0.60 10 (0.05)

0.0015

0.15 2 (8.05)

9.7204

Variance

σ

2

15.8475

Standard deviation of return

σ

x

= 15.8475 = 3.98 .

(b) Security Y

EV of return (

x

)

= (0.25 x 20) + (0.60 x 8) + (0.15 x (6)) = 8.90

Probability Return y – y p(y – y )

2

p y

0.25 20 11.10

30.8025

0.60 8 (0.90)

0.4860

0.15 (6) (14.90)

33.3015

Variance

σ

2

64.5900

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Standard deviation of return

σ

y

= 64.59 = 8.04.

(c)

Probability x –

x

y – y p(x –

x

)

2

p

0.25 4.95 11.10

13.7363

0.60 (0.05) (0.90)

0.0270

0.15 (8.05) (14.90)

17.9917

Cov

x,

y

31.7550

(d)

Correlation coefficient

8.04 3.98

31.7550

yx,

×

=ρ

= + 0.992.

This shows a high level of positive correlation between the returns from

Security X and the returns from Security Y.

(e) The

EV of the return from a portfolio consisting of 50% Security X and 50%

Security Y

= (0.50 x 10.05) + (0.50 x 8.90) = 9.475%.

The

variance of the returns from this portfolio would be:

[(0.50)

2

× 15.8475] + [(0.50)

2

× 64.5900] + [2 × 0.50 × 0.50 × 31.7550]

= 3.9619 + 16.1475 + 15.8775 = 35.9869.

The

standard deviation of the portfolio returns =

35.9869 = 6.0%.

(f) For a portfolio consisting of 80% Security X and 20% Security Y:

The

EV of the return

= (0.80 × 10.05) + (0.20 × 8.90) = 9.82%.

The

variance of the returns from this portfolio would be:

[(0.80)

2

× 15.8475] + [(0.20)

2

× 64.5900] + [2 × 0.80 × 0.20 × 31.7550]

= 10.1424 + 2.5836 + 10.1616 = 22.8876.

The

standard deviation of the portfolio returns = √22.8876 = 4.78%.

Note: In this example, since Security Y has a lower expected return than

Security X and a higher standard deviation, expected returns will be highest

and risk lowest with a ‘portfolio’ consisting of Security X only, and none of

Security Y.

Answers

9 Risk and return

(a)

Project 3 Project 4

Expected

return

(0.6 × 6) + (0.4 × 1) = + 4.0

(0.5 × 8) + (0.5 ×

–

1) = + 3.5

Return r Probability p

(r-

r)

2

Return r Probability p

(r- r

)

2

6.0 0.6 2.40 8.0 0.5 10.125

1.0

0.4

3.60

–

1.0

0.5 10.125

Variance (σ)

2

6.00

20.250

σ

2.45

4.5

(b) The divisional manager will invest in projects that are more risky provided

that they offer a higher return.

The manager will not invest in Project 4 because it offers a lower expected

return than Project 3 but higher risk.

The expected return from Project 1 is (0.8 × 4) + (0.2 × 2) = + 3.6.

The expected return from Project 2 is (0.7 × 5) + (0.3 × 1.5) = + 3.95.

The highest expected return is offered by Project 3, which has a higher risk

than Project 1 and Project 2. It would seem that the divisional manager will

invest in Project 3 because he is prepared to take the higher risk for a higher

expected return. However, Project 2 might seem more attractive: its expected

return is almost as high as for Project 3 and the risk is much less.

10 Coefficient of variation

Portfolio Expected return

50% Country A, 50% Country B (0.5 × 16) + (0.5 × 22) 19.0

50% Country A, 50% Country C (0.5 × 16) + (0.5 × 30)

23.0

50% Country B, 50% Country C (0.5 × 22) + (0.5 × 30)

26.0

The standard deviation of a portfolio is:

σρ = σ

A

2

x

2

+σ

B

2

1− x

()

+ 2x 1− x

()

ρ

A,B

σ

A

σ

B

2

However, since the returns from each country are independent of each other, the

covariance of returns (

ρ

A,B

) is 0; therefore the second half of the formula can be

ignored because its value is zero.

Portfolio

Standard deviation

of returns

50% Country A, 50% Country B [(22

2

× 0.5

2

) + (36

2

× 0.5

2

)]

1/2

21.9

50% Country A, 50% Country C [(22

2

× 0.5

2

) + (45

2

× 0.5

2

)]

1/2

25.7

50% Country B, 50% Country C [(36

2

× 0.5

2

) + (45

2

× 0.5

2

)]

1/2

28.8

(Tutorial note: ‘To the power of ½’ is the same as ‘the square root’.)

Paper P4: Advanced Financial Management

Coefficient of variation

The coefficient of variation is the ratio of the risk (standard deviation of returns) to

the expected return.

Portfolio Coefficient

of variation

50% Country A, 50% Country B 21.9/19.0 = 1.15

50% Country A, 50% Country C 25.7/23.0 =

1.12

50% Country B, 50% Country C 28.8/26.0 =

1.11

The ratio of risk to expected returns is roughly the same for all three portfolios.

11 Capital market line

The investor wanting a return of 7% can invest x% of his funds in risk-free securities

earning 3% and (1 – x)% in the market portfolio earning 9%.

3x + 9 (1 – x) = 7

6x = 2

x = 1/3 or 33.33%.

The investor should invest one-third of his funds in risk-free securities and two-

thirds in the market portfolio.

12 Obtaining a beta factor

(a)

Month Market portfolio Security Y

x –

x

(x –

x

)

2

y – y (y – y )

2

1 + 1.5 2.25

+ 2

4

2 (1.5) 2.25

(3)

9

3 (2.5) 6.25

(3)

9

4 + 2.5 6.25

+ 4

16

17.00

38

Standard deviation of market returns =

17.00

=

4.123%.

Standard deviation of Security Y returns =

38

=

6.164%.

(b)

Month

x –

x

y – y

(x

–

x

)

(y – y )

1 + 1.5 + 2 + 3.0

2 (1.5) (3)

+ 4.5

3 (2.5) (3)

+ 7.5

4 + 2.5 + 4

+ 10.0

+ 25.0

Covariance of returns = 25.0

ACCA P4 Advanced Financial Management - 2010 - Study text - Emile Woolf Publishing

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