ACCA P4 Advanced Financial Management - 2010 - Study text

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Answers

termination of the currency swap, and a further 3,000,000 zants for the remainder of

the sale price of the operations centre.

The project cash flows will therefore be as follows:

Year

0 £(333,333)

1 200,000 zants at the end of Year 1 spot rate

2 200,000 zants at the end of Year 2 spot rate

3 200,000 zants at the end of Year 3 spot rate

3 3,000,000 zants at the end of Year 3 spot rate

3 3,000,000 zants at the swap rate of 9.00, therefore £333,333.

Year Spot rate

Best case Worst case

10% inflation 50% inflation

0 9.00 9.00

1 9.90 13.50

2 10.89 20.25

3 11.98 30.38

Year Cash flow DCF factor

at 15%

Best case Worst case

Cash flow PV Cash flow PV

zants £ £ £ £

0 1.000 (333,333) (333,333) (333,333) (333,333)

1 200,000 0.870 20,202 17,576 14,815 12,889

2 200,000 0.756 18,365 13,884 9,877 7,467

3 3,200,000 0.658 267,112 175,760 105,332 69,308

3 3,000,000 0.658 333,333 219,333 333,333 219,333

NPV + 93,220 (24,336)

Conclusion

On the basis of the assumptions used, the project would have a positive NPV if

inflation in Zantland exceeds inflation in the UK by 10% per year, but will have a

negative NPV if inflation in Zantland exceeds inflation in the UK by 50% per year.

There is consequently an element of risk in the project due to uncertainty about the

spot exchange rate, and this risk element should be assessed more closely before a

decision is taken about the investment.

37 Currency futures

(a) The company must make a payment in US dollars in May. It must therefore

buy dollars to make the payment.

Using futures, the company will therefore buy dollars and sell euros. It will

therefore sell euro/US dollar futures, which are for

€125,000 each.

At the futures price of 1.2800, the amount of euros to sell in exchange for

$640,000 is:

$640,000/1.2800 = $500,000.

The number of contracts to sell is therefore: $500,000/$125,000 per contract =

4.0 contracts.

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The company will sell 4 June contracts at 1.2800.

(b) It will close its position in May, when the futures price is 1.2690.

The value of 1 tick for this contract is 125,000 × $0.0001 = $12.50.

Original selling price 1.2800

Buying price to close the position

1.2690

Gain per contract 0.0110

Total gain on futures position = 4 contracts × 110 ticks × $12.50 = $5,500.

The French company must pay $640,000 to its supplier. It has $5,500 profit

from closing the futures position. It therefore needs an additional ($640,000 –

$5,500) = $634,500.

It must buy these dollars at the spot rate of 1.2710. The cost in euros will be

$634,500/1.2710 =

€499,213.

The effective exchange rate for the payment of $640,000 is therefore:

$640,000/

€499,213 = US$1.2820/€1.

This is close to the price at which the futures were originally sold. However,

the hedge is not perfect because the position was closed before the settlement

date for the contract.

38 More currency futures

(a) The US company must make a payment in sterling in January. It will sell the

sterling it receives in exchange for dollars.

Using futures, the company will therefore sell sterling and buy dollars. It will

therefore sell sterling/US dollar futures, which are for £62,500 each.

The number of contracts to sell is therefore: £400,000/£62,500 per contract =

6.4 contracts.

The company will therefore sell either 6 or 7 March contracts at 1.8600.

In the answer in (b), it is assumed that the company will sell 6 March

sterling/US dollar futures.

(b) The US company will close its position in January, when the futures price is

1.8420.

The value of 1 tick for this contract is 62,500 × $0.0001 = $6.25.

Original selling price 1.8600

Buying price to close the position

1.8420

Gain per contract 0.0180

Total gain on futures position = 6 contracts × 180 ticks × $6.25 = $6,750.

The US company will receive £400,000 which it will sell at the spot rate of

1.8450.

From sale of £400,000 spot at $1.8450/£1 738,000

Profit on futures position 6,750

Total income 744,750

Answers

The effective exchange rate for the £400,000 received is therefore:

$744,750/£400,000 = US$1.8619/£1.

This is close to the price at which the futures were originally sold. However,

the hedge is not perfect because the position was closed before the settlement

date for the contract.

39 Basis

(a) On 1st March: Days to settlement of the June futures contracts = 31 + 30 + 31 +

60 = 122 days.

On 1 March

Spot rate 1.8540

Futures price 1.8760

Basis 0.0220

The basis is 220 points, with the futures rate higher than the spot rate.

The basis at the end of June when the futures reach settlement will be 0.

It is assumed that basis will decrease to zero at a constant rate per day. The

basis will therefore reduce by (220 points/122 days) = 1.80328 points per day.

At close of trading on 30th April, there are (31 + 30) 61 days remaining to the

settlement of the June futures. The expected basis at this date is therefore:

1.80328 points per day × 61 days = 110 points.

At the end of 30th April

Spot rate 1.8610

Expected basis 0.0110

Expected futures price (higher)

1.8720

(b) At close of trading on 15th June, there are 15 days remaining to the settlement

of the June futures. The expected basis at this date is therefore:

1.80328 points per day × 15 days = 27 points.

At the end of 30th April

Spot rate 1.8690

Expected basis 0.0027

Expected futures price (higher)

1.8717

40 Imperfect hedge and basis

(a) There is a loss on the underlying currency exposure, because sterling weakens

in value between 20th April and 20th July.

At 20th April: expected value of £625,000 receivable (at 1.8050) 1,128,125

At 20th

July: actual value of £625,000 received (at 1.7700)

1,106,250

Loss on underlying currency exposure

21,875

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The futures position is opened on 20th April by selling futures contracts

(selling British pounds and buying dollars). The US company should sell 10

contracts (£625,000/£62,500 per contract). When the position is closed on 20th

July, there is a gain on the position.

20th April: Open position – Sell at 1.7800

20th July: Close position

–

Buy at

1.7600

Gain on underlying currency exposure

0.0200

Total gain (10 contracts) = 10 contracts × 200 ticks per contract × £6.25 per tick

= $12,500.

The futures position has failed to provide a perfect hedge, resulting in a net

‘loss’ of $9,375.

Effective exchange rate $

Revenue from sale of £625,000 spot on 20th July (at 1.7600) 1,100,000

Gain on futures position 12,500

Total dollar income 1,112,500

Effective exchange rate = $1,112,500/£625,000 = $1.7800.

(b) The reason why the hedge is not perfect in this case is explained by the

existence of basis. When the futures position was opened, the basis was 250

points (1.8050 – 1.7800). When the position was closed, the basis was 100

points (1.7700 – 1.7600). The spot price has moved in value during the three

months by more than the movement in the futures price, by 150 points. The

value of this difference is $9,375 (10 contracts × 150 ticks per contract × £6.25

per tick).

41 Currency hedge

(a) Hedging with a forward exchange contract

Only the net exposure should be hedged. This is a net payment of

€(2,650,000

– 540,000) =

€2,110,000.

The entity will need to buy euros in three months’ time. The three-month

forward rate for the contract would be 1.4443 (the rate more favourable to the

bank).

Cost in sterling =

€2,110,000/1.4443 = £1,460,915.

(b) Money market hedge

The company must pay

€2,110,000 in three months’ time. To create a money

market hedge, it must therefore buy euros spot and invest them for three

months at 3.4% per year. The amount of euros invested, plus accumulated

interest, must be worth

€2,110,000 after three months.

It is assumed that the three-month investment rate for euros is 3.4% × 3/12 =

0.85%.

The amount of euros to invest now is therefore

€2,110,000/1.0085 = €2,092,216.

These must be purchased spot at 1.4537, and the cost in sterling will be:

€2,092,216/1.4537 = £1,439,235.

Answers

With a forward FX contract, the payment of £1,460,915 will be made in three

months’ time. With a money market hedge, the payment of £1,439,235 would

happen immediately. It can therefore be argued that an additional cost of a

money market hedge is the loss of interest (opportunity cost) from investing

£1,439,235 for three months at 5.6% per year. The lost interest would be

£1,439,235 × 5.6% × 3/12 = £20,149.

The overall cost of a money market hedge would therefore be £1,439,235 +

£20,149 = £1,459,384.

(c)

Currency futures hedge

The company must pay euros. It needs to buy euros to make the payments.

The futures are denominated in euros; therefore the company will buy futures.

The number of contracts required = €2,110,000/€100,000 per contract = 21.1

contracts. The company should probably buy 21 contracts.

The payments are due in October. The company should therefore buy futures

with the next settlement date following. It should buy December contracts at

0.6929.

The remaining €10,000 that is not hedged by futures can be purchased

forward at 1.4443, at a cost of £6,924.

If the basis is 0 when the futures position is closed in October, the effective

exchange rate for the €2,100,000 will be £0.6929 = €1, or £1 = €1.4432.

The net cost in sterling will be:

€2,100,000 at $1.4432/£1 1,455,100

€10,000 at €1.4443/£1 6,924

Total cost in sterling 1,462,024

The money market hedge is the cheapest method of hedging.

42 Hedging with STIRs

The company wants a hedge against the risk of higher interest rates. It should

therefore sell short-term interest rate futures.

The borrowing period will begin in February; the company should therefore buy

March futures, which have the next settlement date following the start of the loan

period.

The planned borrowing period is 5 months, but with futures, the notional deposit

period is only 3 months. To get round this difficulty, the number of futures contracts

should be adjusted.

months 3

months

£500,000

million

£4.5

=sell to futuresMarch of number The

= 15 contracts.

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Conclusion

The company should sell 15 March short sterling futures.

43 More hedging with STIRs

(a) The company wants a hedge against the risk of higher interest rates. It should

therefore sell short-term interest rate futures.

The borrowing period will begin in February; the company should therefore

buy March futures, which have the next settlement date following the start of

the loan period.

The planned borrowing period is 4 months, but with futures, the notional

deposit period is only 3 months. To get round this difficulty, the number of

futures contracts should be adjusted.

months 3

months 4

million $1

million $12

=sell to futuresMarch of number The

= 16 contracts.

Conclusion

The company should sell 16 March eurodollar futures at 93.70.

(b) When the futures are sold, the basis is:

Spot LIBOR rate (100

–

5.5)

0.9450

Futures price 0.9370

Basis 0.0080

It is now the end of October. The March futures will reach settlement date in

five months’ time.

If we assume that the basis will reduce from 80 points at the end of October to

0 by the end of March at an equal amount each month, by the end of January

the basis should be:

points 32=points 80

settlement to time original months 5

settlement to months

The futures price is lower than the spot price.

At the beginning of February, if the three-month LIBOR rate is 7.5%, the

futures price should be:

Spot LIBOR rate (100

–

7.5)

0.9250

Basis 0.0032

Futures price 0.9218

The futures position will be closed out, as follows:

Selling price in October 0.9370

Buying price to close 0.9218

Gain 0.0152

Answers

The gain is 152 points or 1.52%

The futures hedge is a perfect hedge, and the effective cost of borrowing can

therefore be calculated as follows:

Borrow $12 million at 7.50

Gain on futures position (1.52)

Net effective borrowing cost

5.98

The net effective borrowing cost is 5.98%.

(Note: This differs from the rate in the futures contracts sold in October. In

October, the interest rate in the sold futures was 6.30% (100 – 93.70). The

difference is 32 points, which is the amount of the basis risk. Here, the

company has benefited from the basis to obtain a lower borrowing cost).

44 FRAs and futures

(a)

FRAs

The company can use an FRA to fix the interest rate receivable on £8.2 million. A

4v9 FRA is required, and the bank will offer a rate of 4.52%.

The company will therefore fix a rate of 4.52% for LIBOR and if it can invest at

LIBOR + 0.40% this means that the effective investment rate will be 4.92%.

Futures

The company wants to fix an interest rate for income, so it should buy futures. The

money for investment will be received at the end of July, so September futures

should be used.

The company should buy (£8.2 million /£500,000) × (5 months/3 months) = 27.33

futures contracts, say 27 futures, and the price is 95.35.

(b)

FRAs

At the end of July when the £8.2 million, the company will invest the money for 5

months. If it can still obtain a rate of LIBOR + 0.40%, it will invest the money at

4.65%.

The FRA contract must also be settled, as follows:

Pay LIBOR (4.25)

Receive 4.52

Profit on settlement 0.27

The company will receive a payment on settlement of the FRA equivalent to 0.27%

in interest, which means that its effective interest income from investing the money

for 5 months will be 4.65% + 0.27% = 4.92%.

Futures

Paper P4: Advanced Financial Management

When the futures contracts were purchased on 1st April, basis was 95.35 – 95.00 =

0.35. This is 0.05833 per month (0.35/6 months). Assuming basis changes by a

constant amount each month, the expected basis at the end of July (2 months to the

end of September) is 0.117.

The expected futures price at the end of July if LIBOR is 4.25% is therefore:

95.75 + 0.117 = 95.867.

The futures position will be closed as follows:

Close: sell at 95.867

Purchase price 95.350

Profit 0.517

Total profit on 27 contracts = 51.7 × £12.50 × 27 = £17,449.

The company can invest £8.2 million + £17,449 for 5 months at 4.65% (LIBOR +

0.40%) and total interest will be £159,213 (£8,217,449 × 4.65% × 5/12).

On the money received of £8.2 million, this represents an effective interest rate of

(£159,213/£8.2 million) × (12/5) = 0.047 or 4.7%.

In this particular case, FRAs would be a better way of hedging the interest rate risk

than futures.

45 Traded equity options

(a) The investor should buy put options on TBA shares.

Strike

price

Cost per option

Number of options

purchased with £12,000

950 (2,000 shares ×

$0.15)

300

1,000 (2,000 shares ×

$0.50)

1,000

The investor could purchase 12 put options at a strike price of 1,000 (£10) or 40

put options at a strike price of 950 (£9.50).

He is more likely to buy the out-of-the-money options at 950.

(b) If the share price is 910 at expiry and the investor still holds the options, the

options will be exercised. It is assumed that he buys the options at 950.

Traded equity options are settled by physical delivery. The investor would

need to buy shares at 910 and exercise the option to sell them at 950.

Buy 40 × 2,000 shares at 910 728,000

Buy 40 ×

2,000 shares at 950

760,000

Profit on exercise 32,000

Cost of options 12,000

Net profit on speculative investment

20,000

Answers

(Note: This calculation of the profit ignores the time value of money. The

options are paid for when they are bought, but the profit is made only when

the options are exercised).

Traded equity options can be bought and sold on the exchange, and the

investor is likely to sell the put options before they expire, making a profit on

the sale. As the options become increasingly in-the-money, their market value

will increase.

46 Currency options

In September, the UK company will want to sell dollars and buy sterling (to convert

its dollar receipts into sterling).

Since it wants to buy sterling in six months’ time, it should buy call options with a

September expiry.

If the strike price is $1.8500, the sterling equivalent of $2 million = £1,081,081

(2,000,000/1.85).

The contract size is £31,250; therefore for a perfect hedge, the company would want

to buy 34.6 contracts (1,081,081/31,250).

Since this is not possible, it should buy either 34 or 35 contracts. In the answer that

follows, it is assumed that the company will buy 35 options.

Premium cost = 35 × 31,250 × $0.019 = $20,781.25.

To pay the premium, the company would have to buy $20,781.25 spot, at a sterling

cost of £11,340.38.

At the expiry date, the options are in-the-money if the spot exchange rate is 1.9200.

They will therefore be exercised, at a profit of $0.07 per £1 (1.9200 – 1.8500).

Gain on exercise of 35 option contracts = 35 × 31,250 × $0.07 = $76,562.50.

The total dollar income of the company will therefore be $2,076,562.50.

This can be exchanged into sterling at the spot rate, to obtain £1,081,543

($2,076,562.50/1.9200).

The option premium cost was £11,340, therefore ignoring the time value of money,

the net revenue for the company is £1,081,543 – £11,340 = £1,070,203.

This gives an effective exchange rate for the $2 million dollar receipts of 1.8688

(2,000,000/1,070,203).

Paper P4: Advanced Financial Management

47 Interest rate hedge

(a) Futures

The company wants a hedge against the risk of a rise in two-month interest rates.

It should therefore sell futures. Since the interest period will be 2 months and

futures are for a three-month deposit, the quantity of futures sold should be:

(£21 million/£500,000) × 2/3 = 28 contracts.

The loan period will begin in mid-June; therefore sell 28 June contracts, at a

price of 94.610.

Options on futures

The company will want options to sell futures; therefore it should buy put

options on 28 June futures. The premium cost will depend on the strike price

chosen. (Since the options are needed for two months, apply a factor of ×

2/12).

Strike price Premium

94750 (£21,000,000 × 0.500% × 2/12) £17,500

95000 (£21,000,000 ×

0.850% ×

2/12)

£29,750

FRA

The company should buy a 3v5 FRA, for a notional principal amount of £21

million. The FRA rate will be 5.38%.

(Note: The FRA rate is more favourable than the futures rate of 5.39% (100 –

94.610). The company would therefore prefer to buy an FRA than sell futures.

However, it might prefer to buy put options on futures rather than buy an

FRA).

In mid-June, the company will borrow £21 million for two months. If the

LIBOR rate is 6%, it will borrow at 6.75% (LIBOR + 0.75%) for two months.

Futures

The futures price in mid-June can be estimated as follows:

June futures price in mid-March

94.610

LIBOR rate in mid-March 95.000

Basis in mid-March 0.390

In mid-March, there were 3.5 months to settlement of the June futures. In mid-

June, there are 0.5 months remaining to settlement. Basis is assumed to have

reduced in size by mid-June to:

(0.5/3.5) × 39 points = 5.6 points, say 5 points.

LIBOR rate in mid-June 94.000

Basis in mid-June 00.005

Estimated futures price in mid-June

93.995

The company will close its position by buying 28 June futures at 93.995.

Original selling price 94.610

Buying price to close 93.995

Gain (ticks) 00.615

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

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