ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing
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41 Diversify
The first step is to use the equity betas of the three chemical manufacturing
companies (proxy companies) to estimate an asset beta for the business risk in
chemicals manufacturing.
Company Estimated asset beta
A
2.66 × [40/40 + 60(1 – 0.25%)] = 2.66 × 0.4706 = 1.25
B
1.56 × [75/75 + 25(1 – 0.25%)] = 1.56 × 0.80 = 1.25
C
1.45 × [80/80 + 20(1 – 0.25%)] = 1.45 × 0.8421 = 1.22
It is assumed that the asset beta is a simple average of these three values:
(1.25 + 1.25 + 1.22)/3 = 1.24.
This asset beta can be used to calculate an equity beta for Bustra, for the investment
in chemicals manufacturing:
1.24 =
β
E
×
60
60 + 40 (1 – 0.25)
0.667
β
E
= 1.24
β
E
= 1.86
If an appropriate equity beta for Bustra in chemicals manufacturing is 1.86, the
cost
of equity
(using the CAPM) is:
5% + 1.86 (9 – 5)% = 12.44%
If the cost of equity is 12.44%, the pre-tax cost of debt is 5% (= risk-free rate) and tax
is 25%,
a suitable discount rate for evaluating the proposed investment would be:
(60% × 12.44%) + [40% × 5 (1 – 0.25)%]
= 8.964%, say 9%.
42 Acquisition
(a) The earnings of Little next year are expected to be $86,000. A forward P/E
multiple of 8.0 could be applied to this estimate, and the valuation of the
equity shares in Little would be:
$86,000 × 8.0 = $688,000.
(b) The cost of equity of Big is expected to be:
6% + 1.60 (11 – 6)% = 14%.
The WACC of Big is expected to be:
[35% × 7.4 (1 – 0.30)] + (65% × 14)
= 10.913%.
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(c) Since Little is in the same industry as Big, it is probably appropriate to use the
WACC of Big to obtain a DCF-based valuation of Little. The WACC of
10.913% will be rounded to 11%.
The cash flows from the acquisition of Little must be calculated.
Year1 Year2 Year3
$ $ $
Sales 200,000 280,000 320,000
Cashcosts (120,000) (160,000) (180,000)
–
–––––––
–
––––––– ––––––––
80,000 120,000 140,000
Capitalallowances (20,000) (30,000) (40,000)
Interest (10,000) (10,000) (10,000)
–
–––––––
–
––––––– ––––––––
Taxableprofit 50,000 80,000 90,000
Taxat30% (15,000) (24,000) (27,000)
–
––––
–
––
–
––––––– ––––––––
Profitaftertax 35,000 56,000 63,000
–
–––––––
–
––––––– ––––––––
Profitaftertax 35,000 56,000 63,000
Addbackcapitalallowances 20,000 30,000 40,000
–
–––––––
–
––––––– ––––––––
55,000 86,000 103,000
Assetreplacement (25,000) (30,000) (35,000)
–
–––––––
–
––––––– ––––––––
Cashflow 30,000 56,000 68,000
–
–––––––
–
––––––– ––––––––
Cash flows will increase by 4% each year from Year 4 onwards.
The dividend growth valuation model can be used to calculate the Year 3
value of these cash flows, using a growth rate of 4% and a cost of capital of
11%:
Year 3 value of cash flows from Year 4 =
$68,000 1.04
(
)
0.11−0.04
()
= $1,010,286
The expected cash flows can now be converted in to a present value:
Year Cashflow
Discount
factorat11% PV
$ $
1 30,000 0.901 27,030
2 56,000 0.812 45,472
3 68,000 0.731 49,708
4onwards 1,010,286 0.731 738,519
–
––––––
Totalvalue 860,729
–
––––––
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43 Interest rate parity
(a) GBP/USD = 1.8000 × (1.035/1.05) = 1.7743
(Note: the interest rate is lower for the dollar than for sterling, therefore the
dollar should increase in value over time against sterling.)
GBP/EUR = 1.5000 × (1.025/1.05) = 1.4643
EUR/USD = 1.2000 × (1.035/1.025) = 1.2117
(b) GBP/USD = 1.8000 × (1.035/1.05)
3
= 1.7240
GBP/EUR = 1.5000 × (1.025/1.05)
3
= 1.3954
EUR/USD = 1.2000 × (1.035/1.025)
3
= 1.2355
44 Foreign exchange
(a) A hedge against the risk can be obtained by entering into a forward rate
agreement to buy $750,000. The forward rate is the forward rate that favours
the bank. This is 1.8535 (and not 1.8543).
The cost of buying the dollars will be $750,000/1.8535 = £404,639.87.
(b) Subtract a premium, add a discount.
Spot rate 1.3025
Premium (0.0018)
Forward rate 1.3007
The $450,000 will be sold in exchange for €345,967.56 (450,000/1.3007).
(c) Forward rates = 1.9757 – 1.9763
The rate for a company to buy sterling (sell dollars) is 1.9763.
Cost of buying £750,000 = 750,000 × 1.9763 = $1,479,750.
45 Money market hedge
(a) The company will receive $600,000 in six months, and will want to receive
sterling and pay dollars.
It can do this with a money market hedge by borrowing US dollars now. The
interest rate for six months in dollars is 3.5% × 6/12 = 1.75%. It will need to
borrow now:
$600,000/1.0175 = $589,680.59.
It can immediately exchange these dollars into sterling at the spot rate of
1.8800, to obtain:
$589,680.59/1.8800 = £313,659.89.
After six months, the dollar loan will be repayable with interest. The total
repayment will be $600,000, and the payment can be made from the $600,000
received from the customer.
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(b) The company can do anything with the sterling it receives now from the
hedging transaction. If it chose to invest the cash for six months at 5% per year
(2.5% for six months), the investment of £313,659.89 would increase to:
£313,659.89 × 1.025 = £321,501.39.
To avoid opportunities for arbitrage between the money markets and the
forward FX markets, the six-month forward exchange rate would therefore
need to be:
$600,000/£321,501.39 = 1.8662.
46 Dunborgen
Forward exchange contract
The six-month forward rate is 1.566 – 1.574.
Dunborgen would need to buy $500,000, and the bank would charge a rate of
$1.566.
The cost to Dunborgen in euros in six months’ time = 500,000/1.566 = €319,285.
Money market hedge
The spot exchange rate is 1.602 – 1.606
Dunborgen could borrow euros now, convert them into dollars and put the dollars
on deposit for six months.
The six month interest rate for US dollar deposits = 2.0% × 6/12 = 1.0%.
To have $500,000 in six months time, Dunborgen would need to deposit:
$500,000 × (1/1.01) = $495,050.
The cost in euros of buying $495,050 spot = 495,050/1.602 = €309,020.
It is assumed that the euros to purchase the dollars spot would be obtained by
borrowing for six months at 4.8%. Interest for six months would be 4.8% × 6/12 =
2.4%.
The cost in euros to Dunborgen of a money market hedge, for comparison with the
cost of a forward contract, would therefore be:
€309,020 × 1.024 = €316,436.
Comparison of hedging methods
A money market hedge would be less expensive in this case, and is therefore
recommended as the method of hedging the currency risk exposure.
47 FRA
(a) The company wants to borrow in three months’ time for a period of six
months; therefore to create a hedge with an FRA, it must buy a 3v9 FRA.
The interest rate for the FRA is 3.97%.
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The company will borrow in three months’ time at the current LIBOR rate
plus 0.50%.
The FRA will be settled in three months’ time.
−
If the six-month LIBOR rate is higher than 3.97%, the company will
receive a payment from the bank to settle the FRA. The amount of this
payment is the value of the difference between the FRA rate of 3.97%
and the LIBOR rate.
−
If the six-month LIBOR rate is lower than 3.97%, the company will
make a payment to the bank to settle the FRA, for the value of the
difference between the two rates.
The effect of the FRA is therefore to ‘lock in an effective interest rate of 3.97%
+ 0.50% = 4.47%.
Tutorial note: For example, if the LIBOR rate in three months is 5.5%, the
situation will be as follows:
%
Company borrows at LIBOR + 0.50% 6.00
Company receives from settlement of FRA (5.50 – 3.97) (1.53)
Effective interest cost 4.47
This is the FRA rate + 0.50%.
(b) An FRA works on the same principles as an interest rate coupon swap. The
main difference is that an FRA is for one interest period only, although a
company can arrange a series of FRAs. A coupon swap is longer-term, and
covers several settlement dates.
48 Swap
The company should enter into a four-year interest rate coupon swap in which it
receives the floating rate and pays the fixed rate (5.25%).
The effective interest rate will change from floating rate to fixed rate, as follows:
%
Bankloaninterest (LIBOR+1.25)
Swap
Pay (5.25)
Receive LIBOR
Effectiverate (6.50)
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49 Credit arbitrage
%
EntityAcanborrowmorecheaplyatafixedrateby(7.25–6.35) 0.90
EntityAcanborrowmorecheaplyatafloatingrateby(1.25–0.75) 0.50
Difference 0.40
Bank’sprofit 0.10
Netbenefittosharebetweenthetwoentities 0.30
If the entities share the benefit equally, each will be able to reduce its effective cost
of borrowing by (0.30/2) 0.15%.
Entity A wants to borrow at a floating rate. It can borrow directly at LIBOR +
0.75%. By borrowing at a fixed rate and swapping into a floating rate, its
effective interest rate will be LIBOR + 0.75% – 0.15% = LIBOR + 0.60%.
Entity B wants to borrow at a fixed rate. It can borrow directly at 7.25%. By
borrowing at a floating rate and swapping into a fixed rate, its effective interest
rate will be 7.25% – 0.15% = 7.10%.
For Entity A, the arrangement could be as follows:
%
Borrowatafixedrate (6.35)
Swappayments
Pay (LIBOR)
Receive(balancingfigure) 5.75
Effectiveinterestcost (LIBOR+0.60)
For Entity A, the arrangement would be as follows:
%
Borrowatafixedrate (LIBOR+1.25)
Swappayments
Pay(balancingfigure) (5.85)
Receive LIBOR
Effectiveinterestcost (7.10)
The bank’s profit would come from the difference between the fixed rate received
from Entity B (5.85%) and the fixed rate paid to Entity A (5.75%).
This assumes that the two Entities each arrange their swap with the bank, and not
directly with each other.
50 Currency futures
(a) The company must make a payment in US dollars in May. It must therefore
buy dollars to make the payment.
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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.
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 × 0.011 × $125,000 = $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.
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Paper F9
Financial management
Appendix
Formula sheet
and tables
Formula Sheet
Economic order quantity
H
C
D2C o
=
Miller – Orr Model
Return point = Lower limit + (
3
1
× spread)
3
1
rate interest
flows cashof variance cost ntransactio
4
3
3 Spread
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
××
=
The Capital Asset Pricing Model
(
)
()
f
mi
f
i
RrER (r E −+=
β
)
The asset beta formula
()
()
(
)
()
()
⎥
⎦
⎤
⎢
⎣
⎡
−+
−
+
⎥
⎦
⎤
⎢
⎣
⎡
+
=
d
de
d
e
de
e
a
T1VV
T1V
T- 1VV
V
βββ
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The Growth Model
()
()
gr
g1D
P
e
o
o
−
+
=
Gordon’s growth approximation
e
br g =
The weighted average cost of capital
()
T1K
VV
V
K
VV
V
WACC
d
de
d
e
de
e
−
⎥
⎦
⎤
⎢
⎣
⎡
+
+
⎥
⎦
⎤
⎢
⎣
⎡
+
=
The Fisher formula
()( )( )
h1r1i1
+
+=+
Purchasing power parity and interest rate parity
()
()
b
c
o1
h1
h1
SS
+
+
×=
(
)
()
b
c
oo
i1
i1
Sf
+
+
×=