Question 1
Part (A)
A.1) ABC Company and XYZ Company need to raise funds to pay for capital improvements
at their manufacturing plants. ABC Company can borrow funds either at a 10% fixed rate or at
LIBOR+1% floating rate. XYZ Company can borrow funds either at an11% fixed rate or at
LIBOR+3 % floating rate.
a. Is there an opportunity here for ABC and XYZ to benefit by means of an interest rate
swap?
[ 5 marks]
b. Suppose you have been hired at a bank that acts as a dealer in the swaps market and
your boss has shown you the borrowing rate information for your clients, ABC and
XYZ. Describe how you could bring these two companies together in an interest rate
swap that would make both firms better off while netting your bank a 0.2% profit.
[10 marks]
Solution
a. XYZ has a comparative advantage relative to ABC in borrowing at fixed interest rates,
while ABC has a comparative advantage relative to XYZ in borrowing at floating
interest rates.
Since the spread between ABC's and XYZ's fixed rate costs is only 1 percent, while
their differential is 2 percent in floating-rate markets, there is an opportunity for a 1
percent total gain by entering into a fixed-for-floating-rate swap agreement.
b. If the swap dealer must capture 0.2 percent of the available gain, there is 0.8 percent
left for ABC and XYZ. Any division of that gain is feasible; in an actual swap deal,
the division would probably be negotiated by the dealer. One possible combination is
.4 percent for ABC and .4 percent for XYZ:
8.6% 8.4%
ABC Dealer XYZ
LIBOR LIBOR
LIBOR
+1% 11%
Debt Market Debt Market
A net payments= LIBOR +1% +8.6-LIBOR=9.6
9.6 less that 10 % fixed rate by0.4
B net payments= 11%+LIBOR+8.4% = LIBOR+2.6%
LIBOR+2.6% less that LIBOR +3% floating rate by 0.4.
Page 1 of 18
,A.2) You are a portfolio manager responsible for derivatives. You observe European options
with the same strike price, expiration, and underlying stock. You have collected the information
in the following table.
Closing stock price £43
Call and put option exercise price 45
1-year put option price 4
1-year risk-free rate 5.50%
Time to expiration One year
Calculate the price of the European call option with the same strike price, expiration, and the
underlying stock as the put option in the table above.
[5 marks]
Solution
C = S0 + P PV(X) = £43 + £4 £45e-0.055 = £4.41
Note: we assume that stock does not pay any dividends.
A.3) If a manufacturer wanted to hedge against adverse movements in oil prices. He can buy
oil futures contracts or buy call options on oil futures contracts. What would be the pros and
cons of the two approaches?
[5 marks]
Solution
A.3) Buying the call options is a form of insurance policy for the firm. If oil prices rise, the
firm is protected by the call, while if prices actually decline, they can just allow the call to
expire worthless. However, options hedges are costly because of the initial premium that
must be paid.
The futures contract can be entered into at no initial cost, with the disadvantage that the firm is
locking in one price for oil; it can't profit from oil price declines.
Part (B)
B.1) DFD corporation is trying to decide between two different models of IT systems. System
A costs £295,000, has a four-year life, and requires £77,000 in pre-tax annual operating costs.
System B costs £355,000, has a six-year life, and requires £83,000 in pre-tax annual operating
costs. Both systems are to be depreciated straight-line to zero over their lives and will have
zero salvage value, whichever project is chosen, the company will replace the system with the
same model, which system should the firm choose if the tax rate is 21% and the discount rate
is 8%.
[15 marks]
Solution
Page 2 of 18
, Both projects only have costs associated with them, not sales, so we will use these to calculate
the NPV of each project. Using the tax shield approach to calculate the OCF, the NPV of
System A is:
OCFA = –£77,000(1 – .21) + .21(£295,000/4)
OCFA = –£45,343
NPVA = –£295,000 – £45,343(PVIFA8%,4)
NPVA = –£445,180.11
And the NPV of System B is:
OCFB = –£83,000(1 – .21) + .21(£355,000/6)
OCFB = –£53,145
NPVB = –£355,000 – £53,145(PVIFA8%,6)
NPVB = –£600,682.94
If the system will be replaced at the end of its useful life, the correct capital budgeting technique
is EAC.
EACA = –£445,180.11/(PVIFA8%,4)
EACA = –£134,409.14
EACB = –£600,682.94/(PVIFA8%,6)
EACB = –£129,936.96
If the system will be continually replaced, we should choose System B since it has a more
positive EAC.
B.2) Suppose TFA corporation needs to raise £65 million and wants to issue 20-year bonds for
this purpose. Assume the required return on the bond issue will be 4.9 per cent. TFA is
evaluating the option of issuing a semiannual coupon bond with a coupon rate of 4.9 per cent
and a par value of £1,000.
a. How many coupon bonds would TFA needs to issue to raise the £65 million?
[ 5 marks ]
b. In 20 years, what will TFA repayment be if it issues the coupon bonds?
[ 5 marks ]
Solution:
Page 3 of 18
Part (A)
A.1) ABC Company and XYZ Company need to raise funds to pay for capital improvements
at their manufacturing plants. ABC Company can borrow funds either at a 10% fixed rate or at
LIBOR+1% floating rate. XYZ Company can borrow funds either at an11% fixed rate or at
LIBOR+3 % floating rate.
a. Is there an opportunity here for ABC and XYZ to benefit by means of an interest rate
swap?
[ 5 marks]
b. Suppose you have been hired at a bank that acts as a dealer in the swaps market and
your boss has shown you the borrowing rate information for your clients, ABC and
XYZ. Describe how you could bring these two companies together in an interest rate
swap that would make both firms better off while netting your bank a 0.2% profit.
[10 marks]
Solution
a. XYZ has a comparative advantage relative to ABC in borrowing at fixed interest rates,
while ABC has a comparative advantage relative to XYZ in borrowing at floating
interest rates.
Since the spread between ABC's and XYZ's fixed rate costs is only 1 percent, while
their differential is 2 percent in floating-rate markets, there is an opportunity for a 1
percent total gain by entering into a fixed-for-floating-rate swap agreement.
b. If the swap dealer must capture 0.2 percent of the available gain, there is 0.8 percent
left for ABC and XYZ. Any division of that gain is feasible; in an actual swap deal,
the division would probably be negotiated by the dealer. One possible combination is
.4 percent for ABC and .4 percent for XYZ:
8.6% 8.4%
ABC Dealer XYZ
LIBOR LIBOR
LIBOR
+1% 11%
Debt Market Debt Market
A net payments= LIBOR +1% +8.6-LIBOR=9.6
9.6 less that 10 % fixed rate by0.4
B net payments= 11%+LIBOR+8.4% = LIBOR+2.6%
LIBOR+2.6% less that LIBOR +3% floating rate by 0.4.
Page 1 of 18
,A.2) You are a portfolio manager responsible for derivatives. You observe European options
with the same strike price, expiration, and underlying stock. You have collected the information
in the following table.
Closing stock price £43
Call and put option exercise price 45
1-year put option price 4
1-year risk-free rate 5.50%
Time to expiration One year
Calculate the price of the European call option with the same strike price, expiration, and the
underlying stock as the put option in the table above.
[5 marks]
Solution
C = S0 + P PV(X) = £43 + £4 £45e-0.055 = £4.41
Note: we assume that stock does not pay any dividends.
A.3) If a manufacturer wanted to hedge against adverse movements in oil prices. He can buy
oil futures contracts or buy call options on oil futures contracts. What would be the pros and
cons of the two approaches?
[5 marks]
Solution
A.3) Buying the call options is a form of insurance policy for the firm. If oil prices rise, the
firm is protected by the call, while if prices actually decline, they can just allow the call to
expire worthless. However, options hedges are costly because of the initial premium that
must be paid.
The futures contract can be entered into at no initial cost, with the disadvantage that the firm is
locking in one price for oil; it can't profit from oil price declines.
Part (B)
B.1) DFD corporation is trying to decide between two different models of IT systems. System
A costs £295,000, has a four-year life, and requires £77,000 in pre-tax annual operating costs.
System B costs £355,000, has a six-year life, and requires £83,000 in pre-tax annual operating
costs. Both systems are to be depreciated straight-line to zero over their lives and will have
zero salvage value, whichever project is chosen, the company will replace the system with the
same model, which system should the firm choose if the tax rate is 21% and the discount rate
is 8%.
[15 marks]
Solution
Page 2 of 18
, Both projects only have costs associated with them, not sales, so we will use these to calculate
the NPV of each project. Using the tax shield approach to calculate the OCF, the NPV of
System A is:
OCFA = –£77,000(1 – .21) + .21(£295,000/4)
OCFA = –£45,343
NPVA = –£295,000 – £45,343(PVIFA8%,4)
NPVA = –£445,180.11
And the NPV of System B is:
OCFB = –£83,000(1 – .21) + .21(£355,000/6)
OCFB = –£53,145
NPVB = –£355,000 – £53,145(PVIFA8%,6)
NPVB = –£600,682.94
If the system will be replaced at the end of its useful life, the correct capital budgeting technique
is EAC.
EACA = –£445,180.11/(PVIFA8%,4)
EACA = –£134,409.14
EACB = –£600,682.94/(PVIFA8%,6)
EACB = –£129,936.96
If the system will be continually replaced, we should choose System B since it has a more
positive EAC.
B.2) Suppose TFA corporation needs to raise £65 million and wants to issue 20-year bonds for
this purpose. Assume the required return on the bond issue will be 4.9 per cent. TFA is
evaluating the option of issuing a semiannual coupon bond with a coupon rate of 4.9 per cent
and a par value of £1,000.
a. How many coupon bonds would TFA needs to issue to raise the £65 million?
[ 5 marks ]
b. In 20 years, what will TFA repayment be if it issues the coupon bonds?
[ 5 marks ]
Solution:
Page 3 of 18
