1) Eurobonds versus Domestic Bonds - International Corporate Finance
The dollar cost of debt for Coval Consulting, a U.S. research firm, is 7.5%. The firm faces a tax
rate of 30% on all income, no matter where it is earned. Managers in the firm need to know its
yen cost of debt because they are considering launching a new bond issue in Tokyo to raise
money for a new investment there.
The risk-free interest rates on dollars and yen are r$ = 5% and r¥ = 1%, respectively. Coval
Consulting is willing to assume that capital markets are internationally integrated and that its free
cash flows are uncorrelated with the yen-dollar spot rate. What is Coval Consulting’s after-tax
cost of debt in yen?
Answer:
We first find the after-tax cost of debt in dollars and then find the yen equivalent.
after-tax cost of debt = (0.075)(1 – 0.30) = 0.0525 or 5.25%
To internationalize the cost of capital we use the following formula:
𝒓¥ =
𝒓¥ =
𝟏 + 𝒓¥
∗ (𝟏 + 𝒓$ ) − 𝟏
𝟏 + 𝒓$
𝟏 + 𝟎. 𝟎𝟏
∗ (𝟏 + 𝟎. 𝟎𝟓𝟐𝟓) − 𝟏 = 𝟏. 𝟐𝟒%
𝟏 + 𝟎. 𝟎𝟓
2) Credit & Exchange Rate Risk -International Corporate Finance
Suppose the interest on Russian government bonds is 7.5%, and the current exchange rate is 28
rubles per dollar. If the forward exchange rate is 28.5 rubles per dollar, and the current U.S. riskfree interest rate is 4.5%, what is the implied credit spread for Russian government bonds?
Answer:
The covered interest parity equation is:
𝑭=𝑺∗
𝟏 + 𝒓𝑹
𝟏 + 𝒓$
where F = forward exchange rate, S = spot exchange rate, rR = risk-free rate in rubles and
r$ = risk-free rate in dollars.
Using this equation, we first find the risk-free rate in rubles rR, then subtract it from the
risk-free rate in dollars to find the implied credit spread for Russian government bonds.
Re-arrange the equation find the risk-free rate in rubles rR:
𝒓𝑹 =
𝑭 ∗ (𝟏 + 𝒓$ )
𝑺
𝒓𝑹 =
𝟐𝟖. 𝟓 ∗ 𝟏. 𝟎𝟒𝟓
= 𝟔. 𝟑𝟕%
𝟐𝟖
Therefore, the implied credit is: 7.5% - 6.37% = 1.13%
3) Forward Market Hedge - Risk Management
You are a broker for frozen seafood products for Choyce Products. You just signed a deal with a
Belgian distributor. Under the terms of the contract, in 1 year, you will deliver 4000 kg of frozen
king crab for 100,000 euros. Your cost for obtaining the king crab is $110,000. All cash flows
occur in exactly 1 year.
a. Plot your profits in 1 year from the contract as a function of the exchange rate in 1 year for
exchange rates from $0.75/€ to $1.50/€. Label this line Unhedged Profits.
Answer:
Unhedged profit = (100,000 euros) * (S1 $/euro) – 110,000 (see Figure 1 below)
Computations:
At $0.75/€:
At $1.00/€:
At $1.25/€:
At $1.50/€:
(100,000 euros) * ($0.75/€) – 110,000 =
(100,000 euros) * ($1.00/€) – 110,000 =
(100,000 euros) * ($1.25/€) – 110,000 =
(100,000 euros) * ($1.50/€) – 110,000 =
($35,000)
($10,000)
$15,000
$40,000
b. Suppose the 1-year forward exchange rate is $1.25/€ and that you enter into a forward contract
to sell the euros you will receive at this rate. In the figure from part (a), plot your combined
profits from the crab contract and the forward contract as a function of the exchange rate in one
year. Label this line Forward Hedge.
Answer:
Forward Hedged profit = (100,000 euros) * (1.25 $/euro) – 110,000 = $15,000 (see Figure 1
below)
Computations:
At $0.75/€:
At $1.00/€:
At $1.25/€:
At $1.50/€:
(100,000 euros) * (1.25 $/€) – 110,000 =
(100,000 euros) * (1.25 $/€) – 110,000 =
(100,000 euros) * (1.25 $/€) – 110,000 =
(100,000 euros) * (1.25 $/€) – 110,000 =
$15,000
$15,000
$15,000
$15,000
c. Suppose that instead of using a forward contract, you consider using options. A 1-year call
option to buy euros at a strike price of $1.25/€ is trading for $0.10/€. Similarly, a 1-year put
option to sell euros at a strike price of $1.25/€ is trading for $0.10/€. To hedge the risk of your
profits, should you buy or sell the call or the put?
Answer:
Since I am selling euros and buying dollars, I should buy the put to hedge the risk of my
profits.
d. In the figure from parts (a) and (b), plot your “all in” profits using the option hedge (combined
profits of crab contract, option contract, and option price) as a function of the exchange rate in
one year. Label this line Option Hedge. (Note: You can ignore the effect of interest on the option
price.)
Answer:
The cost of buying put options for 100,000 euros is 100,000 * $0.10 = $10,000.
Because of the put, the minimum selling price for euros would then be $1.25/euro.
The All-in Option hedged profit is therefore:
Profit = (100,000 euros) * (max[1.25, S1] $/euro) – 110,000 – 10,000
Profit = max [$5,000, (100,000 euros) * (S1 $/euro) – 120,000] (see Figure 1 below)
Computations:
At $0.75/€:
At $1.00/€:
At $1.25/€:
At $1.50/€:
max [$5,000, (€100,000* $0.75/€) – 120,000] =
max [$5,000, (€100,000* $1.00/€) – 120,000] =
max [$5,000, (€100,000* $1.25/€) – 120,000] =
max [$5,000, (€100,000* $1.50/€) – 120,000] =
$5,000
$5,000
$5,000
$30,000
Figure 1
e. Suppose that by the end of the year, a trade war erupts, leading to a European embargo on U.S.
food products. As a result, your deal is cancelled, and you don’t receive the euros or incur the
costs of procuring the crab. However, you still have the profits (or losses) associated with your
forward or options contract. In a new figure, plot the profits associated with the forward hedge
and the options hedge (labeling each line). When there is a risk of cancellation, which type of
hedge has the least downside risk? Explain briefly.
The forward hedge results in profit if the euro depreciates and results in loss if the euro
appreciates. The profit from the forward hedge is:
(100,000 euros)*(1.25 – S1 $/euro) (see Figure 2 below)
Computations:
At $0.75/€:
At $1.00/€:
At $1.25/€:
At $1.50/€:
(100,000 euros)*(1.25 – $0.75/€) =
(100,000 euros)*(1.25 – $1.00/€) =
(100,000 euros)*(1.25 – $1.25/€) =
(100,000 euros)*(1.25 – $1.50/€) =
$50,000
$25,000
$0
($25,000)
The option hedge pays if the euro declines. It is worthless if the euro appreciates and the
maximum loss is the initial cost of $10,000. The profit from the option hedge is:
max [0, (100,000 euros)*(1.25 – S1 $/euro)] – 10,000 (see Figure 2 below)
Computations:
At $0.75/€:
At $1.00/€:
At $1.25/€:
At $1.50/€:
max [0, (100,000 euros)*(1.25 – $0.75/€)] – 10,000 =
max [0, (100,000 euros)*(1.25 – $1.00/€)] – 10,000 =
max [0, (100,000 euros)*(1.25 – $1.25/€)] – 10,000 =
max [0, (100,000 euros)*(1.25 – $1.50/€)] – 10,000 =
Figure 2
$40,000
$25,000
($10,000)
($10,000)