a. What is the dollar cost of this debt if the pound depreciates from $2.0260/£ to $1.9460/£ over the year?
b. What is the dollar cost of this debt if the pound appreciates from $2.0260/£ to $2.1640/£ over the year?
Assumptions
a) Depreciating £b) Appreciating £
Principal borrowed (British pounds) £5,000,000 £5,000,000
Calculation of Principal and Interest
Pound-denominated debt, in pounds sterling:
Cost of funds if pound depreciates versus dollar
Problem 14.1 Copper Mountain Group (USA)
The Copper Mountain Group, a private equity firm headquartered in Boulder, Colorado (US), borrows £5,000,000 for one year at
7.375% interest.
a. If the exchange remains the same S2
We first calculate the percentage change in the exchange rate, s
We then calculate the effective cost of debt after exchange rate changes
kd = [ ( 1 + kdSF ) x ( 1 + s ) ] – 1 5.000%
kd = [ ( 1 + kdSF ) x ( 1 + s ) ] – 1 9.375%
b. If the exchange ends the period at SF1.4400/$: S2
kd = [ ( 1 + kdSF ) x ( 1 + s ) ] – 1 13.636%
c. If the exchange ends the period at SF1.3860/$: S2
We first calculate the percentage change in the exchange rate, s
s = ( S1 – S2 ) / (S2) x 100 1.3860 8.225%
kd = [ ( 1 + kdSF ) x ( 1 + s ) ] – 1 -3.017%
d. If the exchange ends the period at SF1.6240/$: S2
We first calculate the percentage change in the exchange rate, s
Problem 14.2 Foreign Exchange Risk and the Cost of Swiss francs
The chapter demonstrated that a firm borrowing in a foreign currency could potentially end up paying a
very different effective rate of interest than what it expected. Using the same baseline values of a debt
principal of SF1.5 million, a one year period, an initial spot rate of SF1.5000/$, a 5.000% cost of debt, and
a 34% tax rate, what is the effective cost of debt for one year for a U.S. dollar-based company if the
exchange rate at the end of the period was:
Problem 14.3 McDougan Associates (USA)
McDougan Associates, a U.S.-based investment partnership, borrows €80,000,000 at a time when the exchange rate is $1.3460/€. The entire
principal is to be repaid in three years, and interest is 6.250% per annum, paid annually in euros. The euro is expected to depreciate vis à vis
the dollar at 3% per annum. What is the effective cost of this loan for McDougan?
a. Borrow US$25,000,000 in Eurodollars in London at 7.250% per annum
Assumptions Value
Working capital debt needed for one year 5,000,000$
Borrowing US dollars in London:
Calculation of the breakeven exchange rate
Cost of repaying the Hong Kong dollar loan in HK$ 41,730,000
Problem 14.4 Morning Star Air (China)
Morning Star Air, headquartered in Kunming, China, needs US$25,000,000 for one year to finance
working capital. The airline has two alternatives for borrowing:
b. Borrow HK$39,000,000 in Hong Kong at 7.00% per annum, and exchange these Hong Kong dollars
at the present exchange rate of HK$7.8/US$ for U.S. dollars.
At what ending exchange rate would Morning Star Air be indifferent between borrowing U.S. dollars and
borrowing Hong Kong dollars?
Assumptions Value
Face value of each note sold 1,000.00$
Cash Flows Discounted
Days Since Cumultive Days (par x coupon x Compound Factor Discount Factor Cash Flows
Cash payment (payment date) Previous Date From Start days/180) (cum days/180) (1.04) compounded (US dollars)
First coupon (30 June 2011) 122 122 27.11$ 0.6778 1.0269 26.40$
1,000.31$
Note: That the reason these Euro Medium Term Notes each have a market value which exceeds their face value is because the first coupon is paid sooner than the
six month period separating coupon payments. For example, if all coupons payments were made in 180 days increments (“days since previous date”), the
market value of notes would be at the par value of $1,000.
Problem 14.5 Pantheon Capital, S.A.
If Pantheon Capital, S.A., is raising funds via a euro-medium-term note with the following characteristics, how much in dollars will Pantheon receive for each $1,000 note sold?
Coupon rate: 8.00% payable semiannually on June 30 and December 31
Discount Factor Calculation
Assumptions Value
Principal of Euro Commercial Paper issuance 2,000,000$
Problem 14.6 Westminster Insurance Company
Westminster Insurance Company plans to sell $2,000,000 of euro-commercial paper
with a 60-day maturity and discounted to yield 4.60% per annum. What will be the
immediate proceeds to Westminster Insurance?
bonds reflect actual expected interest costs after any exchange rate changes. This calculation assumes there is no expected change in the exchange rate
over the life of the debt issue (which is indeed highly unlikely).
Assumption Value
Tax rate 30.00%
Weighted
US Dollar Pre-tax Post-tax Component
Component Amount Proportion Cost (%) Cost (%) Cost (%)
25 year US dollar bonds 10,000,000$ 12.77% 6.000% 4.200% 0.5363%
Problem 14.7 Sunrise Manufacturing, Inc.
Sunrise Manufacturing, Inc, a U.S. multinational company, has the following debt components in its consolidated capital section. Sunrise’s finance staff
estimates their cost of equity to be 20%. Current exchange rates are also listed below.
Income taxes are 30% around the world after allowing for credits. Calculate Sunrise’s weighted average cost of capital. Are any assumptions implicit in
your calculation?
Interest Costs First 6-months 2nd 6-months
LIBOR 4.000% 4.200%
Spread over LIBOR 0.800% 0.800%
Total interest cost 4.800% 5.000%
Calculation of the effective cost of funds Issuance First 6-months 2nd 6-months
Face value of syndicated loan 650,000,000$
Problem 14.8 Petrol Ibérico
Petrol Ibérico, a European gas company, is borrowing US$650,000,000 via a syndicated eurocredit for 6 years at 80 basis points over
LIBOR. LIBOR for the loan will be reset every six months. The funds will be provided by a syndicate of eight leading investment
bankers, which will charge up-front fees totaling 1.2% of the principal amount. What is the effective interest cost for the first year if
LIBOR is 4.00% for the first six months and 4.20% for the second six months?
in the non-consolidated books of the parent company. In consolidation these two accounts cancel each other out.
Assumptions Value
A-Malaysia (in ringgits):
Long-term debt 11,400,000
Consolidated Balance Sheet (US$) Value Percent
Debt:
Malaysian ringgit debt (RM converted to US$) 3,000,000$
Mexican peso debt (Ps converted to US$) 2,000,000
Problem 14.9 Adamantine Architectonics
Adamantine Architectonics consists of a U.S. parent and wholly owned subsidiaries in Malaysia (A-Malaysia)
and Mexico (A-Mexico). Selected portions of their non-consolidated balance sheets, translated into U.S. dollars,
are shown below.
What are the debt and equity proportions in Adamantine’s consolidated balance sheet?
Petrobrás of Brazil: Estimating its Weighted Average Cost of Capital
Problems 10-15. Petrobras of Brazil
Petrobrás Petróleo Brasileiro S.A. or Petrobras is the national oil company of Brazil. It is publicly
Petrobrás Lukoil
Capital Cost Components (Brazil) (Russia)
Risk Free Rate 4.800% 4.800%
Sovereign Risk 7.000% 3.000%
Debt/Capital ratio 33.300% 47.500%
Equity/Capital ratio 66.700% 52.500%
WACC (calculated) 14.674% 12.217%
JPMorgan’s Latin American Equity Research department produced the following WACC
calculation for Petrobrás of Brazil versus Lukoil of Russia in their June 18, 2004 report.
Evaluate the methodology and assumptions used in the calculation. Assume a 28% tax rate
for both companies.
Problem 14.10 JPMorgan
Capital Cost Components 2004
Risk Free Rate 4.500%
Levered Beta 0.99
Risk Premium 6.000%
Country Risk Premium 5.500%
Cost of equity (US$) 15.940%
UNIBANCO estimated the weighted average cost of capital for Petrobrás to be
13.2% in Brazilian reais in August of 2004. Evaluate the methodology and
assumptions used in the calculation.
This calculation adds the country risk premium to the risk free rate in the cost of
equity, but not the cost of debt (as was the case in the previous problem). This cost
of equity in US$, however, is then compounded by a percentage change in the
Problem 14.11 UNIBANCO
Capital Cost Components 2003A 2004E 2003A 2004E
Risk free rate 9.400% 9.400% 9.000% 9.000%
Levered Beta 1.07 1.09 1.08 1.10
WACC 12.20% 12.30% 12.10% 12.30%
WACC (calculated) 12.25% 12.39% 12.16% 12.30%
Problem 14.12 Citigroup SmithBarney (dollar)
Citigroup regularly performs a U.S. dollar-based discount cash flow (DCF) valuation of Petrobrás in its coverage. That DCF
analysis requires the use of a discount rate which they base on the company’s weighted average cost of capital. Evaluate the
methodology and assumptions used in the 2003 Actual and 2004 Estimates of Petrobras’s WACC below.
July 28, 2005
March 8, 2005
Petrobras Cost of Equity June 2003
Risk-free rate (Brazilian C-Bond) 9.90%
Petrobras Cost of Debt
Petrobras cost of debt 10.00%
Brazilian corporate tax rate 34.00%
Cost of debt, after-tax 6.60%
WACC Calculation (in R$)
Petrobras cost of debt, after-tax 6.60%
In a report dated June 17, 2003, Citigroup SmithBarney calculated a WACC for
Petrobrás denominated in Brazilian reais (R$). Evaluate the methodology and
assumptions used in this cost of capital calculation.
Problem 14.13 Citigroup SmithBarney (Reais)
relatively high. The cost of debt, also high compared to the other estimates,
results in a final WACC calculation, in Brazilian reais, which is similar in value
to other estimates.
Cost of Capital Component 2003 Estimate 2004 Estimate
US 10-year risk-free rate (in US$)
4.10% 4.40%
Cost of equity (in R$) 3
16.75% 14.44%
Petrobras Cost of Debt
Petrobras cost of debt (in R$)
8.50% 8.50%
Brazilian corporate tax rate
35.00% 35.00%
Cost of debt, after-tax (in US$)
5.53% 5.53%
WACC Calculation (in R$)
Petrobras cost of debt, after-tax
5.53% 5.53%
Long-term debt ratio (% of capital)
31.00% 28.00%
16.75% 14.44%
69.00% 72.00%
WACC (calculated) 13.27% 11.95%
WACC (I-Bank report) 13.30% 12.00%
Notes:
2 Cost of equity in US$ = risk free rate + ( beta x market risk premium )
Problem 14.14 BBVA Investment Bank
BBVA utilized a rather innovative approach to dealing with both country and currency risk in their December
20, 2004 report on Petrobras. Evaluate the methodology and assumptions used in this cost of capital calculation.
1 Petrobras premium adjustment is the reduction in country risk given an oil and gas company operating in a global industry
which operates in a market of US dollar denominated returns.
6.00% 4.00%
9.10% 7.40%
Petrobras Cost of Equity
9.10% 7.40%
6.00% 6.00%
13.90% 12.20%
2.50% 2.00%
JPMorgan Citigroup ($) UNIBANCO Citigroup (R$) BBVA
Capital Cost Components (June 18, 2004) (March 8, 2005) (Aug 12, 2004) (June 17, 2003) (Dec 20, 2004)
Risk Free Rate 4.800% 9.400% 4.500% 9.900% 4.400%
Sovereign/Country Risk Premium 7.000% 0.000% 5.500% 0.000% 4.000%
Petrobras Company Premium 0.000% 0.000% 0.000% 0.000% -1.000%
The various estimates of the cost of capital for Petrobras of Brazil appear to be very different, but are they? Reorganize your answers to the previous five problems into those
costs of capital which are in U.S. dollars versus Brazilian reais. Use the estimates for 2004 as the basis of comparison.
U.S. dollar WACCs
Brazilian reais WACCs
Problem 14.15 Petrobras’s WACC Comparison
Which course of action do you recommend Grupo Modelo take and why?
Japanese euro US dollar
Alternatives yen bonds bonds bonds
Coupon rate
3.000% 7.000% 5.000%
Current spot rate, yen/$
106.00 1.1960$
Calculation of the dollar cost debt alternatives Year 0 Year 1 Year 2 Year 3 Year 4
Japanese yen bonds:
Proceeds and principal and interest payments
10,600,000,000 (318,000,000) (318,000,000) (318,000,000) (10,918,000,000)
Expected exchange rate (yen/$)
106.00 103.92 101.88 99.89 97.93
euro-denominated bonds:
1.1960 1.1721 1.1486 1.1257 1.1032
US dollar bonds:
c. Sell U.S. dollar bonds at par yielding 5% per annum.
Problem 14.16 Grupo Modelo S.B.A de C.V.
Grupo Modelo, a brewery out of Mexico that exports such well-known varieties as Corona, Modelo and Pacifico, is Mexican by incorporation. However, the company evaluates all
business results, including financing costs, in U.S. dollars. The company needs to borrow $10,000,000 or the foreign currency equivalent for four years. For all issues, interest is
payable once per year, at the end of the year. Available alternatives are:
b. Sell euro-denominated bonds at par yielding 7% per annum. The current exchange rate is $1.1960/€, and the euro is expected to weaken against the dollar by 2% per annum.
a. Sell Japanese yen bonds at par yielding 3% per annum. The current exchange rate is ¥106/$, and the yen is expected to strengthen against the dollar by 2% per annum.