Converting Hurdle Rates and Expected Cash Flows Across Currencies
The theory of cross-border investments is generally based on the standard concept of discounting a project’s expected operating cash flows back to the present using a cost of capital (or hurdle rate) that reflects the risk. An investment’s net present value (NPV) is the present value of the expected cash flows minus the outlay necessary to undertake the investment. If the NPV is positive, the investment should be accepted, because the intrinsic wealth of the firm’s existing shareholders would rise. If the NPV is negative, the investment should be rejected, because intrinsic wealth of the firm’s existing shareholders would drop.
One issue is whether to consider a foreign investment’s entire cash flow or only the portion repatriated. Our answer is immediate: Consider the investment’s entire cash flow, not just the portion repatriated. The reason is that even the portion reinvested overseas affects the intrinsic wealth of the firm’s shareholders, because the reinvestment increases the value that the overseas investment could be sold for, and thus needs to be included in the analysis. So, we consider an overseas investment’s entire cash flow, not just the portion repatriated.
Another critical issue is the choice of currency perspective to use for the valuation analysis. In the home currency approach, one converts expected foreign currency cash flows into home currency equivalents using forecasted FX rates, and then discounts them using a hurdle rate denominated in the home currency. In the foreign currency approach, the analyst uses the expected cash flows denominated in the foreign currency, and discounts them using a hurdle rate denominated in the foreign currency. This chapter addresses how to convert hurdle rates and expected cash flows between currencies.
In the foreign currency approach, managers need to express a foreign operation’s cost of capital and hurdle rate in the overseas local currency, given the cost of capital and hurdle rate in the parent company’s home currency. For example, a U.S. multinational company may have estimated the hurdle rate for a foreign subsidiary in US dollars, and wants to know the consistent hurdle rate in the local foreign currency. Sometimes, the parent will supply a foreign subsidiary’s managers with the foreign currency hurdle rate, for making local, decentralized investment decisions.
This chapter shows how to convert a hurdle rate in one currency into an equivalent one expressed in a different currency. As part of this analysis, the chapter covers using the ICAPM to estimate a currency risk premium. Finally, the chapter addresses issues in converting expected cash flows from foreign currency to home currency, for applying the home currency approach to international investment decisions.
Converting a Hurdle Rate to an Overseas Currency
We now address the issue of converting an asset’s hurdle rate from one currency to another. To convert a home currency cost of capital estimate for asset i, 
, into an equivalent one in overseas currency C, 
, one can use equation (4.1):
Cost of Capital Conversion
Equation (4.1) says that you first multiply 
times 
, where E*(xC/H) is the equilibrium expected rate of FX change (or the expected rate of intrinsic FX change) of the home currency versus currency C. The asterisk denotes the idea of equilibrium or intrinsic.
Then, you adjust for the interaction between the asset’s return and the FX rate. This interaction adjustment involves 
, which is asset i’s FX exposure to currency C, from the home currency perspective, and which may be estimated by regressing asset i’s returns on percentage changes in currency C versus currency H, xH/C. The interaction adjustment also involves 
, the volatility of xH/C.
The result is 
. Equation (4.1) follows from the definition of asset i’s rate of return in different currencies in equation (1.1a). Only if the asset’s FX exposure to currency C is 0, the cost of capital conversion is the simpler expression: 
.1
Note that we convert an asset’s cost of capital not using a managers’ actual forecasted rate of FX change, but rather using the expected rate of intrinsic FX change, even if it is different from the managers’ FX forecast. The reason is that the cost of capital is a compensation for risk, regardless of the currency perspective. Only the expected rate of intrinsic FX price change is based on systematic risk, and thus preserves a consistent risk and required return relationship across different currencies for a globally traded asset.
Equation (4.1) applies to the hurdle rate for an asset in a developed market, where political risk is ignored. For an emerging market asset, equation (4.1) applies only to the portion of the hurdle rate that is due to the cost of capital and not due to political risk; because a political risk premium has no currency denomination, one would add the political risk premium to the converted cost of capital to get the hurdle rate in currency C.
The tricky aspect of using equation (4.1) is estimating currency H’s expected rate of intrinsic FX change versus currency C, E*(xC/H). To estimate E*(xC/H), we’ll use the definition of the currency risk premium for currency H in terms of currency C, 
, as shown in equation (4.2):
Currency Risk Premium
As equation (4.2) indicates, if one has an estimate of , one can get an estimate of E*(xC/H), because 
and 
are observable. To estimate , we use the ICAPM in equation (2.2), letting asset i be a risk-free deposit in currency H, with required return in currency C of E*(xC/H) + . Thus, the ICAPM estimate for is equal to 
, where 
is the beta of xC/H versus the global market index in currency C, and 
is the FX exposure of xC/H to the foreign currency index from the perspective of currency C. Exhibit 4.1 shows ICAPM currency risk premium estimates for the US dollar versus 20 other currencies, based on the 1999 to 2016 data.
For example, let currency C be the euro and currency H be the US dollar. With the 1999 to 2016 data, the percentage changes in the euro per US dollar FX rate had an estimated 
of 0.155 and 
of 1.15, per Exhibit 4.1. With 
= 5.54% and 
= −0.92%, per Exhibit 2.2, the ICAPM in equation (2.2) yields the currency risk premium estimate of 
= 0.155[0.0554] + 1.15[−0.0092] = −0.002, or −0.20%.
Assume that for the US dollar versus the Swiss franc, the standard risk coefficient estimates are 
= 0.243 (versus the global market index) and 
= 1.27 (versus the foreign currency index), per Exhibit 4.1. Use the ICAPM equation (2.2) to verify the ICAPM currency risk premium estimate in Exhibit 4.1 for the US dollar in terms of the Swiss franc, 0.48%. Assume 
= 6.93% and 
= −0.95%, per Exhibit 2.2.
Answer: 
= 0.243[0.0693] + 1.27[−0.0095] = 0.0048 or 0.48%.
Traditionally, many researchers and analysts have presumed that currency risk premiums are zero, implying the linear version of the traditional uncovered interest rate parity (UIRP) condition: E*(xC/H) = − . However, you can see in Exhibit 4.1 that currency risk premium estimates are not zero using the ICAPM approach.
Now let’s return to the primary tasks of (1) estimating E*(x€/$) using an ICAPM currency risk premium estimate; and (2) converting asset i’s home-currency cost of capital to an overseas-currency cost of capital. Again, let currency C be the euro and currency H be the US dollar, and so the 
estimate is −0.20%.
Assume that the risk-free rates are 3% in US dollars and 4% in euros. Using equation (4.2), the estimated equilibrium expected rate of change of the US dollar versus the euro, E*(x€/$), is −0.20% − 3% + 4% = 0.80%. Note that 0.80% is not an actual FX forecast, but instead is the percentage FX rate change expected as compensation for both the risk-free rate differential (as in the traditional UIRP condition) and ICAPM FX risk. An E*(x€/$) estimate is only a useful forecast if the $/€ FX rate is correctly valued and expected to remain correctly valued. This idea is analogous to stocks: stock i’s cost of equity is not a forecast of an actual expected stock return. Instead, the cost of equity is compensation for time (the risk-free rate) and risk, and would be useful as a forecast only if one assumes that the stock is correctly valued and will remain correctly valued.
Exhibit 4.1 ICAPM currency risk premium estimates: US dollar vs. currency C
Global Market Price of Risk = 2.50 |
||||
Statistical Parameter Estimation Period: 1999 to 2016 |
||||
|
|
|
ICAPM (%) |
GCAPM (%) |
Eurozone (euro) |
0.155 |
1.15 |
−0.20 |
0.79 |
Japan (yen) |
0.273 |
0.92 |
1.33 |
1.98 |
China (yuan) |
−0.003 |
0.10 |
−0.05 |
−0.06 |
Britain (pound) |
0.087 |
1.11 |
−0.30 |
−0.02 |
Canada (dollar) |
−0.080 |
1.06 |
−1.27 |
−0.31 |
Australia (dollar) |
0.159 |
1.17 |
−1.38 |
0.53 |
Taiwan (dollar) |
−0.086 |
0.76 |
−0.61 |
−0.43 |
Switzerland (franc) |
0.243 |
1.27 |
0.48 |
1.45 |
India (rupee) |
−0.041 |
0.95 |
−0.80 |
−0.19 |
Korea (won) |
0.097 |
1.08 |
−1.12 |
0.37 |
Brazil (real) |
0.816 |
1.02 |
2.63 |
5.93 |
Mexico (peso) |
−0.036 |
0.97 |
−1.35 |
0.14 |
Sweden (krona) |
0.130 |
1.30 |
−0.82 |
0.54 |
Hong Kong (dollar) |
−0.001 |
−0.02 |
−0.00 |
0.00 |
Norway (krone) |
0.169 |
1.25 |
−0.57 |
0.77 |
Denmark Krone) |
0.151 |
1.44 |
−0.20 |
0.77 |
New Zealand (dollar) |
0.286 |
1.16 |
−0.92 |
1.10 |
Singapore (dollar) |
−0.081 |
1.45 |
−0.61 |
−0.40 |
South Africa (rand) |
0.495 |
1.05 |
−0.37 |
2.33 |
Thailand (baht) |
0.016 |
0.93 |
−0.50 |
0.08 |
Finally, assume that asset i has a cost of capital in US dollars of 8% and a FX exposure to the euro of 0.40, and the volatility of x$/€ is 0.103. Equation (4.1) says that asset i’s cost of capital estimate in euros is (1 + 0.08)[1 + 0.008] − 0.40(0.103)2 − 1 = 0.0844, or 8.44%.
After a developed country boxed example for Switzerland, there is an emerging market country boxed example for Mexico, with a political risk premium.
Assume that the currency risk premium for the US dollar versus the Swiss franc is 0.48%, per Exhibit 4.1. Let the US dollar risk-free rate be 3% and the Swiss franc risk-free rate be 2%. A U.S. multinational company has estimated that the cost of capital for its Swiss operation is 10% in US dollars. In US dollars, the operation’s FX business exposure to the Swiss franc is 0.50. The volatility of percentage changes in the Swiss franc versus the US dollar FX rate is 0.108. Since the operation is in Switzerland, assume no political risk premium. (a) Use equation (4.2) to find the equilibrium expected rate of change in the US dollar versus the Swiss franc. (b) Find the operation’s hurdle rate estimate in Swiss francs.
Answers: (a) E*(xsf/$) = 0.48% − 3% + 2% = −0.52%. (b) 
= 
= (1 + 0.10)[1 − 0.0052] − 0.50(0.108)2 − 1 = 0.0884, or 8.84%.
Assume that the currency risk premium for the US dollar versus the Mexican peso is −1.35%, per Exhibit 4.1. Let the US dollar risk-free rate be 3% and the Mexican peso risk-free rate be 5%. A U.S. multinational has estimated a hurdle rate for its Mexican operation of 12% in US dollars, including an adjustment for political risk, based on a political risk premium of 0.71% for Mexico, per Exhibit 3.2, and average political risk exposure of 1. The operation’s FX business exposure to the Mexican peso is −0.50. The volatility of changes in the Mexican peso versus the US dollar FX rate is 0.096. (a) Use equation (4.2) to find the equilibrium expected rate of change in the US dollar versus the Mexican peso. (b) Find the operation’s hurdle rate estimate in Mexican pesos.
Answers: (a) E*(xPe/$) = −1.35% − 3% + 5% = 0.65%. (b) For the cost of capital component (without political risk), 
= 0.12 − 1[0.0071] = 0.1129; therefore, the operation’s cost of capital in pesos is 
= (1 + 0.1129)[1 + 0.0065] − (−0.50)(0.096)2 − 1 = 0.125, or 12.5%. Adjusting for political risk, the operation’s hurdle rate in pesos is: 
= 0.125 + 1[0.0071] = 0.132, or 13.2%.
Short-Cut Cost of Capital Conversion Practices
The traditional UIRP approach to the intrinsic rate of FX change, and ignoring the interaction between returns and FX changes, has led to simpler “short-cut” cost of capital conversion practices. One approach is to use: 
. This approach is sometimes an acceptable approximation to the one in equation (4.1), and is easy to apply. An even easier approximation in use, based on the same idea, is: 
. In the Swiss franc boxed example problem, we’d get that the 
estimate would be 0.02 − 0.03 + 0.10 = 0.09, or 9%, whereas the ICAPM “correct” answer is 8.84%.
Notice in Exhibit 4.1 that the 
estimate for Australia is the lowest, −1.38%, and the estimate for Brazil is the highest, 2.63%. It is no accident that the global risk premium estimates for the Australian dollar and Brazilian real (in Exhibit 2.2) are 3.29% and 7.28%, respectively, compared to the GRP$ estimate, 5.92%. That is, a currency’s estimate is one of the drivers of a currency’s global risk premium estimate (in local currency). It is logical that from the perspective of euros, worldwide investors will require a global risk premium that includes a currency risk premium for the uncertainty in the FX price of the US dollar versus the euro, in addition to the global risk premium in US dollars.
The last column in Exhibit 4.1 shows currency risk premium estimates using the GCAPM in currency C, with the global beta for xC/$ and the correct (ICAPM) estimate for GRPC, per Exhibit 2.2. The average absolute difference between the ICAPM and GCAPM currency risk premium estimates for the US dollar is about 110 basis points. The highest absolute difference is for the Brazilian real (330 basis points), followed by the New Zealand dollar (202 basis points). In general, the GCAPM does not appear to provide a useful approximation to the ICAPM in estimating many currency risk premiums for the US dollar in terms of currency C.
Verify the GCAPM currency risk premium estimate for the US dollar versus the euro, 0.79%, per Exhibit 4.1. Hint: The estimate for GRP€ is 5.12%, per Exhibit 2.2.
Answer: With the GCAPM approach, you get 
= 0.155[0.0512] = 0.0079, or 0.79%.
To better understand why the GCAPM does not provide a good approximation to the ICAPM currency risk premium estimates, look at the ICAPM risk coefficient estimates in Exhibit 4.1. The “beta” estimates resemble traditional equity “gamma” estimates, and the “gamma” estimates resemble traditional equity “beta” estimates. That is, whereas equity returns “load” mainly on the market index factor, FX changes are mainly exposed to (load on) the foreign currency index factor, which makes sense. The ICAPM “prices” systematic FX risk separately from systematic market risk and using the foreign currency index risk premium, which is much lower than the global risk premium. So, the GCAPM gives poor approximations to the ICAPM currency risk premium estimates because FX risk in the GCAPM can load only on the market factor and is therefore “priced” with the global risk premium.
Converting Expected Cash Flows
As we said, in the home currency approach to international capital budgeting, a project’s expected foreign currency cash flows are converted to equivalent expected home currency cash flows. A standard practice is to simply multiply the expected foreign currency operating cash flow by the expected spot FX rate, expressed in direct terms of the home currency. That is, the standard practice is to find 
by the product 
, where 
denotes the expected time-N operating cash flow in euros (the representative foreign currency), and 
denotes the expected time-N spot FX rate in US dollars (the representative home currency) per euro.
Technically however, the standard practice is correct only in the special case where the foreign currency cash flow and the spot FX rate are independent, which means that the foreign currency cash flow has zero FX operating exposure to the home currency: 
. The standard practice calculation does not give the correct expected cash flow in the home currency in the more general situation where the foreign currency cash flow and the FX rate are not independent, that is, when the foreign currency cash flow has a nonzero FX operating exposure to the home currency. Instead, equation (4.3) gives a reasonable approximation to the correct expected time-N cash flow in the home currency, where the US dollar represents the home currency and the euro represents the foreign currency.2
Expected Operating Cash Flow Conversion
Home Currency = US Dollar; Foreign Currency = Euro
Equation (4.3) adjusts the “standard-practice” formula, 
, by multiplying by the term 
, where 
denotes the foreign project’s FX operating exposure to the home currency (the US dollar) and 
denotes the variance (squared volatility) of the annualized percentage changes in the spot FX rate.
For example, assume that Aerotech Components Co. is a U.S. firm considering the acquisition of Vienna Gear Plc., a small aerospace components business in Austria, in the Eurozone. Aerotech expects that under its ownership, Vienna’s expected time-1 cash flow in euros, 
, would be €10,000. A “what if” analysis shows that the FX operating exposure to the US dollar from the euro point of view, , is 0.60.
Assume that the expected time-1 spot FX rate is 1.20 $/€ and the volatility of the euro (versus the US dollar), 
, is 10.3%, or 0.103 (per annum). Equation (4.3) says that 
is (approximately) €10,000(1.20 $/€)[1 − 0.60(0.103)2] = $11,924. Using the standard practice of implicitly assuming zero FX exposure to the US dollar, you would get €10,000(1.20 $/€) = $12,000, which would overestimate the expected time-1 operating cash flow in US dollars.
The U.S. firm Sanders Appliance Co. is considering opening a business operation in England. The English operation is expected to generate operating cash flows of £500,000 per year. Using a “what if” analysis, managers estimated that from the British pound perspective, the operation would have an FX business exposure to the US dollar of 0.80. The volatility of the British pound versus the US dollar is 0.085. Given a forecasted time-1 spot FX rate of 1.50 $/£, find the operation’s expected time-1 cash flow in US dollars and compare to the standard practice “estimate.”
Answer: Equation (4.3) says that 
is (approximately) £500,000 (1.50 $/£)[1 − 0.80(0.085)2] = $745,665. Using the standard practice of implicitly assuming zero FX exposure to the US dollar, you would get £500,000(1.50 $/£) = $750,000, which would overestimate the expected time-1 operating cash flow in US dollars.
If the foreign asset’s FX exposure to the home currency is negative, the standard practice calculation will underestimate the correct expected cash flow in the home currency. The next boxed example demonstrates this point, and relates to the “Illuminating Example” box.
Stanwick Chemical Co. is a U.S. firm considering an acquisition in Brazil that has an FX operating exposure to the US dollar of −0.80. The target’s expected time-1 operating cash flow is Re100,000. The expected time-1 spot FX rate is 0.533 $/Re. The volatility of the real is 0.245. (a) Use equation (4.3) to find the approximate expected time-1 operating cash flow in US dollars. (b) Compare the answer in (a) with that of the standard practice approach.
Answers: (a) = Re100,000(0.533 $/Re)[1 − (−0.80)(0.245)2] = $55,859. (b) Re100,000(0.533 $/Re) = $53,300. Here, the standard practice answer underestimates the equation (4.3) answer because the foreign asset’s FX exposure to the home currency is negative.
Assume three equally likely outcomes for the time-1 spot FX rate for Brazilian real per US dollar: 1.4 Re/$, 2.0 Re/$, and 2.6 Re/$, with an expected spot FX rate of 2.0 Re/$. In US dollars per Brazilian real, the outcomes are: 0.714 $/Re, 0.50 $/Re, and 0.385 $/Re, with an expected time-1 spot FX rate of (0.714 $/Re + 0.50 $/Re + 0.385 $/Re)/3 = 0.533 $/Re. From the Brazilian real perspective, the standard deviation of the percentage differences between the spot FX rate outcome and the mean outcome is 0.245. So, we estimate that 
= 0.245.
Using a “what if” analysis, if the spot FX rate is 1.40 Re/$, the US dollar is 30% lower than expected. So, given 
= −0.80, the operating cash flow in Brazilian real is higher than expected by 0.80(30%) = 24%, and thus would be 24% higher than Re100,000, or Re124,000. Similarly, if the time-1 spot FX rate is 2.60 Re/$, the US dollar is 30% higher than expected. So, the operating cash flow in Brazilian real would be lower than expected by 24%, and thus would be Re76,000.
Therefore, in US dollars, the actual time-1 operating cash flow will be one of three equally likely outcomes: (1) Re124,000(0.714 $/Re) = $88,536; (2) Re100,000(0.50 $/Re) = $50,000; or (3) Re76,000(0.385 $/Re) = $29,260. The expected time-1 operating cash flow in US dollars is thus ($88,536 + 50,000 + 29,260)/3 = $55,932. The approximation in the boxed example using equation (4.3), $55,859, is close to the actual answer, and much closer than the standard practice answer, $53,300.
Probability |
|
|
|
|
1/3 |
1.4 Re/$ |
0.714 $/Re |
Re124,000 |
$88,536 |
1/3 |
2.0 Re/$ |
0.500 $/Re |
Re100,000 |
$50,000 |
1/3 |
2.6 Re/$ |
0.385 $/Re |
Re76,000 |
$29,260 |
Expected |
2.0 Re/$ |
0.533 $/Re |
Re100,000 |
$55,859 |
Be sure to see that in equation (4.3) is the euro cash flow’s FX exposure to the US dollar, that is, exposure to uncertain changes in the FX price of the US dollar versus the euro. This exposure is the inverse of the cash flow’s FX exposure to the euro from the US dollar perspective, 
which is used in equation (4.1) to convert an asset’s US dollar cost of capital to a euro cost of capital. Note that the two FX exposure estimates are related as shown in equation (4.4):
FX Exposures: Different Currency Directions
For example, assume that Aerotech Components’ analysis of Vienna Gear’s FX exposure was easier to conduct from the US dollar perspective. If the “what if” analysis showed that the FX operating exposure to the euro from the US dollar perspective is 0.40, equation (4.4) may be used to find that is 1 − 0.40 = 0.60, for use in equation (4.3).
Houston Marine Electronics Co. has an Australian operation that has an FX operating exposure to the Australian dollar of 1.40 from the US dollar perspective. Find the operation’s FX operating exposure to the US dollar, from the Australian dollar perspective, for use in converting the operation’s expected cash flows in Australian dollars to the equivalent expected cash flows in US dollars.
Answer: 
= 1 − 1.40 = −0.40.
Summary Action Points
• In the home currency approach to cross-border valuation, the analyst converts the expected foreign currency cash flows into home currency equivalents using forecasted FX rates, and then discounts them using a cost of capital denominated in the home currency.
• In the foreign currency approach to cross-border valuation, the analyst converts the home currency cost of capital into an equivalent foreign currency cost of capital and then discounts the expected foreign currency cash flows to get an intrinsic value from the foreign currency perspective.
• The expected rate of intrinsic FX change of one currency versus another is helpful in converting an asset’s cost of capital from one currency to another.
• Estimates of the expected rate of intrinsic FX change of one currency versus another may be based on ICAPM currency risk premium estimates.
• The correct conversion of an expected foreign currency cash flow to the home currency often depends on the cash flow’s FX exposure and the currency’s volatility, and is usually slightly more involved than the simple standard practice of multiplying the expected foreign currency cash flow by the forecasted spot FX price of the foreign currency.
Problems
1. Assume that for the FX rate for the US dollar versus the Korean won, the standard risk coefficient estimates are 
= 0.097 (versus the global market index) and 
= 1.08 (versus the foreign currency index), per Exhibit 4.1. Use the ICAPM risk return expression in equation (2.2) to verify the ICAPM currency risk premium estimate in Exhibit 4.1 for the US dollar versus the Korean won, −1.12%. Assume 
= 4.14% and 
= −1.41%, per Exhibit 2.2.
2. Assume that the currency risk premium for the US dollar versus the Korean won is −1.12%, per Exhibit 4.1. Let the US dollar risk-free rate be 3% and the Korean won risk-free rate be 2.50%. A U.S. multinational company has estimated a hurdle rate for its Korean operation of 12% in US dollars. In US dollars, the operation’s FX business exposure to the Korean won is −0.70. The volatility of percentage changes in the Korean won versus the US dollar FX rate is 0.111. Assume no political risk premium. (a) Use equation (4.2) to find the equilibrium expected rate of change in the US dollar versus the Korean won. (b) Find the operation’s hurdle rate estimate in Korean won.
3. Assume that the currency risk premium for the US dollar versus the Brazilian real is 2.63%, per Exhibit 4.1. Let the risk-free rate be 3% in US dollars and 4% in Brazilian real. A U.S. multinational has estimated a hurdle rate for its Brazilian operation of 16.5% in US dollars, including political risk adjustment of 1.15%, per Exhibit 3.2. The operation’s FX business exposure to the Brazilian real is −0.40. The volatility of changes in the Brazilian real versus the US dollar FX rate is 0.245. (a) Use equation (4.2) to find the equilibrium expected rate of change in the US dollar versus the Brazilian real. (b) Find the operation’s hurdle rate estimate in Brazilian real.
4. Verify the GCAPM currency risk premium estimate for the US dollar versus the Swiss franc, 1.45%, per Exhibit 4.1. Hint: The estimate for GRPSf is 5.97%, per Exhibit 2.2.
5. The U.S. firm Houston Marine Electronics Co. is considering opening a business operation in Australia. The Australian operation is expected to generate operating cash flows of A$2.5m per year. Using a “what if” analysis, managers estimated that from the Australian dollar perspective, the operation would have an FX business exposure to the US dollar of −0.40, inclusive of an economic “demand effect” of changes in the $/A$ FX rate. The volatility of the Australian dollar versus the US dollar is 0.127. Given a forecasted time-1 spot FX rate of 1.05 $/A$, find the operation’s expected time-1 cash flow in US dollars and compare to the standard practice “estimate.”
6. A U.S. firm has an operation in the United Kingdom, which has an FX operating exposure to the British pound of 0.20 from the US dollar perspective. Find the operation’s FX operating exposure to the US dollar, from the British perspective, for use in converting the operation’s expected cash flows in British pounds to the equivalent expected cash flows in US dollars.
Answers to Problems
1. 
= 0.097[0.0414] + 1.08[−0.0141] = −0.0112 or −1.12%.
2. a. 
= −1.12% − 3% + 2.50% = −1.62%.
b. 
= (1 + 0.12)[1 − 0.0162] − (−0.70)(0.111)2 − 1
= 0.110 (11.0%)
3. (a) E*(xRe/$) = 2.63% − 3% + 4% = 3.63%. (b) 
= 0.165 − 0.0115 = 0.1535; so, 
= (1 + 0.1535)[1 + 0.0363] + 0.40(0.245)2 − 1 = 0.219. (b) Adding the political risk adjustment, the operation’s hurdle rate in Brazilian real is: 
= 0.219 + 0.0115 = 0.231, or 23.1%.
4. 0.243[0.0597] = 0.0145, or 1.45%.
5. Equation (4.3) says that 
is (approximately) A$2.5m(1.05 $/A$) × [1 − (−0.40)( 0.127)2] = $2.642m. Using the standard practice of implicitly assuming zero FX exposure to the US dollar, you would get A$2.5m(1.05 $/A$) = $2.625m, which would underestimate the expected time-1 operating cash flow in US dollars.
6. 
= 1 − 0.20 = 0.80.
Discussion Questions
1. In overseas investment decisions, should one consider the investment’s overall cash flow or just the portion to be repatriated? Explain.
2. Zero is a reasonable assumption for a currency risk premium. Discuss.
3. If an asset’s cost of capital is 10% in US dollars, the cost of capital will be 10% in any currency or else financial arbitrage would be possible. Evaluate this statement.
4. The expected cash flow in home currency is equal to the product of the expected cash flow in the foreign currency and the expected spot FX price of the foreign currency. Evaluate this statement.