Test Bank Chapter 13 Multinational Capital Budgeting

PART IV Valuation and the Structure of Multinational Operations

Chapter 13 Multinational Capital Budgeting

Notes to instructors:

Answers to non-numeric multiple choice questions are arranged alphabetically, so that answers are randomly assigned to the five outcomes.

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1. Because of different currencies and interest rates in each country, capital budgeting analysis for cross-border investments is radically different from capital budgeting analysis for domestic investments.

Although the opportunities and risks differ, the underlying analysis is the same.

2. In order to compensate for the effects of inflation, nominal cash flows should be discounted with a real discount rate.

Nominal (real) cash flows must be discounted with a nominal (real) discount rate.

3. In perfect financial markets in which the international parity conditions hold, discounting may be done either in the domestic or in the foreign currency.

4. The discount rate should always be in the parent firm’s functional currency.

The discount rate should be in the currency in which the cash flows are received.

5. If the international parity conditions hold, then nominal required returns in two different currencies are identical on comparable-risk assets.

Real (not nominal) required returns are equal.

6. In capital budgeting, repatriation occurs when expatriate employees return to the parent firm.

Repatriation is the act of remitting cash flows to the parent firm.

7. Relevant cash flows from the parent’s point of view are those that are remitted to the parent in its functional currency.

8. In order to compensate for the effects of inflation, nominal cash flows should be discounted with a real discount rate.

Nominal (real) cash flows should be discounted with a nominal (real) discount rate.

9. Blocked funds are cash flows generated by a foreign project that are not immediately repatriated to the parent because the project has better opportunities than the parent corporation.

Blocked funds are blocked because of restrictions imposed by host governments.

10. Blocked funds in a foreign country should be discounted at the risk-free rate of interest in the foreign currency.

The discount rate should depend on the systematic risk of the asset in which they are invested.

11. Cash flows from subsidized financing are necessarily tied to a specific project.

Financial subsidies are sometimes separable from any particular project.

12. According to finance theory, the value of subsidized financing that is separable from a particular project must still be added to the value of the project in calculating project value.

Separable financial subsidies may not be incremental cash flows to a particular project.

13. Developing countries sometimes require that foreign companies investing capital locally take on additional development or infrastructure projects.

14. Project-specific expropriation risk has no effect on expected future cash flows from a project, but can increase the discount rate.

Asset-specific risks (including expropriation risk) do influence cash flows but are usually not systematic risks and hence do not affect the discount rate.

15. Managers care only about systematic risk and hence should not hedge political risk.

Undiversified managers care about total risk and so have an incentive to hedge.

Multiple Choice Select the BEST ANSWER

1. Expected future cash flows are estimated by ____ only incremental cash flows and ____ all opportunity costs.

a. including; including

b. including; excluding

c. excluding; including

d. excluding; excluding

e. none of the above

2. Nominal cash flows in a foreign currency should be discounted ____.

a. at a nominal discount rate in the foreign currency

b. at a rate reflecting the parent’s opportunity cost of capital in the domestic currency

c. at a weighted average cost of capital

d. at the cost of debt

e. at the cost of equity

3. Which of the following is ?

a. Cash flows in a particular currency should be discounted in that currency.

b. Cash flows should be discounted at the opportunity cost of capital.

c. Cash flows to equity should be discounted at the weighted average cost of capital.

d. Nominal cash flows should be discounted at nominal discount rates.

e. Real cash flows should be discounted at real discount rates.

4. Which of steps (a) through (d) is inappropriate when discounting foreign currency cash flows using the parent’s perspective?

a. Estimate expected future cash flows from the project in the foreign currency and put them on a timeline.

b. Convert expected future cash flows into the domestic currency at the current spot exchange rate.

c. Identify the appropriate risk-adjusted discount rate in the domestic currency for the project.

d. Calculate the NPV in the domestic currency.

e. Each of the above is appropriate.

5. If a project has a positive NPV from both the parent’s (V^d|i^d) and the project’s perspective (V^d|i^f), then the parent firm should ____.

a. accept the project

b. reject the project

c. accept the project and try to capture the value in the foreign currency today

d. reject the project and continue to look for positive-NPV projects in the foreign currency

e. none of the above

6. If a project has a positive NPV from the parent’s perspective (V^d|i^d) but a negative NPV from the project’s perspective (V^d|i^f), then the parent firm should ____.

a. accept the project

b. reject the project

c. accept the project and try to capture the value in the foreign currency today

d. reject the project and continue to look for positive-NPV projects in the foreign currency

e. none of the above

7. If a project has a negative NPV from the parent’s perspective (V^d|i^d) but a positive NPV from the project’s perspective (V^d|i^f), then the parent firm should ____.

a. accept the project

b. reject the project

c. accept the project and try to capture the value in the foreign currency today

d. reject the project and continue to look for positive-NPV projects in the foreign country

e. none of the above

8. If a project has a positive NPV but the NPV is greater from the project’s (V^d|i^f) than from the parent’s perspective (V^d|i^d), then the parent firm should ____.

a. accept the project

b. reject the project

c. accept the project and hedge the foreign currency cash flows

d. reject the project and continue to look for positive-NPV projects in the foreign country

e. none of the above

9. A project has a net present value of V^€ = €10,000. In order to invest in the project, the German government requires that you undertake another project with the following cash flow stream: CF₀^€ = –€5000, E[CF₁^€] = €1000, E[CF₂^€] = €1000, and E[CF₃^€] = €1000. The appropriate discount rate for this project is i^€ = 10%. What affect does this tie-in project have on your original V^€ estimate?

a. It increases V^€ from €10,000 to €12,513.15.

b. It increases V^€ from €10,000 to €17,486.85.

c. It decreases V^€ from €10,000 to €7,486.85.

d. It increases V^€ from €10,000 to €2,513.15.

e. It is a separate project and has no effect on NPV.

10. Suppose the government of Germany offers you a three-year, nonamortizing €50,000 loan to entice you to undertake a particular project within its borders. In addition, the government offers you an attractive rate of i^€ = 10% when loans of similar risk yield a return of i^€ = 15%. The German tax rate is 50%. What is the present value of the interest subsidy on this loan?

a. €2854.03

b. €3108.56

c. €3250.66

d. €4895.60

e. €5708.06

Exhibit 13.1

€10,000 €10,000 €10,000 S₀^£/€ = £2.00/€

├───────────────────┼───────────────────┼───────────────────┤

–€1,000 i^€ = 5%

time 0 1 2 3 i^£ = 7%

11. Refer to Exhibit T13.1. What is net present value in euros, V^€|i^€?

a. €25,598.43

b. €26,232.48

c. €27,232.48

d. €29,000.00

e. €29,432.52

12. Refer to Exhibit T13.1. Assume the international parity conditions hold . What is the expected future spot rate [E(S₃^£/€ )] at time t = 3?

a. £1.890/€

b. £1.963/€

c. £2.020/€

d. £2.116/€

e. £2.250/€

13. Refer to Exhibit T13.1. Assume the international parity conditions hold . What is net present value in pounds, V^£?

a. £48,591.54

b. £50,786.92

c. £52,464.96

d. £54,527.33

e. £55,328.10

14. Refer to Exhibit T13.1. Assume the international parity conditions do not hold. Expected future spot rates are: E(S₁^£/€) = £2.060/€, E(S₂^£/€) = £2.100/€, and E(S₃^£/€) = £2.220/€. Calculate the net present value of the project V^£|i^£ by converting euros to pounds at the expected future spot rates and discounting in pounds. Assume S₀^£/€ = £2/€ and i^£ = 7%.

a. NPV^£ = £52,464.96

b. NPV^£ = £52,978.31

c. NPV^£ = £53,015.25

d. NPV^£ = £53,716.36

e. NPV^£ = £54,142.84

15. Refer to Exhibit T13.1. Suppose there is a 10 percent chance that the host government will seize the assets of the project in year 3. If the assets are not seized, you expect to receive the cash flows as shown. If the assets are seized, you expect to receive repatriated funds in year 1 and year 2 only. Assume the international parity conditions hold. What is V^£?

a. £42,431.49

b. £47,018.46

c. £47,368.32

d. £49.652.21

e. £50,737.29

16. Refer to Exhibit T13.1. Suppose that beginning in year 1, there is a 10 percent chance each year the host government will seize the project’s assets. If the assets are not seized, you expect to receive the cash flows as stated above. If the assets are seized in a particular year, you expect to receive no repatriated funds thereafter. Assume the international parity conditions hold. What is V^£?

a. £42,431.49

b. £47,018.46

c. £47,368.32

d. £49.652.21

e. £50,737.29

17. Refer to Exhibit T13.1. Assume 50 percent of the project’s expected cash flows are retained in the host country until the project is three years old. The opportunity cost of these funds is i^€ = 5 percent, but these blocked funds earn no interest. What is the NPV of the opportunity cost from these blocked funds?

a. €569.16

b. €598.24

c. €625.80

d. €658.68

e. €683.22

18. You invest BRL 1 million in land on the coast of Brazil. You expect the land to retain its BRL 1 million real value for the foreseeable future. The annual risk-free rate of interest in BRL is 10 percent. The market risk premium on the local Brazilian stock market is 5 percent per year. Expected annual inflation in BRL is 8 percent. The Brazilian corporate income tax rate is 40 percent. What is the expected nominal value of the land in two years before taxes?

a. BRL 1,000,000

b. BRL 1,102,500

c. BRL 1,166,400

d. BRL 1,210,000

e. BRL 1,322,500

19. You invest BRL 1 million in land on the coast of Brazil. You expect the land to retain its BRL 1 million real value for the foreseeable future. The annual risk-free rate of interest in BRL is 10 percent. The market risk premium on the local Brazilian stock market is 5 percent per year. Expected annual inflation in BRL is 8 percent. The Brazilian corporate income tax rate is 40 percent. If you plan on selling the land in two years, what is your expected tax payment on the sale?

a. BRL 0

b. BRL 41,000

c. BRL 66,560

d. BRL 84,000

e. BRL 129,000

20. You invest BRL 100 million in a factory in Brazil. The factory will be depreciated at the rate of BRL 5 million per year for 20 years to a zero salvage value. You expect the factory will be worth BRL 90 million in nominal terms after four years. You plan on selling the factory in four years. The Brazilian corporate income tax rate is 40 percent. What is your expected tax liability on the sale?

a. BRL 0 million

b. BRL 4 million

c. BRL 10 million

d. BRL 36 million

e. BRL 80 million

21. You invest BRL 10 million in inventory for your Brazilian factory. You expect to make no further investment or disinvestment in inventory over the five-year life of your project. You expect the inventory will retain its real value. Inventory costing is done on a LIFO (last in/first out) basis. Expected annual inflation in BRL is 8 percent. The Brazilian corporate income tax rate is 40 percent. What is the expected nominal value of the inventory in five years before taxes (approximately)?

a. BRL 4.0 million

b. BRL 6.8 million

c. BRL 10.0 million

d. BRL 10.8 million

e. BRL 14.7 million

22. You invest BRL 10 million in inventory for your Brazilian factory. You expect to make no further investment or disinvestment in inventory over the five-year life of your project. You expect the inventory will retain its real value. Inventory costing is done on a LIFO (last in/first out) basis. Expected annual inflation in BRL is 8 percent. The Brazilian corporate income tax rate is 40 percent. If you plan on selling the inventory in five years, your expected tax liability on the sale is about ___.

a. BRL 0.0 million

b. BRL 0.3 million

c. BRL 1.6 million

d. BRL 1.9 million

e. BRL 4.0 million

Problems (Many of these can be converted into ‘Multiple Choice’ questions.)

PROBLEMS 1-7 ARE BASED ON THE DATA IN EXHIBIT T13.2

Exhibit T13.2

Wine production in Vino

U.K. Vino

Nominal risk-free government T-bill rate i_F^£ = 7.1% i_F^V = 12.2%

Real required return on T-bills q_F^£ = 2.0% q_F^V = 2.0%

Expected future inflation p^£ = 5.0% p^V = 10.0%

Real required return on wine production i^£ = 12.0% i^V = 12.0%

Current spot exchange rate S₀^V/£ = V10/£

The following information is known about the project:

• The project has a 3-year life. Assume all operating cash flows occur at year-end.
• An investment of V800,000 will purchase the vineyard. Its real value will remain constant throughout the investment’s life and the vineyard will be sold at the end of the project.
• The winery, wine presses, and installation will cost V500,000. Annual depreciation for winery and wine presses is 33%, 45%, 15%, and 7% over the four-year project. (This happens to be identical to 3-year ACRS in the United States.) The winery and presses are expected to have a total market value of V45,000 in nominal terms at the end of the project’s life in three years.
• No investment in net working capital is necessary. All of the business’s transactions are conducted in cash, and just-in-time inventory control will be used.
• Annual sales revenues are expected to be V700,000, V800,000, V900,000 in nominal terms over the next 3 years. Variable operating costs are 10% of sales. Fixed costs are V5,000 each year in nominal terms.
• Income and capital gains taxes are 50% in each country.

Cross-border capital budgeting when the international parity conditions hold.

1. You are a successful U.K. wine producer and are considering investing in a second operation in the country of Vino (with currency V). International parity conditions hold, and the investment will be 100 percent equity-financed. Interest and inflation rates and the characteristics of the investment project are as given in Exhibit T13.2.

a. What is the nominal required return on wine investments in the United Kingdom? in Vino?

b. Identify expected future cash flows on this foreign investment project. Discount these cash flows at the vino-unit discount rate from a) to find NPV₀^V. Use the current spot rate to transfer this value to NPV₀^£.

1. Translate vino-unit cash flows to pounds at expected future spot rates and discount at the pound discount rate from a) to find NPV₀^£. Is the answer the same as in b?

Cross-border capital budgeting when the international parity conditions do not hold.

2. Consider the Vino project described in Exhibit T13.2. Suppose the international parity conditions do not hold. In particular, assume real rates q^£ = 0.0% and q^V = 12.0%, and inflation p^£ = 17.6% and p^V = 10.0%, so that nominal interest rates are i^£ = 17.6% and i^V = 23.2% from the Fisher equation. In addition, the expected spot rate is assumed to hold its nominal value such that E[S_t^£/V] = £0.10/V in years 1 through 3. Calculate V^£ using Recipes #1 and #2 from the chapter. Should you invest in the project? How do you respond to this market disequilibrium?

3. Consider the Vino project described in Exhibit T13.2. Suppose the international parity conditions do not hold with real rates of q^£ = 12.0% and q^V = 0.0%, and inflation of p^£ = 5.0% and p^V = 23.2%, so that nominal interest rates are i^£ = 17.6% and i^V = 23.2%. The expected spot rate is expected to remain at E[S_t^£/V ] = £0.08/V in years 1 through 3. Calculate V^£ using Recipes #1 and #2 from the chapter. Should you invest in the project? How do you respond to this market disequilibrium?

Cross-border capital budgeting when there are investment or financial side effects.

4. Consider the Vino project described in Exhibit T13.2. Suppose the government of Vino requires that you operate a local crisis center for alcoholics. Your refusal to do so will result in a government veto of your investment project. Although the crisis center is expected to generate positive cash flow, you are not sure if it will be sufficient to compensate you for your initial investment and the opportunity cost of capital. The estimated cash flows associated with the crisis center are as follows:

Assume the appropriate vino-unit discount rate for the crisis center is i_B^V = 28% and answer the following questions:

a. What name do we attach to this type of scenario?

b. Calculate NPV₀^V for the Vino project without and then with this side effect. Should you accept the project described in Exhibit T14.2 if you must accept the crisis center project?

5. Consider the Vino project described in Exhibit T13.2. Suppose the government of Vino offers you a three-year, subsidized, nonamortizing V500,000 loan if (and only if) you undertake the wine production investment. Assume they offer you an attractive loan rate of 12.2 percent even though corporate debt on similar investments yields 15 percent in vino-unit currency.

a. What is the effect of this offer on the vino-unit NPV of the project?

b. Suppose that the Vino government offers you the same loan regardless of whether you invest in the wine production project. What course of action would you take?

6. Consider the Vino project described in Exhibit T13.2. Suppose that beginning in year 2, there is a 20 percent chance each year the government will seize your assets in Vino. Specifically, if the assets are not seized, you expect to receive the cash flows described in Exhibit T14.2. However, if they are seized, you expect to receive only the repatriated funds from the previous year and none thereafter. What effect does this expropriation risk have on NPV₀^£?

7. Consider the Vino project described in Exhibit T13.2. Suppose 70 percent of your cash flow must be retained in Vino until the investment is three years old. Blocked funds are stored with the aging wine for luck and earn no interest. Assume the discount rate that appropriately reflects the riskiness of the blocked funds is i^V = 15%. The corporate income tax rate is 40 percent. Funds that are not blocked can be repatriated at the end of the year in which they are earned.

a. What is the opportunity cost of the blocked funds? What is the value of the project with these blocked funds?

b. What is the advantage of separating the value of the project into two separate parts (i.e., V_{project w/ blocked funds} = V_{project w/ out blocked funds} + V_{blocked funds} )?

8. You are considering investing in an oil well in Azerbaijan. The well costs £40 million and generates end-of-year expected after-tax cash flow of £10 million per year in perpetuity. The appropriate risk-adjusted discount rate is 20 percent per year. There is a 20 percent chance that the Azerbaijan government will expropriate your asset immediately after you invest.

a. What is the value of the oil well in the absence of expropriation risk?

b. What is the expected loss in value from expropriation risk?

c. What is the value of the oil well in the presence of expropriation risk?

9. The World Bank offers you a subsidized loan if you undertake a power generation project in Kenya. The nonamortized loan will be for £100 million and is to be repaid over five years at 10 percent compounded quarterly (2.5 percent per quarter) with quarterly interest payments. The market rate of interest on similar loans is 12 percent compounded quarterly (3 percent per quarter). The corporate income tax rate is 35 percent both domestically and in Kenya. What is the value of this subsidy?

10. You have invested in a diamond mine in Nigeria. The mine is expected to generate nominal, after-tax cash flows of £1 million per year in perpetuity at a risk-adjusted discount rate of 12.5 percent per year. Unfortunately, the Nigerian government requires that you leave each year’s cash flow in the Nigerian treasury for five years after it is earned. The discount rate on five-year Nigerian bonds is 10 percent. Assume end-of-year cash flows.

a. What is the value of the diamond mine in the absence of blocked funds?

b. What is the loss in value if blocked funds earn 0 percent interest?

c. What is the loss in value if blocked funds earn 5 percent interest?

d. What is the loss in value if blocked funds earn 10 percent interest?

Problem Solutions

PROBLEMS 1-7 ARE BASED ON THE DATA IN EXHIBIT T13.2

Cross-border capital budgeting when the international parity conditions hold.

1. a. (1 + i^£) = (1 + p^£)(1 + q^£) ⇒ i^£ = (1.12)(1.05) – 1 = 0.176 or 17.6%

(1 + i^V) = (1 + p^V)(1 + q^V) ⇒ i^V = (1.12)(1.10) – 1 = 0.232 or 23.2%

b. Initial Outlay = (V800,000) + (V425,000) + (V47,500) + (V27,500) = (V1,300,000)

Depreciation tax shield calculation: (Depreciable base = V500,000)

Beginning Depr Depr Ending Tax

Year balance % expense balance shield

1 V500,000 33% V165,000 V335,000 V82,500

2 V335,000 45% V225,000 V110,000 V112,500

3 V110,000 15% V75,000 V35,000 V37,500

4 V35,000 7% V35,000 V0 V17,500

After-tax operating cash flows:

CF₁ = (V700,000 – V70,000 – V5,000)(1–0.5) + V82,500 = V395,000

CF₂ = (V800,000 – V80,000 – V5,000)(1–0.5) + V112,500 = V470,000

CF₃ = (V900,000 – V90,000 – V5,000)(1–0.5) + V37,500 = V440,000

Terminal Cash Flow = V800,000(1.10)³ – {[ V800,000(1.10)³ – V800,000]0.5}

+ V45,000 – [(V45,000 –V35,000)0.5] = V972,400

V^V|i^V = V85,581 at i^V = 23.2%

V^£|i^V = V85,581/(V10/£) = £8,558 at V10/£

c. E(S₁ ^V/£) = V10/£ (1.232/1.176) = V10.47619/£

E(S₂ ^V/£) = V10/£ (1.232/1.176)² = V10.97506/£

E(S₃ ^V/£) = V10/£ (1.232/1.176) ³ = V11.49768/£

£122,807

£42,824

£37,704

-£130,000

t = 2

t = 3

t = 1

NPV^£ = £8,558 at i^£ = 17.6%

This is the same as in (b) because the international parity conditions hold.

Cross-border capital budgeting when the international parity conditions do not hold.

2. Recipe #1: As calculated in Problem 1: V^V|i^V = V85,581

V^£|i^V = V85,581/(V10/£) = £8,558

Recipe #2:

£141,240

£47,000

£39,500

-£130,000

t = 2

t = 3

t = 1

V^£|i^£ = £24,416 > V^£|i^V = £8,558 at i^£ = 17.6%. Although the project is positive-NPV regardless of the perspective, it has a higher value from the parent firm’s perspective than from the local project perspective. This is because the expected future value of the dollar is less than under the equilibrium conditions. You may choose to leave your cash flows from the project unhedged in order to benefit from the below-parity value of the dollar (and the above-parity value of the vino), although this exposes you to currency risk. If you hedge the expected cash flows, you can reduce your exposure to currency risk but at the cost of a lower expected value.

3. Recipe #1: As calculated in Problem 1: V^V|i^V = V85,581

V^£|i^V = V85,581/(V10/£) = £8,558

Recipe #2:

£112,992

£37,600

£31,600

-£130,000

t = 2

t = 3

t = 1

V^£|i^£ = –£6,467 < 0 < V^£|i^V = £8,558 at i^£ = 17.6%. Now, the project looks negative-NPV from the parent’s perspective but positive-NPV from the project’s perspective in the foreign currency. Exchange rates are going against the project in this case. If you do decide to invest, you should hedge the vino cash flows to try to capture the local project expected value. For example, you could borrow a portion of the initial investment in the local vino currency, which are at a low interest rate relative to the forward premium on the vino.

Cross-border capital budgeting when there are investment or financial side effects.

4. a. The crisis center is a negative NPV tie-in project. Cash flows should be discounted at the market’s required return of i_B^V = 28% on similar projects.

b. NPV₀^V_{project w/o tie-in} = V85,367 as in problem 1

NPV₀^V_tie-in = –£100k + £40k/(1.28)¹ + £40k/(1.28)² + £50k/(1.28)³ = –V20,494

NPV₀^V_{project w/tie-in} = V85,367 – V20,494 = V64,873

NPV₀^V_{project w/tie-in} is greater than zero, so the project is attractive even with the negative-NPV tie-in project. You should attempt to renegotiate the terms of the negative-NPV tie-in project. If the project is vitally important to the local government, perhaps there is a way that you can deliver similar value to the local government and its populace at less cost to you.

5. a. V500,000(0.122) = V61,000 interest/year vs. V500,0000.15 = V75,000 at market

Interest savings per year = V75,000 – V61,000 = V14,000

After-tax interest savings per year = V14,000(1 – 0.5) = V7,000

Present value of interest subsidy = V18,204 at i^V(1 – T) = 15%(1 – 0.50) = 7.5%

NPV₀^V_{project w/subsidy} = V85,367 + V18,204 = V103,571

b. Accept the subsidized loan if there are no other (explicit or implicit) obligations to the Vino government. When the subsidized financing is separable from the project, the additional value from the subsidized financing should not be allocated to the project. Instead, the subsidized loan should be used to displace other firm debt.

6.

where: Year 2 cash flow = V470,000(1 – 0.20) = V376,000

Year 3 cash flow = V1,412,400(1 – 0.20)² = V903,936

NPV₀^V = (V248,398) and NPV₀^£ = V248,398/(V10/£) = (£24,839.8)

Both NPV^V and NPV^£ are less than zero, so the investment should no longer be accepted.

7. a. Step 1: Determine the value of blocked funds assuming they are not blocked. At the after-tax discount rate of i^V(1 – T) = 15%(1 – 0.4) = 9%, the present value of the blocked funds would have been V395,000(0.7)/(1.09) + V470,000(0.7)/(1.09)² = V530,582.

Step 2: Determine the opportunity cost of the blocked funds. After three years, the blocked funds would have grown in value to (0.7)(V395,000 + V470,000) = V605,500. The after-tax value of blocked funds is V605,500/(1.09)³ = V467,577. The opportunity cost of the blocked funds is V530,582 – V467,577 = V63,025. Project value is reduced by V63,025 with the blocked funds.

b. This side effect reduces the NPV of the project to V_{w/ blocked funds} = V_{w/o blocked funds} + V_{blocked funds} = V85,367 – V63,025 = V225342. You have an incentive to negotiate with the host government so that both parties can benefit. The value of the project without the side effect establishes a reservation price for the amount that you can afford to lose on side effects.

8. a. In the absence of expropriation risk, NPV^£ = [(£10 million) / 0.10] – £40 million = £60 million.

b. The expected loss due to expropriation risk (£40 million) (0.20) = £8 million.

c. The value of the well including the expected loss from expropriation risk is V_project = V_{project w/o side effect} + V_{side effect} = £60 million – £8 million = £52 million.

9. The quarterly savings in after-tax interest payments is £100(0.030 – 0.025)(1 – 0.35) = £325,000. The present value of 20 quarters of £325,000 discounted at the after-tax market rate of (3%)(1 – 0.35) = 1.95% on similar-risk loans is £5,338,947.

10. a. PV^£ = (£1 million) / 0.125 = £8 million

b. The present value of an investment in the Nigerian treasury without blocked funds is (£1 million) / 0.10 = £10 million. The present value of funds blocked in the Nigerian treasury at zero percent interest for five year is [(£1 million) / 0.10] / (1.10)⁵ = £6,209,213. The forgone value is £10,000,000 – £6,209,213 = £3,790,787.

c. Each year’s cash flow left in the Nigerian treasury will grow to £1,000,000(1.05)⁵ = £1,276,281 after five years. The present value of an annual stream of £1,276,281 beginning at time five is [(£1,276,281) / 0.10] / (1.10)⁵ = £7,924,704. The forgone value is £10,000,000 – £7,924,704 = £2,075,296.

d. In this case, funds are earning their required return and the forgone value is zero. Algebraically, as in (c), [(£1 million) (1.10)⁵ / 0.10] / (1.10)⁵ = £10 million, as in part (a). Quantitatively, there is no loss of value. Qualitatively, the parent corporation will prefer the flexibility of having access to the funds. (Immediate access to the funds also may reduce the firm’s external borrowing needs.)