CH-18 International Capital Budgeting – International Financial Management : Book Guide

CHAPTER 18 INTERNATIONAL CAPITAL BUDGETING ANSWERS & SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS QUESTIONS 1. Why is capital budgeting analysis so important to the firm? Answer: The fundamental goal of the financial manager is to maximize shareholder wealth. Capital investments with positive NPV or APV contribute to shareholder wealth. Additionally, capital investments generally represent large expenditures relative to the value of the entire firm. These investments determine how efficiently and expensively the firm will produce its product. Consequently, capital expenditures determine the long-run competitive position of the firm in the product marketplace. 2. What is the intuition behind the NPV capital budgeting framework? Answer: The NPV framework is a discounted cash flow technique. The methodology compares the present value of all cash inflows associated with the proposed project versus the present value of all project outflows. If inflows are enough to cover all operating costs and financing costs, the project adds wealth to shareholders. 3. Discuss what is meant by the incremental cash flows of a capital project. Answer: Incremental cash flows are denoted by the change in total firm cash inflows and cash outflows that can be traced directly to the project under analysis. 4. Discuss the nature of the equation sequence, Equation 18.2a to 18.2f. Answer: The equation sequence is a presentation of incremental annual cash flows associated with a capital expenditure. Equation 18.2a presents the most detailed expression for calculating these cash flows; it is composed of three terms. Equation 18.2b shows that these three terms are: i) incremental net profit associated with the project; ii) incremental depreciation allowance; and, iii) incremental after-tax interest expense associated with the borrowing capacity created by the project. Note, the incremental “net profit” is not accounting profit but rather net cash actually available for shareholders. Equation 18.2c cancels out the after-tax interest term in 18.2a, yielding a simpler formula. Equation 18.2d shows that the first term in 18.2c is generally called after-tax net operating income. Equation 18.2e yields yet a computationally simpler formula by combining the depreciation terms of 18.2c. Equation 18.2f shows that the first term in 18.2e is generally referred to as after-tax operating cash flow. 5. What makes the APV capital budgeting framework useful for analyzing foreign capital expenditures? Answer: The APV framework is a value-additivity technique. Because international projects frequently have cash flows not encountered in domestic projects, the APV technique easily allows the analyst to add terms to the model that represent the special cash flows. 6. Relate the concept of lost sales to the definition of incremental cash flow. Answer: When a new capital project is undertaken it may compete with an existing project(s), causing the old project(s) to experience a loss in sales revenue. From an incremental cash flow standpoint, the new project’s incremental revenue is the total sales revenue associated with the new project minus the lost sales revenue from the old project(s). 7. What problems can enter into the capital budgeting analysis if project debt is evaluated instead of the borrowing capacity created by the project? Answer: If project debt is greater (less) than the borrowing capacity created by the capital project, and tax shields on the actual new debt are used in the analysis, the APV will be overstated (understated) making the project unjustly appear more (less) attractive than it actually is. 8. What is the nature of a concessionary loan and how is it handled in the APV model? Answer: A concessionary loan is a loan offered by a governmental body at below the normal market rate of interest as an enticement for a firm to make a capital investment that will economically benefit the lender. The benefit to the MNC is the difference between the face value of the concessionary loan converted into the home currency and the present value of the similarly converted concessionary loan payments discounted at the MNC’s normal domestic borrowing rate. The loan payments will yield a present value less than the face amount of the concessionary loan when they are discounted at the higher normal rate. This difference represents a subsidy the host country is willing to extend to the MNC if the investment is made. The benefit to the MNC of the concessionary loan is handled in the APV model via a separate term. 9. What is the intuition of discounting the various cash flows in the APV model at specific discount rates? Answer: The APV model is a value-additivity technique where total value is determined by the sum of the present values of the individual cash inflows and outflows. Each cash flow will not necessarily have the same amount of risk associated with it. To account for risk differences in the analysis, each cash flow is discounted at a rate commensurate with the inherent riskiness of the cash flow. 10. In the Modigliani-Miller equation, why is the market value of the levered firm greater than the market value of an equivalent unlevered firm? Answer: The levered firm has a greater market value because less money is taken from the firm by the government in taxes due to tax-deductible interest payments. Thus, there is more cash left for investor groups than when the firm is financed with all-equity funds. 11. Discuss the difference between performing the capital budgeting analysis from the parent firm’s perspective as opposed to the subsidiary’s perspective. Answer: The goal of the financial manager of the parent firm is to maximize its shareholders’ wealth. A capital project of a subsidiary of the parent may have a positive NPV (or APV) from the subsidiary’s perspective yet have a negative NPV (or APV) from the parent’s perspective if certain cash flows cannot be repatriated to the parent because of remittance restrictions by the host country, or if the home currency is expected to appreciate substantially over the life of the project, yielding unattractive cash flows when converted into the home currency of the parent. Additionally, a higher tax rate in the home country may cause the project to be unprofitable from the parent’s perspective. Any of these reasons could result in the project being unattractive to the parent and the parent’s stockholders. 12. Define the concept of a real option. Discuss some of the various real options a firm can be confronted with when investing in real projects. Answer: A positive APV project is accepted under the assumption that all future operating decisions will be optimal. The firm’s management does not know at the inception date of a project what future decisions it will be confronted with because all information concerning the project has not yet been learned. Consequently, the firm’s management has alternative paths, or options, that it can take as new information is discovered. The application of options pricing theory to the evaluation of investment options in real projects is known as real options. The firm is confronted with many possible real options over the life of a capital asset. For example, the firm may have a timing option as when to make the investment; it may have a growth option to increase the scale of the investment; it may have a suspension option to temporarily cease production; and, it may have an abandonment option to quit the investment early. 13. Discuss the circumstances under which the capital expenditure of a foreign subsidiary might have a positive NPV in local currency terms but be unprofitable from the parent firm’s perspective. Answer: The project NPV might be negative from the parent firm’s perspective when it is positive in local currency terms if all foreign cash flows cannot be legally repatriated to the parent firm. Additionally, if the PPP assumption does not hold, such that the actual future real exchange rate has depreciated in foreign currency terms, the after-tax cash flows will yield less units of home currency from the parent firm’s perspective than expected, possibly resulting in a negative NPV. PROBLEMS 1. The Alpha Company plans to establish a subsidiary in Hungary to manufacture and sell fashion wristwatches. Alpha has total assets of $70 million, of which $45 million is equity financed. The remainder is financed with debt. Alpha considered its current capital structure optimal. The construction cost of the Hungarian facility in forints is estimated at HUF2,400,000,000, of which HUF1,800,000,and 000 is to be financed at a below-market borrowing rate arranged by the Hungarian government. Alpha wonders what amount of debt it should use in calculating the tax shields on interest payments in its capital budgeting analysis. Can you offer assistance? Solution: The Alpha Company has an optimal debt ratio of .357 (= $25 million debt/$70 million assets) or 35.7%. The project debt ratio is .75 (= HUF1,800/HUF2,400) or 75%. Alpha will overstate the tax shield on interest payments if it uses the 75% figure because the proposed project will only increase borrowing capacity by HUF856,800,000 (=HUF2,400,000,000 x .357). 2. The current spot exchange rate is HUF250/$1.00. Long-run inflation in Hungary is estimated at 10 percent annually and 3 percent in the United States. If PPP is expected to hold between the two countries, what spot exchange should one forecast five years into the future? Solution: HUF250(1 + .10)5/(1 + .03)5 = HUF347.31/$1.00. 3. The Beta Corporation has an optimal debt ratio of 40 percent. Its cost of equity capital is 12 percent and its before-tax borrowing rate is 8 percent. Given a marginal tax rate of 35 percent, calculate (a) the weighted-average cost of capital, and (b) the cost of equity for an equivalent all-equity financed firm. Solution: (a) K = (1 - .40).12 + (.40).08(1 - .35) = .0928 or 9.28% (b) A weighted-average cost of capital of 9.28% for a levered firm implies: K =.0928 = Ku (1-(.35)(.40)). Solving for Ku yields .1079 or 10.79%. 4. Zeda, Inc., a U.S. MNC, is considering making a fixed direct investment in Denmark. The Danish government has offered Zeda a concessionary loan of DKK15,000,000 at a rate of 4 percent per annum. The normal borrowing rate is 6 percent in dollars and 5.5 percent in Danish krone. The loan schedule calls for the principal to be repaid in three equal annual installments. What is the present value of the benefit of the concessionary loan? The current spot rate is DKK5.60/$1.00 and the expected inflation rate is 3% in the U.S. and 2.5% in Denmark. Solution: Year (t) St (a) Principal Payment (b) DKK It (c) DKK StLPt (b + c)/(a) StLPt/(1 + id)t 1 5.57 5,000,000 600,000 1,005,386 948,477 2 5.55 5,000,000 400,000 972,973 865,943 3 5.52 5,000,000 200,000 942,029 790,946 15,000,000 2,605,366 The dollar value of the concessionary loan is $2,678,574 = DKK15,000,000 ÷ 5.60. The dollar present value of the concessionary loan payments is $2,605,366. Therefore, the present value of the benefit of the concessionary loan is $73,208 = $2,678,574 – 2,605,366. 5. Delta Company, a U.S. MNC, is contemplating making a foreign capital expenditure in South Africa. The initial cost of the project is ZAR10,000. The annual cash flows over the five year economic life of the project in ZAR are estimated to be 3,000, 4,000, 5,000, 6000, and 7,000. The parent firm’s cost of capital in dollars is 9.5 percent. Long-run inflation is forecasted to be 3 percent per annum in the U.S. and 7 percent in South Africa. The current spot foreign exchange rate is ZAR/USD = 3.75. Determine the NPV for the project in USD by: a. Calculating the NPV in ZAR using the ZAR equivalent cost of capital according to the Fisher Effect and then converting to USD at the current spot rate. Solution: ZAR equivalent cost of capital according to the Fisher Effect = 1.095 x [(1.07)/(1.03)] – 1 = .1375 or 13.75 percent. NPVUSD = [3,000/(1.1375)1 + 4,000/(1.1375)2 + 5,000/(1.1375)3 + 6,000/(1.1375)4 + 7,000/(1.1375)5 – 10,000]/3.75 = USD1,700 b. Converting all cash flows from ZAR to USD at Purchasing Power Parity forecasted exchange rates and then calculating the NPV at the dollar cost of capital. Solution: The PPP forecasted ZAR/USD exchange rates are: ZAR/USD(t) = 3.75 x [(1.07)/(1.03)]t ZAR/USD(1) = 3.90; ZAR/USD(2) = 4.05; ZAR/USD(3) = 4.20; ZAR/USD(4) = 4.37; and, ZAR/USD(5) = 4.54. NPVUSD = [(3,000/3.90)/(1.095)1 + 4,000/(4.05)/(1.095)2 + 5,000/(4.20)/(1.095)3 + 6,000/(4.37)/(1.095)4 + 7,000/(4.54)/(1.095)5 – 10,000/(3.75)] = USD1,700 Are the two dollar NPVs different or the same? Explain. The two dollar NPVs are identical as they always will be under the assumption that both PPP and the Fisher Effect hold. Note, that both parity conditions incorporate relative differences in inflation. c. What is the NPV in dollars if the actual pattern of ZAR/USD exchange rates is: S(0) = 3.75, S(1) = 5.7, S(2) = 6.7, S(3) = 7.2, S(4) = 7.7, and S(5) = 8.2? Solution: NPVUSD = [(3,000/5.7)/(1.095)1 + 4,000/(6.7)/(1.095)2 + 5,000/(7.2)/(1.095)3 + 6,000/(7.7)/(1.095)4 + 7,000/(8.2)/(1.095)5 – 10,000/(3.75)] = –USD75. The NPV is negative because actual exchange rates did not evolve as forecasted by PPP. Consequently, actual NPV and forecasted NPV may be different. 6. Suppose that in the illustrated mini case in the chapter the APV for Centralia had been $60,000. How large would the after-tax terminal value of the project need to be before the APV would be positive and Centralia would accept the project? Solution: Centralia should not go ahead with its plans to build a manufacturing plant in the Spain unless the terminal value is likely to be large enough to yield a positive APV. The terminal value of the project must be $299,010 in order for the APV to equal zero. This is calculated as follows. Set STTVT/(1+Kud)T = $60,000. This implies TVT = ($60,000/ST)(1+Kud)T = ($60,000/.7261)(1.11)8 = €190,431. 7. With regards to the Centralia illustrated mini case in the chapter, how would the APV change if: a. The forecast of d and/or f are incorrect? Answer: A larger or smaller d will not have any effect because a change will affect the numerator and denominator of each APV term in an offsetting manner. Note that imbedded in each domestic discount rate is the inflation premium d. A larger (smaller) f, however, will decrease (increase) the project APV because the foreign currency received will buy less (more) parent country currency upon repatriation. b. Deprecation cash flows are discounted at Kud instead of id? Answer: The APV would be less favorable because Kud is a larger discount rate than id. c. The host country did not provide the concessionary loan? Answer: The APV would be less favorable because the project would have to cover a higher finance charge, i.e., there would be no benefit received from below market financing. MINI CASE: DORCHESTER, LTD. Dorchester Ltd., is an old-line confectioner specializing in high-quality chocolates. Through its facilities in the United Kingdom, Dorchester manufactures candies that it sells throughout Western Europe and North America (United States and Canada). With its current manufacturing facilities, Dorchester has been unable to supply the U.S. market with more than 225,000 pounds of candy per year. This supply has allowed its sales affiliate, located in Boston, to be able to penetrate the U.S. market no farther west than St. Louis and only as far south as Atlanta. Dorchester believes that a separate manufacturing facility located in the United States would allow it to supply the entire U.S. market and Canada (which presently accounts for 65,000 pounds per year). Dorchester currently estimates initial demand in the North American market at 390,000 pounds, with growth at a 5 percent annual rate. A separate manufacturing facility would, obviously, free up the amount currently shipped to the United States and Canada. But Dorchester believes that this is only a short-run problem. They believe the economic development taking place in Eastern Europe will allow it to sell there the full amount presently shipped to North America within a period of five years. Dorchester presently realizes £3.00 per pound on its North American exports. Once the U.S. manufacturing facility is operating, Dorchester expects that it will be able to initially price its product at $7.70 per pound. This price would represent an operating profit of $4.40 per pound. Both sales price and operating costs are expected to keep track with the U.S. price level; U.S. inflation is forecast at a rate of 3 percent for the next several years. In the U.K., long-run inflation is expected to be in the 4 to 5 percent range, depending on which economic service one follows. The current spot exchange rate is $1.50/£1.00. Dorchester explicitly believes in PPP as the best means to forecast future exchange rates. The manufacturing facility is expected to cost $7,000,000. Dorchester plans to finance this amount by a combination of equity capital and debt. The plant will increase Dorchester’s borrowing capacity by £2,000,000, and it plans to borrow only that amount. The local community in which Dorchester has decided to build will provide $1,500,000 of debt financing for a period of seven years at 7.75 percent. The principal is to be repaid in equal installments over the life of the loan. At this point, Dorchester is uncertain whether to raise the remaining debt it desires through a domestic bond issue or a Eurodollar bond issue. It believes it can borrow pounds sterling at 10.75 percent per annum and dollars at 9.5 percent. Dorchester estimates its all-equity cost of capital to be 15 percent. The U.S. Internal Revenue Service will allow Dorchester to depreciate the new facility over a seven-year period. After that time the confectionery equipment, which accounts for the bulk of the investment, is expected to have substantial market value. Dorchester does not expect to receive any special tax concessions. Further, because the corporate tax rates in the two countries are the same--35 percent in the U.K. and in the United States--transfer pricing strategies are ruled out. Should Dorchester build the new manufacturing plant in the United States? Suggested Solution to Dorchester Ltd. Summary of Key Information The current exchange rate in European terms is So(£/$) = 1/1.50 = .6667. The initial cost of the project in British pounds is SoCo = £0.6667($7,000,000) = £4,666,900. The U.K. inflation rate is estimated at 4.5% per annum, or the mid-point of the 4%-5% range. The U.S. inflation rate is forecast at 3% per annum. Under the simplifying assumption that PPP holds St = .6667(1.045)t/(1.03)t. The before-tax nominal contribution margin per unit at t=1 is $4.40(1.03)t-1. It is assumed that Dorchester will be able to sell one-fifth of the 290,000 pounds of candy it presently sells to North America in Eastern Europe the first year the new manufacturing facility is in operation; two-fifths the second year; etc.; and all 290,000 pounds beginning the fifth year. The contribution margin on lost sales per pound in year t equals £3.00(1.045)t. Terminal value will initially be assumed to equal zero. Straight line depreciation over the seven year economic life of the project is assumed: Dt = $1,000,000 = $7,000,000/7 years. The marginal tax rate, , is the U.K. (or U.S.) rate of 35%. Dorchester will borrow $1,500,000 at the concessionary loan rate of 7.75% per annum. Optimally, Dorchester should borrow the remaining funds it needs, £1,000,000, in pounds sterling because according to the Fisher equation, the real rate is less for borrowing pounds sterling than it is for borrowing dollars: 5.98% or .0598 = (1.1075)/(1.045) - 1.0 versus 6.31% or .0631 = (1.095)/(1.03) - 1.0. Kud = 15%. Calculation of the Present Value of the After-Tax Operating Cash Flows Year (t) St Quantity St x Quantity x $4.40 x (1.03)t-1 Quantity Lost Sales Quantity Lost Sales x £3.00 x (1.045)t St OCFt St OCF t(1-) (1+Kud )t (a) £ (b) £ (a + b) £ £ 1 .6764 390,000 1,160,702 (232,000) (727,320) 433,382 244,955 2 .6863 409,500 1,273,673 (174,000) (570,037) 703,636 345,832 3 .6963 429,975 1,397,548 (116,000) (397,126) 1,000,422 427,566 4 .7064 451,474 1,533,373 (58,000) (207,498) 1,325,875 492,748 5 .7167 474,048 1,682,524 0 0 1,682,524 543,733 6 .7271 497,750 1,846,053 0 0 1,846,053 518,765 7 .7377 522,638 2,025,613 0 0 2,025,613 494,977 3,068,576 Calculation of the Present Value of the Depreciation Tax Shields Year(t) St Dt St Dt t (1+id ) $ £ 2 .6863 1,000,000 195,837 3 .6963 1,000,000 179,404 4 .7064 1,000,000 164,340 5 .7167 1,000,000 150,552 6 .7271 1,000,000 137,911 7 .7377 1,000,000 126,340 1,168,146 Calculation of the Present Value of the Concessionary Loan Payments Year (t) St Principal Payment It St LPt St LPt (1+id )t (a) (b$ ) ($c ) (a) x (b + c£ ) £ 2 .6863 214,286 99,643 215,449 175,654 3 .6963 214,286 83,036 207,025 152,402 4 .7064 214,286 66,429 198,297 131,808 5 .7167 214,286 49,821 189,286 113,605 6 .7271 214,286 33,214 179,957 97,523 7 .7377 214,286 16,607 170,330 83,346 1,500,000 956,211 Calculation of the Present Value of the Benefit from the Concessionary Loan SoCLo - t=T1(1S+t LPid t)t =£0.6667 x $1,500,000 - £956,211 = £43,839 Calculation of the Present Value of the Interest Tax Shields from the $1,500,000 Concessionary Loan Year (t) St (a) It (b) $ StI t (a x b x ) £ StI t (1+id )t £ 2 .6863 99,643 23,935 19,514 3 .6963 83,036 20,236 14,897 4 .7064 66,429 16,424 10,917 5 .7167 49,821 12,497 7,501 6 .7271 33,214 8,452 4,581 7 .7377 16,607 4,288 2,098 84,357 Calculation of the Present Value of the Interest Tax Shields from the £1,000,000 Bond Issue Year(t) OutstandingLoan PaymentPrincipal PaymentInterest It t Balance (1+id ) £ £ £ £ 1 1,000,000 0 107,500 33,973 2 1,000,000 0 107,500 30,675 3 1,000,000 0 107,500 27,698 4 1,000,000 0 107,500 25,009 5 1,000,000 0 107,500 22,582 6 1,000,000 0 107,500 20,390 7 1,000,000 1,000,000 107,500 18,411 178,738 Without considering the terminal value of the project, the APV of the project is negative: APV = £3,068,576 + 1,168,146 + 43,839 + 84,357 + 178,738 - 4,666,900 = -£123,244. Dorchester should not go ahead with its plans to build a manufacturing plant in the U.S. unless the terminal value is likely to be large enough to yield a positive APV. The terminal value of the project must be $444,397 in order for the APV to equal zero. This is calculated as follows. Set STTVT/(1+Kud)T = £123,244. This implies TVT = (£123,244/ST)(1+Kud)T = (£123,244/.7377)(1.15)7 = $444,397. Since the terminal value is expected to be substantial, and the initial cost of the project is $7,000,000, it appears likely that the terminal value will be sufficient to yield a positive APV. Thus, Dorchester should go ahead with its plans to build a manufacturing plant in the U.S. MINI-CASE: STRIK-IT-RICH GOLD MINING COMPANY The Strik-it-Rich Gold Mining Company is contemplating expanding its operations. To do so it will need to purchase land that its geologists believe is rich in gold. Strik-it-Rich’s management believes that the expansion will allow it to mine and sell an additional 2,000 troy ounces of gold per year. The expansion, including the cost of the land, will cost $2,500,000. The current price of gold bullion is $1,400 per ounce and one-year gold futures are trading at $1,484 = $1,400(1.06). Extraction costs are $1,050 per ounce. The firm’s cost of capital is 10%. At the current price of gold, the expansion appears profitable: NPV = ($1,400 – 1,050) x 2,000/.10 - $2,500,000 = $4,500,000. Strik-it-Rich’s management is, however, concerned with the possibility that large sales of gold reserves by Russia and the United Kingdom will drive the price of gold down to $1,100 for the foreseeable future. On the other hand, management believes there is some possibility that the world will soon return to a gold reserve international monetary system. In the latter event, the price of gold would increase to at least $1,600 per ounce. The course of the future price of gold bullion should become clear within a year. Strik-itRich can postpone the expansion for a year by buying a purchase option on the land for $250,000. What should Strik-it-Rich’s management do? Suggested Solution to Strik-it-Rich Gold Mining Company There is considerable risk in expanding operations at the present time, even though the NPV based on the current price of gold is a positive $4,500,000. If the price of gold falls to $1,100 per ounce, the NPV = ($1,100 – 1,050) x 2000/.10 – $2,500,000 = -$1,500,000. On-the-otherhand, if the price of gold increases to $1,600, the NPV is a very attractive NPV = ($1,600 – 1,050) x 2000/.10 – $2,500,000 = $8,500,000. The purchase option for $250,000 on the land is a relatively small amount to have the opportunity to postpone the decision until additional information is learned. Obviously, Strik-it-Rich’s management will only invest if the NPV is positive. The risk-neutral probability of gold increasing to $1,600 per ounce is: q = (F0 – S0·d)/S0(u – d) = (1,484 – 1,100)/(1,600 – 1,100) = .7680. Thus, the value of the timing option to postpone the decision one year is: C = .7680($8,500,000)/(1.06) = $6,158,491. Since this amount is substantially in excess of the $250,000 cost of the purchase option on the land, Strik-it-Rich’s management should definitely take advantage of the timing option it is confronted with to wait and see what the price of gold is in one year before it makes a decision to expand operations. International Capital Budgeting Chapter Eighteen Chapter Outline • Review of Domestic Capital Budgeting • The Adjusted Present Value Model • Capital Budgeting from the Parent Firm’s Perspective • Risk Adjustment in the Capital Budgeting Process • Sensitivity Analysis • Purchasing Power Parity Assumption • Real Options Review of Domestic Capital Budgeting • Identify the size and timing of all relevant cash flows on a time line. • Identify the riskiness of the cash flows to determine the appropriate discount rate. • Find NPV by discounting the cash flows at the appropriate discount rate. • Compare the value of competing cash flow streams at the same point in time. Review of Domestic Capital Budgeting The basic net present value equation is T TV NPVt )t (1 KT )T −C0 Where: CFt = expected incremental after-tax cash flow in year t TVT = expected after-tax terminal value including return of net working capital C0 = initial investment at inception K = weighted average cost of capital T = economic life of the project in years The NPV rule is to accept a project if NPV0 Review of Domestic Capital Budgeting For our purposes it is necessary to expand the NPV equation. CFt = (Rt – OCt – Dt – It)(1 – ) + Dt + It (1 – ) Rt is incremental revenue It is incremental interest OCt is incremental expense operating cash flowis the marginal tax rate Dt is incremental depreciation Review of Domestic Capital Budgeting We can use CFt = (OCFt)(1 – ) + Dt to restate the NPV equation, NPV = t =T 1 ( 1CF+ Kt )t + (1 +TV KT)T – C0 as: TV NPV = T ( OCFt(1)(1+– K))t+ Dt + (1 + KT )T – C0 t = 1 The Adjusted Present Value Model NPV = T ( OCF(1 +t)(1 K)–t ) + D t (1TV+ KT )T + C – t = 1 t = 1 (1 + K )t 0 can be converted to adjusted present value (APV) APV = T (OCFt)(1 – )+ Dt t + (1 +Iti)t + TVT – C0 t = 1 u (1 + Ku)T (1 + K )t (1 + i) by appealing to Modigliani and Miller’s results. The Adjusted Present Value Model It T (OCFt)(1 – )+ (1+Dit)t + (1 + i)t + (1TV+TK )T – APV =t = 1 (1 + Ku)t u C0 • The APV model is a value additivity approach to capital budgeting. Each cash flow that is a source of value to the firm is considered individually. • Note that with the APV model, each cash flow is discounted at a rate that is appropriate to the riskiness of the cash flow. Domestic APV Example Consider a project where the timing and size of the incremental after-tax cash flows for an all-equity firm are: –$1,000 $125 $250 $375 $500 0 1 2 3 4 CF0 = –$1000 The unlevered cost of equity is r0 = 10%: CF1 = $125 The project would be rejected by an all-equity firm: CF2 CF3 = $250 = 10 = $375 CF NPV = –$56.50 = $500 4 Domestic APV Example (continued) • Now, imagine that the firm finances the project with $600 of debt at r = 8%. • The tax rate is 40%, so each year they have an interest tax shield worth $19.20: × I = .40 × ($600 × .08) = .40 × $48 = $19.20 -$1,000 $125 $250 $375 $500 0 1 2 3 4 The APV of the project under leverage is: T (OCF )(1 – ) D I TV APV = 1 (1 + Kt u)t + (1 +ti)t + (1 +t i)t + (1 +TKu)T – C0 t = APV = + + – $1,000 APV = $7.09 The firm should accept the project if it finances with debt. International Capital Budgeting from the Parent Firm’s Perspective APV =t =T 1 (OCF(1 + Kt)(1u t– )+ Dt t + (1 +Iti)t +(1TV+TKu)T – C0 ) (1 + i) • The APV model is useful for a domestic firm analyzing a domestic capital expenditure or for a foreign subsidiary of an MNC analyzing a proposed capital expenditure from the subsidiary’s viewpoint. • The APV model is NOT useful for an MNC in analyzing foreign capital expenditure from the parent firm’s perspective. International Capital Budgeting from the Parent Firm’s Perspective • Donald Lessard developed an APV model for MNCs analyzing a foreign capital expenditure. The model recognizes many of the particulars peculiar to foreign direct investment. APV tT1 StO(1CF Kt (ud1)t τ) tT1 (1StτD id t)t tT1 (1 StτI idt)t STTVT T S LP T S0C0 S0RF0 S0CL0 (1t id t)t (1 Kud ) t 1 Capital Budgeting from the Parent Firm’s Perspective • One recipe for international decision makers: – Estimate future cash flows in foreign currency. – Convert to the home currency at the predicted exchange rate. • Use PPP, IRP, et cetera for the predictions. – Calculate NPV using the home currency cost of capital. Capital Budgeting from the Parent Firm’s Perspective: Example • A U.S.-based MNC is considering a European opportunity. • It’s a simple example: – There is no incremental debt. – There is no incremental depreciation. – There are no concessionary loans. – There are no restricted funds. Capital Budgeting from the Parent Firm’s Perspective: Example • We can use a simplified APV: no restricted funds Capital Budgeting from the Parent Firm’s Perspective: Example A U.S. MNC is considering a European opportunity. The size and timing of the after-tax cash flows are: –€600 €200 €500 €300 0 1 2 3 The inflation rate in the euro zone is = 3%, the inflation rate in dollars is p$ = 6%, and the business risk of the investment would lead an unlevered U.S.based firm to demand a return of Kud = i$ = 15%. The current exchange rate is S0($/€) = $1.25/€. Is this a good investment from the perspective of the U.S. shareholders? Capital Budgeting from the Parent Firm’s Perspective: Example $408.73 0 1 2 3 CF0 = (€600) × S0($/€) = (€600) × = $750 CF1 = €200 × S1($/€) = €200 × = $257.28 $1.25 (1.06)2 CF2 = €500 × S2($/€) = €500 × €1.00 (1.03)2 = $661.94 CF3 = €300 × $1.25€1.00 (1.06)(1.03)33 = $408.73 Capital Budgeting from the Parent Firm’s Perspective: Example –$750 $257.28 $661.94 $408.73 0 1 2 3 Find the NPV using the cash flow menu of your financial calculator and = –$750 an interest rate of i$ = 15%: 0 CF CF1 = $257.28 CF2 = $661.94 I = 15 CF3 = $408.73 NPV = $242.99 Capital Budgeting from the Parent Firm’s Perspective: Alternative • Another recipe for international decisionmakers: – Estimate future cash flows in the foreign currency. – Estimate the foreign currency discount rate. – Calculate the foreign currency NPV using the foreign cost of capital. – Translate the foreign currency NPV into dollars using the spot exchange rate. Foreign Currency Cost of Capital Method 0 = 3% i$ = 15% = 6% 1 2 3 Let’s find i€ and use that on the euro cash flows to find the NPV in euros. Then translate the NPV into dollars at the spot rate. – €600 €200 €500 €300 $1.25 The current exchange rate is S0($/€) = € Finding the Foreign Currency Cost of Capital: i€ Recall that the Fisher Effect holds that: (1 + e) × (1 + ) = (1 + i$) real inflation nominal rate rate rate So, for example, the real rate in the U.S. must be 8.49%: (1 + i$) 1.15 (1 + e) = e = – 1 = 0.0849 (1 + $) 1.06 Finding the Foreign Currency Cost of Capital: i€ If the Fisher Effect holds here and abroad, then: (1 + i$) (1 + i€) (1 + e$) = (1 + $) and (1 + e€) = (1 + €) If the real rates are the same in dollars and euros (e€ = e$) we have a very useful parity condition: (1 + i$) (1 + i€) = (1 + $) (1 + €) Finding the Foreign Currency Cost of Capital: i€ If we have any three of these variables, we can find the fourth: (1 + i$) (1 + i€) = (1 + $) (1 + €) In our example, we want to find i€: (1 + i$) × (1 + €) (1 + i€) = (1 + $) i€ = (1.15)(1.06) × (1.03) –1 i€ = 0.1175 International Capital Budgeting: Example – €600 €200 €500 €300 0 1 2 3 Find the NPV using the cash flow menu and i€ = 11.75%: CF0 I CF1 = –€600 = 11.75 = €200 NPV = €194.39 CF2 = €500 $1.25 €194.39 × = $242.99 CF3 = €300 € – €600 €200 €500 €300 0 1 2 3 €200 €500 €300 NPV = –€600 + + + = €194.39 1.1175 (1.1175)2 (1.1175)3 €194.39 × $1.25 = $242.99 € –$750 $257.28 $661.94 $408.73 0 1 2 3 $257.28 $661.94 $408.73 NPV = –$750 + + + = $242.99 1.15 (1.15)2 (1.15)3 International Capital Budgeting • You have two equally valid approaches: – Change the foreign cash flows into dollars at the exchange rates expected to prevail. Find the $NPV using the dollar cost of capital. – Find the foreign currency NPV using the foreign currency cost of capital. Translate that into dollars at the spot exchange rate. • If you watch your rounding, you will get exactly the same answer either way. • Which method you prefer is your choice. Computing IRR Recall that a project’s Internal Rate of Return (IRR) is the discount rate that gives a project a zero NPV. €200 €500 €300 NPV = –€600 + + 2 + (1+ IRR€)3 = €0 1+IRR€ (1+IRR€) IRR€ = 28.48% $257.28 $661.94 $408.73 NPV = –$750 + 1+IRR + (1+ IRR )2 +(1+ IRR$)3= $0 $ $ IRR$ = 32.23% Directly Computing IRR$ and IRR€ NPV = –€600 + €200 €500 €300 3 = €0 + + 1+IRR€ (1+IRR€)2 (1+IRR€) CF CF CF1 CF3 0 = –€600 2 = €500 = €200= €300 $257.28 $661.94 NPV = –$750 + 1+IRR$ + (1+IRR$)2 CF = –$750 CF 0 2 = $661.94 CF1 = $257.28 CF3 = $408.73 IRR € = 28.48% $408.73 + (1+IRR$)3 = $0 IRR$ = 32.23% Converting from IRR$ to IRR€ • Use the same IRP and PPP conditions that we used to convert from one discount rate to another. 1+IRR € 1+IRR$ =In our example, it was easy to find (1 + $) (1 + IRR€. Finding IRRall cash flows into dollars is $ without converting straightforward: (1+IRR€)(1 + $) (1+IRR$) = (1 + €) (1.2848)(1.06) i€ = – 1 = 3%, = 6% IRR$ = 32.23% Back to the Full APV • Using the intuition just developed, we can modify Lessard’s APV model as shown, if we find it convenient. Risk Adjustment in the Capital Budgeting Process • Clearly risk and return are correlated. • Political risk may exist along side of business risk, necessitating an adjustment in the discount rate. • We can measure this risk with sensitivity analysis, where different estimates are used for expected inflation rates, cost and pricing estimates, and other inputs to give the manager a more complete picture of the planned capital investment. • Lends itself to computer simulation. Real Options • The application of options pricing theory to the evaluation of investment options in real projects is known as real options. – A timing option is an option on when to make the investment. – A growth option is an option to increase the scale of the investment. – A suspension option is an option to temporarily cease production. – An abandonment option is an option to quit the investment early. Value of the Option to Delay –£1,000 £1,150 0project cash flows1 A French firm is considering a 1-year investment in the United Kingdom with a pound-denominated rate of return of i£ = 15%. The firm’s local cost of capital is i€ = 10%. €2.00 The current exchange rate is S0(€|£) = £ Complicating matters, the Bank of England is considering either tightening or loosening its monetary policy.It is believed that in one year there are only two possibilities: S1(€|£) = €2.20/£ or S1(€|£) = €1.80/£ Following revaluation, the exchange rate is expected to remain steady for at least another year. 1 1 IRR = 3.50% IRR = 26.50% Option to Delay • If S1(€|£) = €1.80/£ the project will have turned out to be a loser for the French firm: • If S1(€|£) = €2.20/£ the project will have turned out to be a big winner for the French firm: –€2,000 €2,070 –€2,000 €2,530 Option to Delay: Example • An important thing to notice is that there is an important source of risk (exchange rate risk) that isn’t incorporated into the French firm’s local cost of capital of i€ = 10%. – That’s why there are no NPV estimates on the last slide. • Even with that, we can see that taking the project on today entails a “win big—lose big” gamble on exchange rates. • Analogous to buying an at-the-money call option on British pounds with a maturity of one year. Option to Delay: Example • The remaining slides assume a knowledge of the material contained in Chapter 7, especially the notion of a replicating portfolio. • But, also basic things like a call option give the holder the right to buy a specific asset at a specific price for a specific amount of time. Option to Delay: Example • The payoff in one year of a portfolio consisting of an at-the-money call option written on £2,300 plus a risk-free bond with a future value of €2,070 equals the payoff of the British investment: British Call Replicating S1(€|£) Investment = Bond + Option = Portfolio €2.20/£ €2,530 = €2,070 + €460 = €2,530 €1.80/£ €2,070 = €2,070 + €0 = €2,070 Option to Delay: Example • So the present value of the project at time zero can be found by getting a quote from an option dealer on an at-the-money call on £2,300 and adding to that the present value of €2,070 at the euro-zone risk-free rate. • The NPV of the project is that sum less the cost of the project, –€2,000: €2,070 NPV = –€2,000 + value of option + 1+ i€ Option to Delay: Example • Suppose that our option dealer quotes an option premium of €0.05 per pound and our banker quotes the euro-zone risk-free rate at i€ = 6%. • The NPV of the project at time zero to the French firm is: €2,070 = €67.83 NPV0 = –€2,000 + €115 + 1.06 • Before we accept a positive NPV project, we should make sure that we are not bypassing alternative projects with higher NPVs. • Waiting a year to start the same project is an alternative. Option to Delay: Example • If the firm can wait a year to start the project, the cash flows look like: If S1(€|£) = €1.80 per £ If S1(€|£) = €2.20 per £ –€1,800 €2,070 –€2,200 €2,530 01 01 IRR = 15% €2,070 IRR = 15% NPV1 = €81.82 = –€1,800 + 1.10 NPV1 = €100 Option to Delay: Example • We have a choice: invest in the project today or wait a year. • If we jump in today, the NPV0 is €67.83 and the FV of today’s NPV0 in one year from now is NPV1 = €74.61 = 1.10 × €67.83. • Clearly, it’s better to wait a year. – Worst case, NPV1 = €81.82, but there is a chance that the NPV at time one is €100. – Both of these outcomes beat €74.61. Solution Manual for International Financial Management Cheol S. Eun, Bruce G. Resnick 9780077861605