Capital Budgeting OVERVIEW


 Nathaniel Robertson
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1 WSG12 7/7/03 4:25 PM Page Capital Budgeting OVERVIEW This chapter concentrates on the longterm, strategic considerations and focuses primarily on the firm s investment opportunities. The discussions in the preceding chapters dealt almost entirely with per period profit maximization. That analysis was fundamentally static in nature. By contrast, investment is fundamentally dynamic since it involves streams of expenditures and revenues over time. An essential element of any investment decision is the proper evaluation of alternative investment opportunities involving alternative initial outlays, expected net returns, and time horizons. Capital budgeting is the application of the principle of profit maximization to multiperiod projects. Capital budgeting involves investment decisions in which expenditures and receipts continue over a significant period of time. In general, capital budgeting projects may be classified into one of several major categories, including capital expansion, replacement, new product lines, mandated investments, and miscellaneous investments. Since every investment opportunity involves expenditures (cash outflows) and revenues (cash inflows) that are spread out over a number of time periods, capital budgeting is an especially critical element of effective management decision making. Capital budgeting techniques are used to evaluate the potential profitability of possible new product lines, to plan for the replacement of damaged or worn out (depreciated) plant and equipment, to expand existing production capacity, to engage in research and development, to institute or expand existing worker and management training programs, or evaluate the effectiveness of a major advertising campaign. Managerial Economics: Theory and Practice 191 Copyright 2003 by Academic Press. All rights of reproduction in any form reserved.
2 WSG12 7/7/03 4:25 PM Page Capital Budgeting Capital budgeting involves the subtraction of cash outflows from cash inflows with adjustments for differences in their values over time. Differences in the values of the flows are based on the time value of money, which says that a dollar today is worth more than a dollar tomorrow. There are five standard methods used to evaluate the value of alternative investment projects including payback period, discounted payback period, net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR). The payback period is the number of periods required to recover an original investment. In general, risk averse managers prefer investments with shorter payback periods. The net present value of a project is calculated by subtracting the discounted present value of all outflows from the discounted present value of all inflows. The discount rate is the interest rate used to evaluate the project, and is sometimes referred to as the cost of capital, hurdle rate, cut off rate and required rate of return. If the net present value of an investment is positive (negative), then the project is accepted (rejected). If the net present value of an investment is zero, the manager is indifferent to the project. The internal rate of return is the interest rate that equates the present values of inflows to the present value of outflows, i.e., the rate that causes the net present value of the project to equal zero. If the internal rate of return is greater than the cost of capital, the project is accepted. There are a number of problems associated with using the IRR method for evaluating capital investment projects. One problem is the possibility of multiple internal rates of return. Multiple internal rates of return occur when a project that has two or more internal rates of return. For independent projects both the NPV and the IRR methods will yield the same accept/reject decision rules. For mutually exclusive capital investment projects the NPV and the IRR methods could result in conflicting accept/reject decision rules. This is because the NPV method implicitly assumes that net cash inflows are reinvested at the cost of capital, whereas the IRR method assumes that net cash inflows are reinvested at the internal rate of return. The modified internal rate of return (MIRR) method for evaluating capital investment projects is similar to the IRR method in that it generates accept/reject decision rules based upon interest rate comparisons. But unlike the IRR method, the MIRR method assumes that cash flows are reinvested at the cost of capital, and avoids some of the problems associated with multiple internal rates of return. There are several categories of cost of capital, including the cost of debt, cost of equity, and the weighted cost of capital. The cost of debt is the interest rate that must be paid on aftertax debt. The weighed cost of capital is a measure of the overall cost of capital. It is obtained by weighting the various costs by the relative proportion of each component s value in the total capital structure.
3 WSG12 7/7/03 4:25 PM Page 193 Multiple Choice Questions 193 MULTIPLE CHOICE QUESTIONS 12.1 The process of selecting from alternative longterm investment projects is called: A. Net cash inflow maximization. B. Capital budgeting. C. Discounting cash inflows. D. Cash flow management. E. Capital rationing The time value of money refers to: A. The earning power of an investment or stream of investments over time. B. The opportunity cost of capital. C. The interest rate earned on an investment. D. The discount rate used to calculate the present value of an investment The future value of a lump sum payment is worth $10,000 at the end of 6 years. Suppose that the interest rate is 8 percent compounded semiannually. I. The present value of the $10,000 is greater if the interest rate is compounded monthly instead of semiannually. II. The effective annual rate of return is greater an 8 percent. III. The semiannual interest rate is 4 percent. Which of the following is correct? A. I only. B. II only. C. III only. D. I and II only. E. II and III are correct Future value may be defined as: A. The discounted value of future cash flows. B. The interest rate earned on future cash flows. C. The compounded value of future cash flows. D. The opportunity costs of future cash flows. E. The per period maximization of future cash flows Present value may be defined as: A. The discounted value of future cash flows. B. The interest rate earned on future cash flows. C. The compounded value of future cash flows. D. The opportunity costs of future cash flows. E. The per period maximization of future cash flows.
4 WSG12 7/7/03 4:25 PM Page Capital Budgeting 12.6 If the interest (discount) rate is positive, then: A. The present value of a series of cash flows will be greater than its future value. B. The future value of a series of cash flows will be greater than its present value. C. The present value of a series of cash flows will equal its future value. D. The present value is only greater than the future value for an annuity Suppose that Zoe invests $25,000 into a certificate of deposit that pays 7 percent, compounded annually. How much will Zoe s certificate of deposit be worth in 10 years? A. $47, B. $49, C. $50, D. $50, E. $50, Suppose the Zoe invests $25,000 into a certificate of deposit that pays 7 percent, compounded quarterly. How much will Zoe s certificate of deposit be worth in 10 years? A. $47, B. $49, C. $50, D. $50, E. $50, Suppose the Zoe invests $25,000 into a certificate of deposit that pays 7 percent, compounded monthly. How much will Zoe s certificate of deposit be worth in 10 years? A. $47, B. $49, C. $50, D. $50, E. $50, Suppose the Zoe invests $25,000 into a certificate of deposit that pays 7 percent, compounded continuously. How much will Zoe s certificate of deposit be worth in 10 years? A. $47, B. $49, C. $50, D. $50, E. $50,
5 WSG12 7/7/03 4:25 PM Page 195 Multiple Choice Questions A series of fixed payments that are made fixed intervals for a specified period of time is called: A. An annuity. B. A cash flow. C. A mutually exclusive payments. D. A payback period. E. Compounding A series of fixed payments that are made fixed intervals at the end of each period is called: A. An annuity due. B. An ordinary annuity. C. A payback annuity. D. Discounting. E. Compounding A series of fixed payments that are made fixed intervals at the beginning of each period is called: A. An annuity due. B. An ordinary annuity. C. A payback annuity. D. Discounting. E. Compounding Cletus invests $2,000 annually in an ordinary annuity that pays 9 percent interest compounded annually. The future value of this annuity in 10 years is: A. $28, B. $29, C. $30, D. $32, E. $33, Cletus invests $2,000 annually in an annuity due that pays 9 percent interest compounded annually. The future value of this annuity in 10 years is: A. $28, B. $29, C. $30, D. $33, E. $33,
6 WSG12 7/7/03 4:25 PM Page Capital Budgeting Cletus invests $2,000 annually in an annuity due that pays 9 percent interest compounded quarterly. The future value of this annuity in 10 years is: A. $28, B. $29, C. $30, D. $33, E. $33, Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded annually, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13, Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded semiannually, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13, Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded quarterly, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13,
7 WSG12 7/7/03 4:25 PM Page 197 Multiple Choice Questions Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded monthly, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13, Suppose that Cletus wants a lumpsum investment today to grow to $100,000 in 25 years. If Cletus can reasonably expect to earn 8.5 percent compounded continuously, then the lumpsum investment should be: A. $11, B. $12, C. $12, D. $12, E. $13, Suppose that Cletus decides to invest $4,000 per year into a 25 year annuity due that earns an interest rate of 8.5 percent compounded annually. Calculate the present value of Cletus investment plan? A. $40, B. $41, C. $42, D. $42, E. $44, Suppose that Cletus decides to invest $4,000 per year into a 25 year ordinary annuity that earns an interest rate of 8.5 percent compounded annually. Calculate the present value of Cletus investment plan? A. $40, B. $41, C. $42, D. $42, E. $44,
8 WSG12 7/7/03 4:25 PM Page Capital Budgeting Suppose that Cletus has decided to invest in a retirement annuity. Cletus goal is to have $1,000,000 in his annuity by the time that he is 65 years old. Cletus is confident of earning a 6 percent interest rate compounded annually. Cletus is currently 30 years old and plans to make his first investment today. How much will Cletus have to invest annually to reach is goal? A. $8, B. $8, C. $8, D. $9, E. None of the above Suppose that Chloe borrows $300,000 from the First National State Bank at 2.5 percent interest compounded annually to purchase a new home. Chloe agrees to repay the loan in 30 equal annual installments, with the first payment due at the end of the first year. How much are Chloe s annual payments? A. $14, B. $15, C. $16, D. $17, E. None of the above The payback period is: A. The number cashflow periods of an capital investment project. B. The number of years that it takes to earn a profit of a capital investment project. C. The number of periods required to pay for the original investment. D. The number of periods required to calculate the net present value of an investment project An advantage of the payback period method of evaluating a capital investment project is that it: A. Does not consider the time value of money. B. Ignores cash flows beyond the payback period. C. Provides a rough approximation of a projects liquidity and risk. D. Provides a rough approximation of the present value of net cash flows. E. None of the above.
9 WSG12 7/7/03 4:25 PM Page 199 Multiple Choice Questions An advantage of the discounted payback period method of evaluating a capital investment project is that it: A. Considers the time value of money. B. Ignores cash flows beyond the payback period. C. Provides a rough approximation of a projects liquidity and risk. D. Provides a rough approximation of the present value of net cash flows. E. Both A and C are correct Suppose that the payback period for a particular project is 5 years and 6 months. If the annual cash inflows are $5,000, then the initial investment was: A. $22,500. B. $24,000. C. $27,500. D. $29,000. E. None of the above Two project are independent if: A. Acceptance of one project means rejection of the other. B. Their cash flows are unrelated. C. They have different hurdle rates. D. They have different discounted payback periods The cost of capital is: A. The cost of acquiring funds to finance a capital investment project. B. The minimum rate of return that must be earned to justify a capital investment. C. The same thing as the required rate of return. D. Also referred to as the hurdle rate. E. All of the above statements are true Suppose that a project with an initial investment of $50,000 is expected to generate an annual cash flow of $4,000 for each of the next 7 years. This project should not be accepted if the cost of capital is: A. 8 percent. B. 9 percent. C. 10 percent. D. 11 percent. E. Both C and D are correct.
10 WSG12 7/7/03 4:25 PM Page Capital Budgeting Suppose that a project with an initial investment of $30,000 has the following annual cash inflows: Year Cash inflow $4,000 $3,500 $8,000 $12,000 $8,000 If the cost of capital is 8 percent, then the net present value of the project: A. $3, the project should be rejected. B. $4, the project should be rejected. C. $3, the project should be accepted. D. $4, the project should be accepted. E. None of the above statements are true The internal rate of return (IRR) is: A. The same thing as the discount rate. B. The same thing as the cost of capital. C. The discount rate that equates the present values of inflows and outflows. D. The same thing as the net present value. E. The ratio of average annual profits to average investments Project A and Project B are mutually exclusive. Project A has an IRR of 10 percent. Project B has an IRR of 12 percent. If the marginal cost of capital is 11 percent, then: A. Project A should be accepted and Project B rejected. B. Project B should be accepted and Project A rejected. C. Both projects should be accepted since the decision is not based on the IRR but the NPV. D. Both projects should be rejected since the decision is not based on the IRR but the NPV Project A and Project B are independent. Project A has an IRR of 12 percent. Project B has an IRR of 14 percent. If the marginal cost of capital is 10 percent, then: A. Project A must have a higher NPV than Project B. B. Project B must have a higher NPV than Project A. C. The NPV of both projects must be negative. D. The NPV of both projects is positive.
11 WSG12 7/7/03 4:25 PM Page 201 Multiple Choice Questions Suppose that a firm is considering several mutually exclusive projects. The firm should choose: A. The project with the highest NPV. B. The project with the lowest NPV. C. All projects with a positive NPV. D. The project with the lowest IRR. E. The project with the lowest cost of capital Suppose that a project with an initial investment of $30,000 has the following annual cash inflows: Year Cash inflow $4,000 $3,500 $8,000 $12,000 $8,000 Using a financial calculator, the IRR for this project is: A percent. B percent. C percent. D percent. E. None of the above Suppose that a firm is considering to independent projects. The crossover rate is: A. The IRR at which the NPV of the two projects are equal. B. The cost of capital at which the NPV of the two projects are equal. C. Is the discount rate at which the NPV of the two projects are equal. D. Is the discount rate at which the discounted payback period of the two projects are equal. TABLE 1 Net Cash Flows for Projects Amber and Jade Year (t) Project Amber Project Jade 0 $3,000 $4, ,000 1, ,000 1, ,500 2, Consider the information presented in Table 1. If the discount rate is 9 percent, the NPV of Project Amber is: A. $ B. $ C. $ D. $ E. None of the above.
12 WSG12 7/7/03 4:25 PM Page Capital Budgeting Consider the information presented in Table 1. If the discount rate is 9 percent, the NPV of Project Jade is: A. $ B. $ C. $ D. $ E. None of the above Consider the information presented in Table 1. Suppose that Projects Amber and Jade are mutually exclusive. If the discount rate is 9 percent, then: A. Project Jade is preferred to Project Amber. B. Project Amber is preferred to Project Jade. C. Project Amber is equivalent to Project Jade. D. Both projects will be chosen since the NPV is positive. E. Neither projects will be chosen since they are mutually exclusive Consider the information in Table 1. The IRR for Project Amber is: A percent. B percent. C percent. D percent. E. None of the above Consider the information in Table 1. The IRR for Project Jade is: A percent. B percent. C percent. D percent. E. None of the above When the cost of capital is less than IRR for two mutually exclusive projects, then: A. The NPV and IRR methods will always result in the same accept and reject decisions. B. The NPV method will lead to an accept decision while the IRR method will lead to a reject decision. C. The IRR method will lead to an accept decision while the NPV method will lead to a reject decision. D. The project with the highest IRR should be chosen. E. Both A and E are correct.
13 WSG12 7/7/03 4:25 PM Page 203 Multiple Choice Questions Cyborg Electronics is considering two mutually exclusive capital investment projects. Project A has an IRR of 10 percent. Project B has an IRR of 12 percent. The crossover rate is 8 percent. Cyborg should: I. Invest in both projects if the cost of capital is less than 10 percent. II. Invest in Project A if the cost of capital is less than 8 percent. III. Invest in Project B if the cost of capital is greater than 8 percent but less than 12 percent. IV. Invest in Project A if the cost of capital is greater than 8 percent but less than 10 percent. Which of the following is correct? A. I only. B. II only. C. III only. D. II and III only. E. II and IV only Cyborg Electronics is considering two independent capital investment projects. Project A has an IRR of 10 percent. Project B has an IRR of 12 percent. The crossover rate is 8 percent. Cyborg should: I. Invest in both projects if the cost of capital is less than 10 percent. II. Invest in Project A if the cost of capital is less than 8 percent. III. Invest in Project B if the cost of capital is greater than 8 percent but less than12 percent. IV. Invest in Project A if the cost of capital is greater than 8 percent but less than 10 percent. Which of the following is correct? A. I only. B. II only. C. III only. D. I and III only. E. I, II, III and IV Which of the following statements about the modified internal rate of return (MIRR) is correct? A. The assumption regarding reinvestment underlying the MIRR method is more reasonable than that underlying the IRR method. B. The selection of a capital investment project using the MIRR method is always consistent with that of the IRR method.
14 WSG12 7/7/03 4:25 PM Page Capital Budgeting C. The MIRR method always overcomes the problems associated with multiple IRR. D. All of the above are correct. E. All of the above are incorrect The cost of debt capital is: A. The interest rate that must be paid on the debt. B. The aftertax interest rate that must be paid on the debt. C. The future value of the debt less principal. D. The equivalent rate of return on the company s equity. E. The required rate of return on a company s stock The optimal capital structure of a firm: A. Minimizes the firm s cost of debt capital. B. Is that combination of debt, preferred and common stock that maximizes the firm s share values. C. Is one in which the weighted cost of capital is less than the IRR. D. All of the above are correct. E. None of the above are correct. SHORTER PROBLEMS 12.1 Adam wants to borrow $15,000 at 7.5 percent interest compounded monthly from the Cedar Federal Credit Union to purchase a new car. If the loan principal is to be repaid in a lump sum, how much will Adam repay the bank in 3 years? 12.2 Andrew deposits $25,000 in a certificate of deposit that pays 6 percent interest compounded continuously. How much money will Andrew s certificate of deposit be worth at the end of 25 years? 12.3 Alex wants to invest $2,500 a year into an annuity that can reasonably expect to earn 7 percent compounded annually. If Alex makes his first $2,500 investment immediately, how much will his annuity be worth in 20 years? 12.4 Alex wants to invest $2,500 a year into an annuity that can reasonably expect to earn 7 percent compounded annually. Suppose that Alex is uncertain as to whether to open the annuity immediately, or wait until the end of the year to make his first deposit since he can earn $250 in interest the first year by lending
15 WSG12 7/7/03 4:25 PM Page 205 Longer Problems 205 $2,500 to his brother, Adam. Suppose that Alex plans to deposit the $2,750 into a certificate of deposit earning 6 percent interest compounded annually for 19 years. Should Alex loan $2,500 to Adam, or should he open the annuity immediately? 12.5 Suppose that Folderol Savings and Loan is offering 10year certificates of deposit earning a 7.5 interest rate compounded quarterly. How much would Nina have to deposit today in order for the certificate of deposit to be worth $250,000 at the end of 10 years? 12.6 Suppose that Zelda borrows $500,000 at 6.5 percent to purchase a luxury condominium in downtown Toledo, Ohio. Zelda will to repay the loan in 20 equal annual installments, with the first payment due at the end of the first year. A. What are Zelda s annual mortgage payments? B. How much interest will Zelda be paying? 12.7 Calculate the weighted average cost of capital of a project that is 35 percent debt and 65 percent equity. Assume that the firm pays 10 percent on debt and 15 percent on equity. Assume that the firm s marginal tax rate is 33 percent. LONGER PROBLEMS 12.1 The Finance & Economics Department of the Hobgoblin School of Business is considering purchasing a new photocopying machine for use by faculty and doctoral candidates. Dr. Windsock, the department chair, has asked Dr. Steadfast, a finance professor, to determine which of two models, the Galaxy 5000 or the Nova 2700, should be purchased. In addition to the cost of the photocopy machine itself, the manufacturer of each model offers 5year service contract. The cash outflows for each photocopy machine is summarized in the following table. Net Cash Flows (CF t ) for the Galaxy 5000 and Nova 2700 Year (t) Galaxy 5000 Nova $10,500 $11,
16 WSG12 7/7/03 4:25 PM Page Capital Budgeting If the cost of capital is 5.5 percent compounded annually, which photocopy machine should the department purchase if the estimated salvage values for the Galaxy 500 and Nova 2700 after five years are $1,000 and $2,000, respectively? 12.2 Samuel Adams of Niagra Company is a leading producer of natural gas. Adams is considering two mutually exclusive projects involving drilling operations Alaska. The projected net cash flows for each project are summarized in the following table. Net Cash Flows (CF t ) for Projects A and B ($millions) Year (t) Project A Project B 0 $4,000 $5, ,000 2, ,000 2, ,000 Determine which project should be accepted if the cost of capital is 9 percent Mandalay Enterprises is considering two mutually exclusive projects. The projected net cash flows for Projects A and B are summarized in the following table. Net Cash Flows (CF t ) for Projects A and B Year (t) Project A Project B 0 $27,000 $20, ,000 6, ,000 6, ,000 6, ,000 6, ,000 6,500 A. Calculate the NPV for both projects if the cost of capital is 15 percent. B. Based on your answer to part A, which project should be accepted? C. Calculate the IRR for both projects. D. Based on your answer to part C, which project should be accepted? E. If Projects A and B are independent and the cost of capital is 18.5 percent, then which project(s) should be accepted?
17 WSG12 7/7/03 4:25 PM Page 207 Answers to Multiple Choice Questions Consider, again, the net cash flows the two projects being considered by Mandalay Enterprises in the previous question. A. Illustrate the net present value profiles for Projects A and B. B. What is the crossover rate for the two projects? C. Assuming that Projects A and B are mutually exclusive, which project should be selected if the cost of capital is greater than the crossover rate? Which project should be selected if the cost of capital is less than the crossover rate? 12.5 Consider the following cash flows for a capital investment project: Net Cash Flows (CF t ) Year (t) CF t 0 $1, , ,000 A. Summarize the projects net present value profile for selected costs of capital? B. Does the project have multiple internal rates of return? What are they? C. What is the IRR that maximizes the projects NPV? D. Diagram your answer. ANSWERS TO MULTIPLE CHOICE QUESTIONS 12.1 B A D C A B B C D E A B A C D E E D C B A E A B A C C E C B E E A C B D A D B C A B D C A D E A B B.
18 WSG12 7/7/03 4:25 PM Page Capital Budgeting SOLUTIONS TO SHORTER PROBLEMS 12.1 FV n = PV 0 (1 + i/m) mn FV 3 = $15,000( /12) 3 12 = $15,000( ) 36 = $15,000( ) = $18, FV n = PV 0 e in FV 25 = $25,000e = $25,000e 1.5 = $25,000(4.4817) = $112, This is an example of an annuity due. The future value of Alex s annuity will be FVAD n = A{[(1 + i) n  1]/i}(1 + i) = $2,500{[(1.07) 201]/0.07}(1.07) = $2,500[( )/0.07](1.07) = $2,500(40.995)(1.07) = $109, From the previous problem we saw that if Alex opens the annuity immediately, then its value in 20 years will be $109,663. If Alex waits for a year before making the first deposit then the future value of an ordinary annuity is FVOA n = A[(1 + i) n  1]/i = $2,500[( )/0.07] = $2,500( )/0.07 = $2,500( ) = $102, To this amount must be added the future value of $2,750 compounded annually for 19 years at an interest rate of 6 percent. This amount is given as FV n = PV 0 (1 + i) n = $2,500(1.06) 19 = $2,500(3.0256) = $7,564 Adding this amount to the future value of an ordinary annuity yields $102, $7,564 = $110, which is greater than the amount that Alex can earn by opening the annuity immediately. Thus, Alex should lend to his brother.
19 WSG12 7/7/03 4:25 PM Page 209 Solutions to Longer Problems PV 0 = FV n /(1 + i/m) nm = $250,000/( /4) 10 4 = $250,000/ = $118, A. A = PVOA n /S t=1æn [1/(1 + i)] t = $500,000/S t=1æ20 [1/(1.065)] t = $500,000/ = $45, B. Zelda will make total mortgage payments of 20(45,378.23) = $907, Thus, the total amount of interest paid will be $907, $500,000 = $407, WACC = w d k d (1  t) + w e k e = 0.35(0.1)(10.33) (0.15) = or percent SOLUTIONS TO LONGER PROBLEMS 12.1 The NPV for the Galaxy 5000 (NPV G ) and the Nova 2700 (NPV N ) are NPV G = CF 0 /(1 + k) 0 + CF 1 /(1 + k) 1 + CF 2 /(1 + k) CF 5 /(1 + k) 5 =10,500/(1.055) 0320/(1.055) 1320/(1.055) 2320/(1.055) 3320/(1.055) 4320/(1.055) 5 + 1,000/(1.055) 5 =$11, NPV N =11,500/(1.055) 0230/(1.055) 1230/(1.055) 2230/(1.055) 3230/(1.055) 4230/(1.055) 5 + 2,000/(1.055) 5 =$10, Since /NPV N / < /NPV G /, Windsock will purchase the Nova Since the projects have different lives, they must be compared over the least common multiple of years, which in this case is 6 years. NPV A = CF 0 /(1 + k) 0 + CF 1 /(1 + k) 1 + CF 2 /(1 + k) CF 6 /(1 + k) 6 =4,000/(1.09) 0 + 2,000/(1.09) 1 + 3,000/(1.09) 24,000/(1.09) 2 + 2,000/(1.09) 3 + 3,000/(1.09) 44,000/(1.09) 4 + 2,000/(1.09) 5 + 3,000/(1.09) 6 = $ NPV B =5,000/(1.09) 0 + 2,000/(1.09) 1 + 2,500/(1.09) 2 + 3,000/(1.09) 35,000/(1.09) 3 + 1,000/(1.09) 4 + 2,500/(1.09) 5 + 3,000/(1.09) 6 = $1, Since NPV B > NPV A, then Adams will choose Project B over Project A.
20 WSG12 7/7/03 4:25 PM Page Capital Budgeting 12.3 A. NPV A = CF 0 /(1 + k) 0 + CF 1 /(1 + k) 1 + CF 2 /(1 + k) CF 5 /(1 + k) 5 =27,000/(1.15) 0 + 8,000/(1.15) 1 + 9,000/(1.15) ,000/(1.15) ,000/(1.15) 4 + 6,000/(1.15) 5 = $2, NPV B =20,000/(1.15) 0 + 6,500/(1.15) 1 + 6,500/(1.15) 2 + 6,500/(1.15) 3 + 6,500/(1.15) 4 + 6,500/(1.15) 5 = $1, B. Since NPV A > NPV B, then Project A should be accepted. C. To determine the internal rate of return for Projects A and B, substitute the isnformation provided in the table into the Equation (12.27) and solve for IRR. NPV A = CF 0 + CF 1 /(1 + IRR A ) 1 + CF 2 /(1 + IRR A ) CF 5 /(1 + IRR A ) 5 =$27,000 + $8,000/(1 + IRR A ) 1 + $9,000/(1 + IRR A ) 2 + $10,000/(1 + IRR A ) 3 + $10,000/(1 + IRR A ) 4 + $6,000/(1 + IRR A ) 5 = 0 NPV B =$20,000 + $6,500/(1 + IRR B ) 1 + $6,500/(1 + IRR B ) 2 + $6,500/(1 + IRR B ) 3 + $6,500/(1 + IRR B ) 4 + $6,500/(1 + IRR B ) 5 = 0 Since calculating IRR A and IRR B by trial and error is time consuming and tedious, the solution values were obtained by using a financial calculator. The internal rates of return for Projects A and B are IRR A = percent IRR B = percent D. Since IRR B > IRR A, then Project B should be accepted. E. The internal rate of return is greater than the hurdle rate for Project B and less than the hurdle rate for Project B. Thus, Project B should be accepted and Project A rejected A. With the use of a financial calculator, the net present values for Projects A and B for various interest rates are summarized in the following table.
21 WSG12 7/7/03 4:25 PM Page 211 Solutions to Longer Problems 211 Net Present Value Profiles for Projects A and B Cost of Capital Project A Project B 0.00 $16,000 $12, ,383 8, ,358 7, ,496 5, ,780 4, ,195 3, ,729 2, ,371 1, ,003 1, , B. To determine the crossover rate, equate the net present value of Project A with the net present value of Project B and solve for the cost of capital, k. NPV A = NPV B $27,000/(1 + k) 0 + $8,000/(1 + k) 1 + $9,000/(1 + k) 2 + $10,000/(1 + k) 3 + $10,000/(1 + k) 4 + $6,000/(1 + k) 5 =$20,000/(1 + k) 0 + $6,500/(1 + k) 1 + $6,500/(1 + k) 2 + $6,500/(1 + k) 3 + $6,500/(1 + k) 4 + $6,500/(1 + k) 5 Bringing all of the terms in this expression to the lefthand side of the equation we obtain $7,000/(1 + k) 0 + $1,500/(1 + k) 1 + $2,500/(1 + k) 2 + $3,500/(1 + k) 3 + $3,500/(1 + k) 4  $500/(1 + k) 5 = 0 The value for k in this expression may be found using the IRR function of a financial calculator. Solving for k we obtain Crossover rate = percent C. From the previous problem, the internal rates of return for the two projects is IRR A = percent IRR B = percent Finally, calculating the net present value of Projects A and B using the crossover rate yields NPV A = CF 0 /(1 + k) 0 + CF 1 /(1 + k) 1 + CF 2 /(1 + k) CF 5 /(1 + k) 5 =27,000/(1.1657) 0 + 8,000/(1.1657) 1 + 9,000/(1.1657) ,000/(1.1657) ,000/(1.1657) 4 + 6,000/(1.1657) 5 = $1,003 NPV B =20,000/(1.1657) 0 + 6,500/(1.1657) 1 + 6,500/(1.1657) 2 + 6,500/(1.657) 3 + 6,500/(1.1657) 4 + 6,500/(1.1657) 5 = $1,003
22 WSG12 7/7/03 4:25 PM Page Capital Budgeting With this information, the net present value profiles for Project A and Project B may be illustrated in the following diagram. From the above diagram, if the cost of capital is greater than percent, but less than percent, then Project B is preferred to Project A since NPV B > NPV A. This choice of projects is consistent with the IRR method since IRR B > IRR A. On the other hand, if the cost of capital is less than percent, then Project A is preferred to Project B since NPV A > NPV B. This result, however, is in conflict with the choice of projects based on the IRR method A. Net Present Value Profile k NPV $2, ,
23 WSG12 7/7/03 4:25 PM Page 213 Solutions to Longer Problems 213 B. NPV = 1, ,000/(1 + IRR) 16,000/(1 + IRR) 2 = 06,000[1/(1 + IRR)] 2 + 5,000[1/(1 + IRR)]  1,000 = 0 a[1/(1 + IRR)] 2 + b[1/(1 + IRR)] + c = 0 [1/(1 + IRR)] 1,2 = {b [b 24ac]}/2a = {5,000 ± [(5,000) 24(6,000)(1,000)]}/2(6,000) = [5,000 ± (1,000,000)]/12,000 = (5,000 ± 1,000)/12,000 [1/(1 + IRR)] 1 = (5, ,000)/12,000 = (1 + IRR) 1 = 3.00 IRR 1 = 2.00 or 200 percent [1/(1 + IRR)] 2 = (5,0001,000)/12,000 = 0.5 (1 + IRR) 2 = 2.00 IRR 2 = 1.00 or 100 percent Thus, and this was illustrated NPV profile, the project has internal rates of return of 100 percent and 200 percent. C. NPV = 1, ,000(1 + IRR) 16,000/(1 + IRR) 2 dnpv/d(1 + IRR) = 5,000(1 + IRR) ,000/(1 + IRR) 3 = 0 5,000(1 + IRR) = 12, IRR = 12,000/5,000 IRR* = 1.40 or 140 percent The value of IRR that maximizes the NPV of the firm is 140 percent, which is highlighted in the NPV profile. D.
24 WSG12 7/7/03 4:25 PM Page 214
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