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After reading this chapter, students should be able to: • Define capital budgeting, explain why it is important, and state how project proposals are generally classified. • List the steps involved in evaluating a capital budgeting project. • Calculate payback period, discounted payback period, Net Present Value (NPV), and Internal Rate of Return (IRR) for a given project and evaluate each method. • Define NPV profiles, and explain the rationale behind the NPV and IRR methods, their reinvestment rate assumptions, and which method is better when evaluating independent versus mutually exclusive projects. • Briefly explain the problem of multiple IRRs and when this situation could occur. • Calculate the Modified Internal Rate of Return (MIRR) for a given project and evaluate this method. • Identify at least one relevant piece of information provided to decision makers for each capital budgeting decision method discussed in the chapter. • Identify and explain the purposes of the post-audit in the capital budgeting process. • Identify a number of different types of decisions that use the capital budgeting techniques developed in this chapter.
After reading this chapter, students should be able to: • Define capital budgeting, explain why it is important, and state how project proposals are generally classified. • List the steps involved in evaluating a capital budgeting project. • Calculate payback period, discounted payback period, Net Present Value (NPV), and Internal Rate of Return (IRR) for a given project and evaluate each method. • Define NPV profiles, and explain the rationale behind the NPV and IRR methods, their reinvestment rate assumptions, and which method is better when evaluating independent versus mutually exclusive projects. • Briefly explain the problem of multiple IRRs and when this situation could occur. • Calculate the Modified Internal Rate of Return (MIRR) for a given project and evaluate this method. • Identify at least one relevant piece of information provided to decision makers for each capital budgeting decision method discussed in the chapter. • Identify and explain the purposes of the post-audit in the capital budgeting process. • Identify a number of different types of decisions that use the capital budgeting techniques developed in this chapter. Learning Objectives: 10 - 1 Chapter 10 The Basics of Capital Budgeting LEARNING OBJECTIVES This is a relatively straight-forward chapter, and, for the most part, it is a direct application of the time value concepts first discussed in Chapter 6. We point out that capital budgeting is to a company what buying stocks or bonds is to an individual an investment decision, when the company wants to know if the expected value of the cash flows is greater than the cost of the project, and whether or not the expected rate of return on the project exceeds the cost of the funds required to take on the project. We cover the standard capital budgeting procedures payback, discounted payback, NPV, IRR, and MIRR. At this point, students who have not yet mastered time value concepts and how to use their calculator efficiently get another chance to catch on. Students who have mastered those tools and concepts have fun, because they can see what is happening and the usefulness of what they are learning. The details of what we cover, and the way we cover it, can be seen by scanning Blueprints, Chapter 10. For other suggestions about the lecture, please see the “Lecture Suggestions” in Chapter 2, where we describe how we conduct our classes. DAYS ON CHAPTER: 3 OF 58 DAYS (50-minute periods) Lecture Suggestions: 10 - 2 LECTURE SUGGESTIONS 10-1 Project classification schemes can be used to indicate how much analysis is required to evaluate a given project, the level of the executive who must approve the project, and the cost of capital that should be used to calculate the project’s NPV. Thus, classification schemes can increase the efficiency of the capital budgeting process. 10-2 The NPV is obtained by discounting future cash flows, and the discounting process actually compounds the interest rate over time. Thus, an increase in the discount rate has a much greater impact on a cash flow in Year 5 than on a cash flow in Year 1. 10-3 This question is related to Question 10-2 and the same rationale applies. With regard to the second part of the question, the answer is no; the IRR rankings are constant and independent of the firm’s cost of capital. 10-4 The NPV and IRR methods both involve compound interest, and the mathematics of discounting requires an assumption about reinvestment rates. The NPV method assumes reinvestment at the cost of capital, while the IRR method assumes reinvestment at the IRR. MIRR is a modified version of IRR that assumes reinvestment at the cost of capital. 10-5 The statement is true. The NPV and IRR methods result in conflicts only if mutually exclusive projects are being considered since the NPV is positive if and only if the IRR is greater than the cost of capital. If the assumptions were changed so that the firm had mutually exclusive projects, then the IRR and NPV methods could lead to different conclusions. A change in the cost of capital or in the cash flow streams would not lead to conflicts if the projects were independent. Therefore, the IRR method can be used in lieu of the NPV if the projects being considered are independent. 10-6 Yes, if the cash position of the firm is poor and if it has limited access to additional outside financing it might be better off to choose a machine with a rapid payback. But even here, the relationship between present value and cost would be a better decision tool. 10-7 a. In general, the answer is no. The objective of management should be to maximize value, and as we point out in subsequent chapters, stock values are determined by both earnings and growth. The NPV calculation automatically takes this into account, and if the NPV of a long-term project exceeds that of a short-term project, the higher future growth from the long-term project must be more than enough to compensate for the lower earnings in early years. Answers and Solutions: 10 - 3 ANSWERS TO END-OF-CHAPTER QUESTIONS b. If the same $100 million had been spent on a short-term project one with a faster payback reported profits would have been higher for a period of years. This is, of course, another reason why firms sometimes use the payback method. 10-8 Mutually exclusive projects are a set of projects in which only one of the projects can be accepted. For example, the installation of a conveyor-belt system in a warehouse and the purchase of a fleet of forklifts for the same warehouse would be mutually exclusive projects accepting one implies rejection of the other. When choosing between mutually exclusive projects, managers should rank the projects based on the NPV decision rule. The mutually exclusive project with the highest positive NPV should be chosen. The NPV decision rule properly ranks the projects because it assumes the appropriate reinvestment rate is the cost of capital. 10-9 Project X should be chosen over Project Y. Since the two projects are mutually exclusive, only one project can be accepted. The decision rule that should be used is NPV. Since Project X has the higher NPV, it should be chosen. The cost of capital used in the NPV analysis appropriately includes risk. Answers and Solutions: 10 - 4 10-1 $52,125/$12,000 = 4.3438, so the payback is about 4 years. 10-2 Financial Calculator Solution: Input CF 0 = -52125, CF 1-8 = 12000, I = 12, and then solve for NPV = $7,486.68. 10-3 Financial Calculator Solution: Input CF 0 = -52125, CF 1-8 = 12000, and then solve for IRR = 16%. 10-4 Project K’s discounted payback period is calculated as follows: Annual Discounted @12% Period Cash Flows Cash Flows Cumulative 0 ($52,125) ($52,125.00) ($52,125.00) 1 12,000 10,714.29 (41,410.71) 2 12,000 9,566.33 (31,844.38) 3 12,000 8,541.36 (23,303.02) 4 12,000 7,626.22 (15,676.80) 5 12,000 6,809.12 (8,867.68) 6 12,000 6,079.57 (2,788.11) 7 12,000 5,428.19 2,640.08 8 12,000 4,846.60 7,486.68 The discounted payback period is 6 + 19.8$5,42 11$2,788. years, or 6.51 years. Alternatively, since the annual cash flows are the same, one can divide $12,000 by 1.12 (the discount rate = 12%) to arrive at CF 1 and then continue to divide by 1.12 seven more times to obtain the discounted cash flows (Column 3 values). The remainder of the analysis would be the same. 10-5 MIRR: PV Costs = $52,125. FV Inflows: PV FV 0 1 2 3 4 5 6 7 8 | | | | | | | | | 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 13,440 15,053 16,859 18,882 21,148 23,686 Answers and Solutions: 10 - 5 SOLUTIONS TO END-OF-CHAPTER PROBLEMS 12% × 1.12 × (1.12) 2 × (1.12) 3 × (1.12) 4 × (1.12) 5 × (1.12) 6 × (1.12) 7 26,528 52,125 MIRR = 13.89% 147,596 Financial Calculator Solution: Obtain the FVA by inputting N = 8, I = 12, PV = 0, PMT = 12000, and then solve for FV = $147,596. The MIRR can be obtained by inputting N = 8, PV = -52125, PMT = 0, FV = 147596, and then solving for I = 13.89%. 10-6 Project A: Using a financial calculator, enter the following: CF 0 = -15000000 CF 1 = 5000000 CF 2 = 10000000 CF 3 = 20000000 I = 10; NPV = $12,836,213. Change I = 10 to I = 5; NPV = $16,108,952. Change I = 5 to I = 15; NPV = $10,059,587. Project B: Using a financial calculator, enter the following: CF 0 = -15000000 CF 1 = 20000000 CF 2 = 10000000 CF 3 = 6000000 I = 10; NPV = $15,954,170. Change I = 10 to I = 5; NPV = $18,300,939. Change I = 5 to I = 15; NPV = $13,897,838. 10-7 Truck: Financial Calculator Solution: Input CF 0 = -17100, CF 1-5 = 5100, I = 14, and then solve for NPV = $408.71 ≈ $409 and IRR = 1499% ≈ 15%. MIRR: PV Costs = $17,100. FV Inflows: PV FV 0 1 2 3 4 5 | | | | | | 5,100 5,100 5,100 5,100 5,100 5,814 6,628 Answers and Solutions: 10 - 6 14% × (1.14) 2 × 1.14 × (1.14) 3 7,556 8,614 17,100 MIRR = 14.54% (Accept) 33,712 Financial Calculator Solution: Obtain the FVA by inputting N = 5, I = 14, PV = 0, PMT = 5100, and then solve for FV = $33,712. The MIRR can be obtained by inputting N = 5, PV = -17100, PMT = 0, FV = 33712, and then solving for I = MIRR = 14.54%. Pulley: Financial Calculator Solution: Input CF 0 = -22430, CF 1-5 = 7500, I = 14, and then solve for NPV = $3,318.11 ≈ $3,318 and IRR = 20%. MIRR: PV Costs = $22,430. FV Inflows: PV FV 0 1 2 3 4 5 | | | | | | 7,500 7,500 7,500 7,500 7,500 8,550 9,747 11,112 12,667 22,430 MIRR = 17.19% (Accept) 49,576 Financial Calculator Solution: Obtain the FVA by inputting N = 5, I = 14, PV = 0, PMT = 7500, and then solve for FV = $49,576. The MIRR can be obtained by inputting N = 5, PV = -22430, PMT = 0, FV = 49576, and then solving for I = 17.19%. 10-8 Using a financial calculator: NPV S = $448.86; NPV L = $607.20. IRR S = 15.24%; IRR L = 14.67%. MIRR: PV costs S = $15,000. FV inflows S = $29,745.47. MIRR S = 14.67%. PV costs L = $37,500. FV inflows L = $73,372.16. MIRR L = 14.37%. Thus, NPV L > NPV S , IRR S > IRR L , and MIRR S > MIRR L . The scale difference between Projects S and L results in IRR and MIRR selecting S over L. However, NPV favors Project L, and hence Project L should be chosen. Answers and Solutions: 10 - 7 14% × (1.14) 4 × (1.14) 3 × (1.14) 4 × (1.14) 2 × 1.14 10-9 a. The IRRs of the two alternatives are undefined. To calculate an IRR, the cash flow stream must include both cash inflows and outflows. b. The PV of costs for the conveyor system is -$556,717, while the PV of costs for the forklift system is -$493,407. Thus, the forklift system is expected to be -$493,407 - (-$556,717) = $63,310 less costly than the conveyor system, and hence the forklifts should be used. 10-10 Project X: 0 1 2 3 4 | | | | | -1,000 100 300 400 700.00 448.00 376.32 140.49 1,000 13.59% = MIRR X 1,664.81 $1,000 = $1,664.81/(1 + MIRR X ) 4 . Project Y: 0 1 2 3 4 | | | | | -1,000 1,000 100 50 50.00 56.00 125.44 1,404.93 1,000 13.10% = MIRR Y 1,636.37 $1,000 = $1,636.37/(1 + MIRR Y ) 4 . Thus, since MIRR X > MIRR Y , Project X should be chosen. Alternate step: You could calculate NPVs, see that Project X has the higher NPV, and just calculate MIRR X . NPV X = $58.02 and NPV Y = $39.94. 10-11 Input the appropriate cash flows into the cash flow register, and then calculate NPV at 10 percent and the IRR of each of the projects: Project S: NPV S = $39.14; IRR S = 13.49%. Project L: NPV L = $53.55; IRR L = 11.74%. Since Project L has the higher NPV, it is the better project. IRR L = 11.74%. 10-12 Step 1: Determine the PMT: 0 1 10 Answers and Solutions: 10 - 8 12% 12% 12% × 1.12 × (1.12) 2 × (1.12) 3 × 1.12 × (1.12) 2 × (1.12) 3 | | • • • | -1,000 PMT PMT With a financial calculator, input N = 10, I = 12, PV = -1000, and FV = 0 to obtain PMT = $176.98. Step 2: Calculate the project’s MIRR: 0 1 2 9 10 | | | • • • | | -1,000 176.98 176.98 176.98 176.98 194.68 . . . 379.37 417 .31 1,000 10.93% = MIRR FV of inflows: With a financial calculator, input N = 10, I = 10, PV = 0, and PMT = -176.98 to obtain FV = $2,820.61. Then input N = 10, PV = -1000, PMT = 0, and FV = 2820.61 to obtain I = MIRR = 10.93%. 10-13 a. Purchase price $ 900,000 Installation 165,000 Initial outlay $1,065,000 CF 0 = -1065000; CF 1-5 = 350000; I = 14; NPV = ? NPV = $136,578; IRR = 19.22%. b. Ignoring environmental concerns, the project should be undertaken because its NPV is positive and its IRR is greater than the firm’s cost of capital. c. Environmental effects could be added by estimating penalties or any other cash outflows that might be imposed on the firm to help return the land to its previous state (if possible). These outflows could be so large as to cause the project to have a negative NPV, in which case the project should not be undertaken. 10-14 a. Year Sales Royalties Marketing Net 0 ($20,000) ($20,000) 1 75,000 ($5,000) ($10,000) 60,000 2 52,500 (3,500) (10,000) 39,000 3 22,500 (1,500) 21,000 Payback period = $20,000/$60,000 = 0.33 year. Answers and Solutions: 10 - 9 10% × 1.10 × (1.10) 8 × (1.10) 9 NPV = $60,000/(1.11) 1 + $39,000/(1.11) 2 + $21,000/(1.11) 3 - $20,000 = $81,062.35. Using a financial calculator, input CF 0 = -20000; CF 1 = 60000, CF 2 = 39000, CF 3 = 21000, and then solve for IRR = 261.90%. b. Finance theory dictates that this investment should be accepted. However, ask your students “Does this service encourage cheating?” If yes, does a businessperson have a social responsibility not to make this service available? 10-15 Facts: 5 years remaining on lease; rent = $2,000/month; 60 payments left, payment at end of month. New lease terms: $0/month for 9 months; $2,600/month for 51 months. Cost of capital = 12% annual (1% per month). a. 0 1 2 59 60 | | | • • • | | -2,000 -2,000 -2,000 -2,000 PV cost of old lease: N = 60; I = 1; PMT = -2000; FV = 0; PV = ? PV = -$89,910.08. 0 1 9 10 59 60 | | • • • | | • • • | | 0 0 -2,600 -2,600 -2,600 PV cost of new lease: CF 0 = 0, CF 1-9 = 0; CF 10-60 = -2600; I = 1. NPV = -$94,611.45. Sharon should not accept the new lease because the present value of its cost is $94,611.45 - $89,910.08 = $4,701.37 greater than the old lease. b. 0 1 2 9 10 59 60 | | | • • • | | • • • | | -2,000 -2,000 -2,000 PMT PMT PMT FV of first 9 months’ rent under old lease: N = 9; I = 1; PV = 0; PMT = -2000; FV = ? FV = $18,737.05. The FV of the first 9 months’ rent is equivalent to the PV of the 51- period annuity whose payments represent the incremental rent during months 10-60. To find this value: N = 51; I = 1; PV = -18737.05; FV = 0; PMT = ? PMT = $470.80. Thus, the new lease payment that will make her indifferent is $2,000 + $470.80 = $2,470.80. Check: Answers and Solutions: 10 - 10 1% 1% 1% [...]... THE CASE OF CAPITAL PROJECTS 2 ASSESS THE RISKINESS OF THE CASH FLOWS 3 DETERMINE THE APPROPRIATE DISCOUNT RATE, BASED ON THE RISKINESS OF THE CASH FLOWS AND THE GENERAL LEVEL OF INTEREST RATES THIS IS CALLED THE PROJECT COST OF CAPITAL IN CAPITAL BUDGETING 4 FIND (A) THE PV OF THE EXPECTED CASH FLOWS AND/OR (B) THE ASSET’S RATE OF RETURN 5 IF THE PV OF THE INFLOWS IS GREATER THAN THE PV OF THE OUTFLOWS... VALUE OF THE FIRM D 3 WOULD THE NPVs CHANGE IF THE COST OF CAPITAL CHANGED? ANSWER: THE NPV OF A PROJECT IS DEPENDENT ON THE COST OF CAPITAL USED THUS, IF THE COST OF CAPITAL CHANGED, THE NPV OF EACH PROJECT WOULD CHANGE NPV DECLINES AS k INCREASES, AND NPV RISES AS k FALLS E 1 DEFINE THE TERM INTERNAL RATE OF RETURN (IRR) WHAT IS EACH PROJECT’S IRR? ANSWER: [SHOW S10-14 HERE.] THE INTERNAL RATE OF RETURN... AVERAGE PROJECT COST OF CAPITAL IS 10 PERCENT ALLIED’S WEIGHTED AVERAGE YOU MUST NOW DETERMINE WHETHER ONE OR BOTH OF THE PROJECTS SHOULD BE ACCEPTED A WHAT IS CAPITAL BUDGETING? ARE THERE ANY SIMILARITIES BETWEEN A FIRM’S CAPITAL BUDGETING DECISIONS AND AN INDIVIDUAL’S INVESTMENT DECISIONS? Integrated Case: 10 - 24 ANSWER: [SHOW S10-1 THROUGH S10-3 HERE.] CAPITAL BUDGETING IS THE PROCESS OF ANALYZING ADDITIONS... EQUATES THE PRESENT VALUE OF THE TERMINAL VALUE OF THE INFLOWS, COMPOUNDED AT THE COST OF CAPITAL, TO THE PRESENT VALUE OF THE COSTS HERE IS THE SETUP FOR CALCULATING PROJECT L’S MODIFIED IRR: 0 k = 10% | PV OF COSTS = (100.00) 1 | 10 2 | 60 1.10 × 3 | 80.00 66.00 × (1.10)2 12.10 TV OF INFLOWS = 158.10 PV OF TV = 100.00 MIRR = ? $158.10 $100 = (1 + MIRR)3 n PV COSTS = TV = (1 + MIRR)n COFt = (1 + k)t t =0... COST OF CAPITAL, THEN ITS CASH FLOWS ARE JUST SUFFICIENT TO PROVIDE INVESTORS WITH THEIR REQUIRED RATES OF RETURN AN IRR Integrated Case: 10 - 31 GREATER THAN k IMPLIES AN ECONOMIC PROFIT, WHICH ACCRUES TO THE FIRM’S SHAREHOLDERS, WHILE AN IRR LESS THAN k INDICATES AN ECONOMIC LOSS, OR A PROJECT THAT WILL NOT EARN ENOUGH TO COVER ITS COST OF CAPITAL PROJECTS’ IRRs ARE COMPARED TO THEIR COSTS OF CAPITAL, ... the MIRR and NPV decisions Answers and Solutions: 10 - 22 SPREADSHEET PROBLEM 10-24 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of South-Western’s web site, http://brigham.swlearning.com Spreadsheet Problem: 10 - 23 INTEGRATED CASE Allied Components Company Basics of Capital Budgeting 10-25 ASSUME THAT YOU RECENTLY... VERTICAL AXIS INTERCEPTS THE SLOPE OF THE NPV PROFILE DEPENDS ENTIRELY ON THE TIMING PATTERN OF THE CASH FLOWS LONG-TERM PROJECTS HAVE STEEPER NPV PROFILES THAN SHORT-TERM ONES THUS, WE CONCLUDE THAT NPV PROFILES CAN CROSS IN TWO SITUATIONS: (1) WHEN MUTUALLY EXCLUSIVE PROJECTS DIFFER IN SCALE (OR SIZE) AND (2) WHEN THE PROJECTS’ CASH FLOWS DIFFER IN TERMS OF THE TIMING PATTERN OF THEIR CASH FLOWS (AS FOR... percent, the IRR of Project ∆, the difference between the cash flow streams of the two projects b Yes Assuming (1) equal risk among projects, and (2) that the cost of capital is a constant and does not vary with the amount of capital raised, the firm would take on all available projects with returns greater than its 12 percent cost of capital If the firm had invested in all available projects with returns... A 10 PERCENT COST OF CAPITAL: YEAR 0 1 2 3 EXPECTED NET CASH FLOWS DISCOUNTED CUMULATIVE ($100.00) ($100.00) 9.09 (90.91) 49.59 (41.32) 60.11 18.79 RAW ($100) 10 60 80 DISCOUNTED PAYBACKL = 2 + ($41.32/$60.11) = 2.69 = 2.7 YEARS VERSUS 2.4 YEARS FOR THE REGULAR PAYBACK C 4 WHAT IS THE MAIN DISADVANTAGE OF DISCOUNTED PAYBACK? IS THE PAYBACK METHOD OF ANY REAL USEFULNESS IN CAPITAL BUDGETING DECISIONS?... so both projects should be d At a discount rate of 5 percent, NPVA = $18,243,813 At a discount rate of 5 percent, NPVB = $14,964,829 At a discount rate of 5 percent, Project A has the higher NPV; consequently, it should be accepted e At a discount rate of 15 percent, NPVA = $8,207,071 At a discount rate of 15 percent, NPVB = $8,643,390 At a discount rate of 15 percent, Project B has the higher NPV; consequently, . ) 5 MIRR A = 10. 85%. Answers and Solutions: 10 - 13 × (1 .10) 2 × 1 .10 × (1 .10) 3 × (1 .10) 4 × (1 .10) 2 × 1 .10 × (1 .10) 3 × (1 .10) 4 According to the MIRR criterion, Project A is the superior project. 10- 17. = $17 ,100 . FV Inflows: PV FV 0 1 2 3 4 5 | | | | | | 5 ,100 5 ,100 5 ,100 5 ,100 5 ,100 5,814 6,628 Answers and Solutions: 10 - 6 14% × (1.14) 2 × 1.14 × (1.14) 3 7,556 8,614 17 ,100 MIRR. 176.98 194.68 . . . 379.37 417 .31 1,000 10. 93% = MIRR FV of inflows: With a financial calculator, input N = 10, I = 10, PV = 0, and PMT = -176.98 to obtain FV = $2,820.61. Then input N = 10, PV = -100 0, PMT = 0, and