Consider The Following Two Mutually Exclusive Projects:

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Consider The Following Two Mutually Exclusive Projects:

Year Cash Flow (A) Cash Flow (B) 0 -$ 344,000 -$ 49,000 1 51,000 24,600 2 71,000 22,600 3 71,000 20,100 4 446,000 15,200 Whichever project you choose, if any, you require a 15 percent return on your investment. a-1 What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Payback period Project A years Project B years a-2 If you apply the payback criterion, which investment will you choose? Project A Project B b-1 What is the discounted payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Discounted payback period Project A years Project B years b-2 If you apply the discounted payback criterion, which investment will you choose? Project A Project B c-1 What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) NPV Project A $ Project B $ c-2 If you apply the NPV criterion, which investment will you choose? Project A Project B d-1 What is the IRR for each project? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) IRR Project A % Project B % d-2 If you apply the IRR criterion, which investment will you choose? Project A Project B e-1 What is the profitability index for each project? (Do not round intermediate calculations and round your answers to 3 decimal places, e.g., 32.161.) Profitability index Project A Project B e-2 If you apply the profitability index criterion, which investment will you choose? Project A Project B f. Based on your answers in (a) through (e), which project will you finally choose?
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a. The payback period for each project is: A: 3 + ($151,000 / $446,000) = 3.34 years B: 2 + ($1,800 / $20,100) = 2.09 years The payback criterion implies accepting Project B because it pays back sooner than Project A. b. The discounted payback for each project is: A: $51,000 / 1.15 + $71,000 / 1.152 + $71,000 / 1.153 = $144,717.68 $446,000 / 1.154 = $255,001.95 Discounted payback = 3 + ($344,000 - 144,717.68) / $255,001.95 = 3.78 years B: $24,600 / 1.15 + $22,600 / 1.152 = $38,480.15 $20,100 / 1.153 = $13,216.08 Discounted payback = 2 + ($49,000 - 38,480.15) / $13,216.08 = 2.80 years The discounted payback criterion implies accepting Project B because it pays back sooner than A. c. The NPV for each project is: A: NPV = -$344,000 + $51,000 / 1.15 + $71,000 / 1.152 + $71,000 / 1.153 + $446,000 / 1.154 NPV = $55,719.63 B: NPV = -$49,000 + $24,600 / 1.15 + $22,600 / 1.152 + $20,100 / 1.153 + $15,200 / 1.154 NPV = $11,386.88 The NPV criterion implies we accept Project A because Project A has a higher NPV than Project B. d. The IRR for each project is: A: $344,000 = $51,000 / (1 + IRR) + $71,000 / (1 + IRR)2 + $71,000 / (1 + IRR)3 + $446,000 / (1 + IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 20.43% B: $49,000 = $24,600 / (1 + IRR) + $22,600 / (1 + IRR)2 + $20,100 / (1 + IRR)3 + $15,200 / (1 + IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 27.05% The IRR decision rule implies we accept Project B because the IRR for B is greater than the IRR for A. e. The profitability index for each project is: A: PI = ($51,000 / 1.15 + $71,000 / 1.152 + $71,000 / 1.153 + $446,000 / 1.154) / $344,000 = 1.162 B: PI = ($24,600 / 1.15 + $22,600 / 1.152 + $20,100 / 1.153 + $15,200 / 1.154) / $49,000 = 1.232 The profitability index criterion implies we accept Project B because its PI is greater than Project A's. f. The final decision should be based on the NPV since it does not have the ranking problem associated with the other capital budgeting techniques. Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. CF(A) c. d. e. CFo -$344,000 CFo -$344,000 CFo $0 C01 $51,000 C01 $51,000 C01 $51,000 F01 1 F01 1 F01 1 C02 $71,000 C02 $71,000 C02 $71,000 F02 2 F02 2 F02 2 C03 $446,000 C03 $446,000 C03 $446,000 F03 1 F03 1 F03 1 I = 15% IRR CPT I = 15% NPV CPT 20.43% NPV CPT $55,719.63 $399,719.63 PI = $399,719.63 / $344,000 = 1.162 CF(B) c. d. e. CFo -$49,000 CFo -$49,000 CFo $0 C01 $24,600 C01 $24,600 C01 $24,600 F01 1 F01 1 F01 1 C02 $22,600 C02 $22,600 C02 $22,600 F02 1 F02 1 F02 1 C03 $20,100 C03 $20,100 C03 $20,100 F03 1 F03 1 F03 1 C04 $15,200 C04 $15,200 C04 $15,200 F04 1 F04 1 F04 1 I = 15% IRR CPT I = 15% NPV CPT 27.05% NPV CPT $11,386.88 $60,386.88 PI = $60,386.88 / $49,000 = 1.232 f. The final decision should be based on the NPV since it does not have the ranking problem associated with the other capital budgeting techniques.
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