Consider the following two mutually exclusive projects:
Explanation: a.
b.
c.
d.
e.
f.
| Year | Cash Flow (A) | Cash Flow (B) | |||||
| 0 | –$ | 348,000 | –$ | 51,000 | |||
| 1 | 47,000 | 24,200 | |||||
| 2 | 67,000 | 22,200 | |||||
| 3 | 67,000 | 19,700 | |||||
| 4 | 442,000 | 14,800 | |||||
| Whichever project you choose, if any, you require a 14 percent return on your investment. |
| a-1 |
What is the payback period for each project? (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 B |
| b-1 |
What is the discounted payback period for each project? (Do not round intermediate calculations and round your final 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 B |
| c-1 |
What is the NPV for each project? (Do not round intermediate calculations and round your final 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 |
| d-1 |
What is the IRR for each project? (Round your answers 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 B |
| e-1 |
What is the profitability index for each project? (Do not round intermediate calculations and round your final 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 B |
| f | Based on your answers in (a) through (e), which project will you finally choose? |
| Project A |
Explanation: a.
| The payback period for each project is: | |
| A: | 3 + ($167,000/$442,000) = 3.38 years |
| B: | 2 + ($4,600/$19,700) = 2.23 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: | $47,000/1.14 + $67,000/1.142 + $67,000/1.143 = $138,005.49 |
| $442,000/1.144 = $261,699.48 | |
| Discounted payback = 3 + ($348,000 – 138,005.49)/$261,699.48 = 3.80 years | |
| B: | $24,200/1.14 + $22,200/1.142 = $38,310.25 |
| $19,700/1.143 = $13,296.94 | |
| Discounted payback = 2 + ($51,000 – 38,310.25)/$13,296.94 = 2.95 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 = –$348,000 + $47,000/1.14 + $67,000/1.142 + $67,000/1.143 + $442,000/1.144 |
| NPV = $51,704.97 | |
| B: | NPV = –$51,000 + $24,200/1.14 + $22,200/1.142 + $19,700/1.143 + $14,800/1.144 |
| NPV = $9,369.98 | |
| 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: | $348,000 = $47,000/(1+IRR) + $67,000/(1+IRR)2 + $67,000/(1+IRR)3 + $442,000/(1+IRR)4 |
| Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: | |
| IRR = 18.89% | |
| B: | $51,000 = $24,200/(1+IRR) + $22,200/(1+IRR)2 + $19,700/(1+IRR)3 + $14,800/(1+IRR)4 |
| Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: | |
| IRR = 23.47% | |
| IRR decision rule implies we accept Project B because IRR for B is greater than IRR for A. | |
e.
| The profitability index for each project is: | |
| A: | PI = ($47,000/1.14 + $67,000/1.142 + $67,000/1.143 + $442,000/1.144) / $348,000 = 1.149 |
| B: | PI = ($24,200/1.14 + $22,200/1.142 + $19,700/1.143 + $14,800/1.144) / $51,000 = 1.184 |
| Profitability index criterion implies accept Project B because its PI is greater than Project A’s. | |
| 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
| –$348,000 |
CFo
| –$348,000 |
CFo
| $0 | |
C01
| $47,000 |
C01
| $47,000 |
C01
| $47,000 | |
F01
| 1 |
F01
| 1 |
F01
| 1 | |
C02
| $67,000 |
C02
| $67,000 |
C02
| $67,000 | |
F02
| 2 |
F02
| 2 |
F02
| 2 | |
C03
| $442,000 |
C03
| $442,000 |
C03
| $442,000 | |
F03
| 1 |
F03
| 1 |
F03
| 1 | |
| I = 14% | IRR CPT | I = 14% | ||||
| NPV CPT | 18.89% | NPV CPT | ||||
| $51,704.97 | $399,704.97 | |||||
| PI = $399,704.97 / $348,000 = 1.149 |
| CF(B) | c. | d. | e. | |||
CFo
| –$51,000 |
CFo
| –$51,000 |
CFo
| $0 | |
C01
| $24,200 |
C01
| $24,200 |
C01
| $24,200 | |
F01
| 1 |
F01
| 1 |
F01
| 1 | |
C02
| $22,200 |
C02
| $22,200 |
C02
| $22,200 | |
F02
| 1 |
F02
| 1 |
F02
| 1 | |
C03
| $19,700 |
C03
| $19,700 |
C03
| $19,700 | |
F03
| 1 |
F03
| 1 |
F03
| 1 | |
C04
| $14,800 |
C04
| $14,800 |
C04
| $14,800 | |
F04
| 1 |
F04
| 1 |
F04
| 1 | |
| I = 14% | IRR CPT | I = 14% | ||||
| NPV CPT | 23.47% | NPV CPT | ||||
| $9,369.98 | $60,369.98 | |||||
| PI = $60,369.98 / $51,000 = 1.184 |
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. |
