| Garage, Inc., has identified the following two mutually exclusive projects: |
| Year | Cash Flow (A) | Cash Flow (B) | |||||
| 0 | –$ | 29,800 | –$ | 29,800 | |||
| 1 | 15,200 | 4,700 | |||||
| 2 | 13,100 | 10,200 | |||||
| 3 | 9,600 | 16,000 | |||||
| 4 | 5,500 | 17,600 | |||||
| a-1 | What is the IRR for each of these projects? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)) |
| IRR | ||
| Project A | % | |
| Project B | % | |
| a-2 | Using the IRR decision rule, which project should the company accept? | ||||
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| a-3 | Is this decision necessarily correct? | ||||
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| b-1 | If the required return is 10 percent, what is the NPV for each of these projects? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)) |
| NPV | ||
| Project A | $ | |
| Project B | $ | |
| b-2 | Which project will the company choose if it applies the NPV decision rule? | ||||
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| c. | At what discount rate would the company be indifferent between these two projects? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) |
| Discount rate |
| Project A | |
| 0 | 29800 |
| 1 | 15200 |
| 2 | 13100 |
| 3 | 9600 |
| 4 | 5500 |
The formula for IRR is:
0 = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n
IRR OF THE PROJECT A IS =20.36%
where P0, P1, . . . Pn equals the cash flows in periods 1, 2, . . . n, respectively; and
IRR equals the project’s internal rate of return.
Let’s look at an example to illustrate how to use IRR.
AsHere is how the IRR equation looks in this scenario:
0 = -$29800 + ($15200)/(1+.2036) + ($13100)/(1+.2036)2 + ($9600)/(1+.2036)3 + $5,500/(1+.2036)4
| Year | Project B |
| 0 | 29800 |
| 1 | 4700 |
| 2 | 10200 |
| 3 | 16000 |
| 4 | 17600 |
IRR OF THE PROJECT B IS 18.46%
0 = -$29800 + ($15200)/(1+.1846) + ($13100)/(1+.1846)2 + ($9600)/(1+.1846)3 + $5,500/(1+.1846)4
| IRR | ||
| Project A | 20.36% | |
| Project B | 18.46 % | |
A-2
Using the IRR decision rule, which project should the company accept?
Project A is accepted because it has higher IRR
A-3
| Is this decision necessarily correct? = Yes
If you look at IRR, you might be tempted to choose project A. But the IRR calculation implicitly assumes that the interim cash flows are invested at the same rate. But this assumption is not likely to be true. Interim cash flows are more likely to be invested at the required rate of return. So, use NPV to decide. Based on NPV you will choose project B. NPV of the project A
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NPV of the project B
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| NPV | ||
| Project A | $ 5813.82 | |
| Project B | $ 6944.55 | |
B-2
| Which project will the company choose if it applies the NPV decision rule? |
Based on NPV you will choose project B.
