Question
In: Finance
(Payback period, NPV, PI, and IRR calculations) You are considering a project with an initial cash...
(Payback period, NPV, PI, and IRR calculations) You are considering a project with an initial cash outlay of $70,000 and expected free cash flows of $28,000 at the end of each year for 5 years. The required rate of return for this project is 8 percent.
a. What is the project's payback period?
b. What is the project's NPV?
c. What is the project's PI?
d. What is the project's IRR?
Solutions
Expert Solution
a)
| Year | Cash flow stream | Cumulative cash flow |
| 0 | -70000 | -70000 |
| 1 | 28000 | -42000 |
| 2 | 28000 | -14000 |
| 3 | 28000 | 14000 |
| 4 | 28000 | 42000 |
| 5 | 28000 | 70000 |
| Payback period is the time by which undiscounted cashflow cover the intial investment outlay | |||||
| this is happening between year 2 and 3 | |||||
| therefore by interpolation payback period = 2 + (0-(-14000))/(14000-(-14000)) | |||||
| 2.5 Years |
b
| Project | |||||
| Discount rate | 8.000% | ||||
| Year | 0 | 1 | 2 | 3 | 4 |
| Cash flow stream | -70000 | 28000 | 28000 | 28000 | 28000 |
| Discounting factor | 1.000 | 1.080 | 1.166 | 1.260 | 1.360 |
| Discounted cash flows project | -70000.000 | 25925.926 | 24005.487 | 22227.303 | 20580.836 |
| NPV = Sum of discounted cash flows | |||||
| NPV Project = | 41795.88 | ||||
| Where | |||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | ||||
| Discounted Cashflow= | Cash flow stream/discounting factor | ||||
c
| PI= (NPV+initial inv.)/initial inv. |
| =(41795.88+70000)/70000 |
| 1.6 |
d
| Project | ||||||
| IRR is the rate at which NPV =0 | ||||||
| IRR | 28.65% | |||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Cash flow stream | -70000.000 | 28000.000 | 28000.000 | 28000.000 | 28000.000 | 28000.000 |
| Discounting factor | 1.000 | 1.286 | 1.655 | 2.129 | 2.739 | 3.524 |
| Discounted cash flows project | -70000.000 | 21764.597 | 16917.775 | 13150.306 | 10221.825 | 7945.497 |
| NPV = Sum of discounted cash flows | ||||||
| NPV Project = | 0.000 | |||||
| Where | ||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | |||||
| Discounted Cashflow= | Cash flow stream/discounting factor | |||||
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