(Payback period, NPV, PI, and IRR calculations) You are considering a project with an initial cash outlay of $80,000 and expected free cash flows of $26,000 at the end of each year for 6 years. The required rate of return for this project is 7 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?
a. The project's payback period is nothing years. (Round to two decimal places.)
b. The project's NPV is $ . (Round to the nearest cent.)
c. The the project's PI is . (Round to three decimal places.)
d. The project's IRR is %. (Round to two decimal places.)
| year | cashflow | factor | Present value of cash flow |
| 1-6 | 26,000 | 4.766 | 123916 |
| Now | (80,000) | 1 | (80,000) |
| NPV | = 43,916 |
Payback period
| year | Total flow | Cumulative |
| 0 | (80,000) | (80,000) |
| 1 | 26,000 | (54,000) |
| 2 | 26,000 | (28,000) |
| 3 | 26,000 | (2,000) |
| 4 | 26,000 | 24,000 |
| 5 | 26,000 | 50,000 |
| 6 | 26,000 | 76,000 |
Payback period is 3 year + 2,000 / 26,000
= 3 + .076 = 3.076 years
PI = present value of inflows / outflows
= 123,916 / 80,000 = 1.55
IRR
| year | cash inflows | p.v @7 | Discounted pv |
| 1 -6 | 26000 | 4.766 | 123916 |
| Intial | 80000 | 1 | (80,000) |
| NPV | = 43,916 | ||
| P.v @ 20% | |||
| 1 -6 | 26000 | 3.3255 | 86463 |
| intial | 80000 | 1 | (80,000) |
| 18,394 | |||
| P.v @ 24% | |||
| 1 -6 | 26000 | 3.0204 | 78530.4 |
| intial | 80000 | 1 | (80,000) |
| NPV | (1469.6) | ||
IRR = 20% + Npv at 20% / Total diff ) x diff in rate
= 20 + 18394 / (18394 +1470) x (24-20)
= 20 + (18394/19864 ) x 4
= 20 + .9259 x 4
= 20 +3.7036 = 23.70
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