A project has an initial cost of $52,125, expected net cash inflows of $12,000 per year for 8 years, and a cost of capital of 12%. What is the project's NPV? (Hint: Begin by constructing a time line.)
, What is the project IRR?
What is the project's payback period?
What is the project's discounted period?
| Discount rate | 12.000% | ||||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Cash flow stream | -52125 | 12000 | 12000 | 12000 | 12000 | 12000 | 12000 | 12000 | 12000 |
| Discounting factor | 1.000 | 1.120 | 1.254 | 1.405 | 1.574 | 1.762 | 1.974 | 2.211 | 2.476 |
| Discounted cash flows project | -52125.000 | 10714.286 | 9566.327 | 8541.363 | 7626.217 | 6809.122 | 6079.573 | 5428.191 | 4846.599 |
| NPV = Sum of discounted cash flows | |||||||||
| NPV Project = | 7486.68 | ||||||||
| Where | |||||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | ||||||||
| Discounted Cashflow= | Cash flow stream/discounting factor | ||||||||
| Project | |||||||||
| IRR is the rate at which NPV =0 | |||||||||
| IRR | 16.00% | ||||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Cash flow stream | -52125.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 |
| Discounting factor | 1.000 | 1.160 | 1.346 | 1.561 | 1.811 | 2.100 | 2.436 | 2.826 | 3.278 |
| Discounted cash flows project | -52125.000 | 10344.929 | 8918.130 | 7688.118 | 6627.753 | 5713.636 | 4925.597 | 4246.246 | 3660.592 |
| 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 | ||||||||
| IRR= | 16.00% | ||||||||
| Project | Discount rate= | 12.00% | |||
| Year | Cash flow stream | Cumulative cash flow | Discounting factor | Discounted cash flows project | Cumulative discounted CF |
| 0 | -52125 | -52125 | 1 | -52125 | -52125.00 |
| 1 | 12000 | -40125 | 1.12 | 10714.28571 | -41410.71 |
| 2 | 12000 | -28125 | 1.2544 | 9566.326531 | -31844.39 |
| 3 | 12000 | -16125 | 1.404928 | 8541.362974 | -23303.02 |
| 4 | 12000 | -4125 | 1.57351936 | 7626.216941 | -15676.81 |
| 5 | 12000 | 7875 | 1.762341683 | 6809.122269 | -8867.69 |
| 6 | 12000 | 19875 | 1.973822685 | 6079.573454 | -2788.11 |
| 7 | 12000 | 31875 | 2.210681407 | 5428.190584 | 2640.08 |
| 8 | 12000 | 43875 | 2.475963176 | 4846.598736 | 7486.68 |
| Payback period is the time by which undiscounted cashflow cover the intial investment outlay | |||||
| this is happening between year 4 and 5 | |||||
| therefore by interpolation payback period = 4 + (0-(-4125))/(7875-(-4125)) | |||||
| 4.34 Years | |||||
| Discounted payback period is the time by which discounted cashflow cover the intial investment outlay | |||||
| this is happening between year 6 and 7 | |||||
| therefore by interpolation payback period = 6 + (0-(-2788.11))/(2640.08-(-2788.11)) | |||||
| 6.51 Years | |||||
| Where | |||||
| Discounting factor =(1 + discount rate)^(corresponding year) | |||||
| Discounted Cashflow=Cash flow stream/discounting factor |
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