A firm evaluates all of its projects by using the NPV decision rule. Year Cash Flow 0 –$27,000 1 20,000 2 13,000 3 8,000 a. At a required return of 13 percent, what is the NPV for this project? b. At a required return of 33 percent, what is the NPV for this project?
| A project that provides annual cash flows of $10,600 for 8 years costs $56,550 today. |
| a. If the required return is 7 percent, what is the NPV for this project? |
| b. Determine the IRR for this project. |
a
| Project | ||||
| Discount rate | 13.000% | |||
| Year | 0 | 1 | 2 | 3 |
| Cash flow stream | -27000 | 20000 | 13000 | 8000 |
| Discounting factor | 1.000 | 1.130 | 1.277 | 1.443 |
| Discounted cash flows project | -27000.000 | 17699.115 | 10180.907 | 5544.401 |
| NPV = Sum of discounted cash flows | ||||
| NPV Project = | 6424.42 | |||
| Where | ||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | |||
| Discounted Cashflow= | Cash flow stream/discounting factor | |||
b
| Project | ||||
| Discount rate | 33.000% | |||
| Year | 0 | 1 | 2 | 3 |
| Cash flow stream | -27000 | 20000 | 13000 | 8000 |
| Discounting factor | 1.000 | 1.330 | 1.769 | 2.353 |
| Discounted cash flows project | -27000.000 | 15037.594 | 7349.200 | 3400.440 |
| NPV = Sum of discounted cash flows | ||||
| NPV Project = | -1212.77 | |||
| Where | ||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | |||
| Discounted Cashflow= | Cash flow stream/discounting factor | |||
a
| Project | |||||||||
| Discount rate | 7.000% | ||||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Cash flow stream | -56550 | 10600 | 10600 | 10600 | 10600 | 10600 | 10600 | 10600 | 10600 |
| Discounting factor | 1.000 | 1.070 | 1.145 | 1.225 | 1.311 | 1.403 | 1.501 | 1.606 | 1.718 |
| Discounted cash flows project | -56550.000 | 9906.542 | 9258.451 | 8652.757 | 8086.689 | 7557.654 | 7063.228 | 6601.147 | 6169.297 |
| NPV = Sum of discounted cash flows | |||||||||
| NPV Project = | 6745.76 | ||||||||
| Where | |||||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | ||||||||
| Discounted Cashflow= | Cash flow stream/discounting factor | ||||||||
b
| Project | |||||||||
| IRR is the rate at which NPV =0 | |||||||||
| IRR | 10.00% | ||||||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Cash flow stream | -56550.000 | 10600.000 | 10600.000 | 10600.000 | 10600.000 | 10600.000 | 10600.000 | 10600.000 | 10600.000 |
| Discounting factor | 1.000 | 1.100 | 1.210 | 1.331 | 1.464 | 1.611 | 1.772 | 1.949 | 2.144 |
| Discounted cash flows project | -56550.000 | 9636.354 | 8760.314 | 7963.914 | 7239.915 | 6581.734 | 5983.389 | 5439.439 | 4944.940 |
| 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= | 10.00% | ||||||||
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