Consider a project that costs $200,000 to build, provides an income of $75,000 a year for...
Consider a project that costs $200,000 to build, provides an income of $75,000 a year for five years starting in year 1, and costs $200,000 to dispose of at the very end of the fifth year. Assume that the first payment comes at the start of the year after the project is undertaken. Should the project be pursued at a 0% discount rate? How about 2%? 5%? 10%?
Homework Answers
| Project | ||||||
| Discount rate | 0 | |||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Cash flow stream | -200000 | 75000 | 75000 | 75000 | 75000 | -125000 |
| Discounting factor | 1 | 1 | 1 | 1 | 1 | 1 |
| Discounted cash flows project | -200000 | 75000 | 75000 | 75000 | 75000 | -125000 |
| NPV = Sum of discounted cash flows | ||||||
| NPV Project = | -25000 | |||||
| Where | ||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | |||||
| Discounted Cashflow= | Cash flow stream/discounting factor | |||||
| Reject project as NPV is negative | ||||||
| Project | ||||||
| Discount rate | 0.02 | |||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Cash flow stream | -200000 | 75000 | 75000 | 75000 | 75000 | -125000 |
| Discounting factor | 1 | 1.02 | 1.0404 | 1.061208 | 1.0824322 | 1.104081 |
| Discounted cash flows project | -200000 | 73529.41 | 72087.66 | 70674.18 | 69288.407 | -113216 |
| NPV = Sum of discounted cash flows | ||||||
| NPV Project = | -27636.7 | |||||
| Where | ||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | |||||
| Discounted Cashflow= | Cash flow stream/discounting factor | |||||
| Reject project as NPV is negative | ||||||
| Project | ||||||
| Discount rate | 0.05 | |||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Cash flow stream | -200000 | 75000 | 75000 | 75000 | 75000 | -125000 |
| Discounting factor | 1 | 1.05 | 1.1025 | 1.157625 | 1.2155063 | 1.276282 |
| Discounted cash flows project | -200000 | 71428.57 | 68027.21 | 64787.82 | 61702.686 | -97940.8 |
| NPV = Sum of discounted cash flows | ||||||
| NPV Project = | -31994.48 | |||||
| Where | ||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | |||||
| Discounted Cashflow= | Cash flow stream/discounting factor | |||||
| Reject project as NPV is negative | ||||||
| Project | ||||||
| Discount rate | 0.1 | |||||
| Year | 0 | 1 | 2 | 3 | 4 | 5 |
| Cash flow stream | -200000 | 75000 | 75000 | 75000 | 75000 | -125000 |
| Discounting factor | 1 | 1.1 | 1.21 | 1.331 | 1.4641 | 1.61051 |
| Discounted cash flows project | -200000 | 68181.82 | 61983.47 | 56348.61 | 51226.009 | -77615.2 |
| NPV = Sum of discounted cash flows | ||||||
| NPV Project = | -39875.26 | |||||
| Where | ||||||
| Discounting factor = | (1 + discount rate)^(Corresponding period in years) | |||||
| Discounted Cashflow= | Cash flow stream/discounting factor | |||||
| Reject project as NPV is negative | ||||||
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