Question
In: Finance
You are considering a project that costs $500 to invest in today, and will pay you $100 next year, $50 in two years, and $100 in three years.
You are considering a project that costs $500 to invest in today, and will pay you $100 next year, $50 in two years, and $100 in three years. The cash inflow will grow at a constant rate of 3% per year after year 3, and you will receive cash inflows for 25 years (total including the first three CFs). Your discount rate is 14%. What is the NPV of the project? Also, what would the NPV be if the cash inflows continued forever? Show your work.
Solutions
Expert Solution
Question 1
| Year | Cash flow calculation | Cash flow | Present value calculation | Present value |
| 1 | 100 | 100 | =100 / (1+14%) ^ 1 | 87.72 |
| 2 | 50 | 50 | =50 / (1+14%) ^ 2 | 38.47 |
| 3 | 100 | 100 | =100 / (1+14%) ^ 3 | 67.5 |
| 4 | =100 * (1+3%) | 103 | =103 / (1+14%) ^ 4 | 60.98 |
| 5 | =103 * (1+3%) | 106.09 | =106.09 / (1+14%) ^ 5 | 55.1 |
| 6 | =106.09 * (1+3%) | 109.27 | =109.27 / (1+14%) ^ 6 | 49.78 |
| 7 | =109.27 * (1+3%) | 112.55 | =112.55 / (1+14%) ^ 7 | 44.98 |
| 8 | =112.55 * (1+3%) | 115.93 | =115.93 / (1+14%) ^ 8 | 40.64 |
| 9 | =115.93 * (1+3%) | 119.41 | =119.41 / (1+14%) ^ 9 | 36.72 |
| 10 | =119.41 * (1+3%) | 122.99 | =122.99 / (1+14%) ^ 10 | 33.18 |
| 11 | =122.99 * (1+3%) | 126.68 | =126.68 / (1+14%) ^ 11 | 29.97 |
| 12 | =126.68 * (1+3%) | 130.48 | =130.48 / (1+14%) ^ 12 | 27.08 |
| 13 | =130.48 * (1+3%) | 134.39 | =134.39 / (1+14%) ^ 13 | 24.47 |
| 14 | =134.39 * (1+3%) | 138.42 | =138.42 / (1+14%) ^ 14 | 22.11 |
| 15 | =138.42 * (1+3%) | 142.57 | =142.57 / (1+14%) ^ 15 | 19.97 |
| 16 | =142.57 * (1+3%) | 146.85 | =146.85 / (1+14%) ^ 16 | 18.05 |
| 17 | =146.85 * (1+3%) | 151.26 | =151.26 / (1+14%) ^ 17 | 16.31 |
| 18 | =151.26 * (1+3%) | 155.80 | =155.80 / (1+14%) ^ 18 | 14.73 |
| 19 | =155.80 * (1+3%) | 160.47 | =160.47 / (1+14%) ^ 19 | 13.31 |
| 20 | =160.47 * (1+3%) | 165.28 | =165.28 / (1+14%) ^ 20 | 12.03 |
| 21 | =165.28 * (1+3%) | 170.24 | =170.24 / (1+14%) ^ 21 | 10.87 |
| 22 | =170.24 * (1+3%) | 175.35 | =175.35 / (1+14%) ^ 22 | 9.82 |
| 23 | =175.35 * (1+3%) | 180.61 | =180.61 / (1+14%) ^ 23 | 8.87 |
| 24 | =180.61 * (1+3%) | 186.03 | =186.03 / (1+14%) ^ 24 | 8.01 |
| 25 | =186.03 * (1+3%) | 191.61 | =191.61 / (1+14%) ^ 25 | 7.24 |
|
Total present value = 757.91 NPV (Total PV - Initial cost) |
=757.91 - 500 | |||
| NPV | 257.91 |
If cash flow continues to grow forever
| Year | Cash flow calculation | Cash flow | Present value calculation | Present value |
| 1 | 100 | 100 | =100 / (1+14%) ^ 1 | 87.72 |
| 2 | 50 | 50 | =50 / (1+14%) ^ 2 | 38.47 |
| 3 | 100 | 100 | =100 / (1+14%) ^ 3 | 67.5 |
| 4 | =100 * (1+3%) | 103 | =103 / (1+14%) ^ 4 | 60.98 |
| 5 | =103 * (1+3%) | 106.09 | =106.09 / (1+14%) ^ 5 | 55.1 |
| 6 | =106.09 * (1+3%) | 109.27 | =109.27 / (1+14%) ^ 6 | 49.78 |
| 7 | =109.27 * (1+3%) | 112.55 | =112.55 / (1+14%) ^ 7 | 44.98 |
| 8 | =112.55 * (1+3%) | 115.93 | =115.93 / (1+14%) ^ 8 | 40.64 |
| 9 | =115.93 * (1+3%) | 119.41 | =119.41 / (1+14%) ^ 9 | 36.72 |
| 10 | =119.41 * (1+3%) | 122.99 | =122.99 / (1+14%) ^ 10 | 33.18 |
| 11 | =122.99 * (1+3%) | 126.68 | =126.68 / (1+14%) ^ 11 | 29.97 |
| 12 | =126.68 * (1+3%) | 130.48 | =130.48 / (1+14%) ^ 12 | 27.08 |
| 13 | =130.48 * (1+3%) | 134.39 | =134.39 / (1+14%) ^ 13 | 24.47 |
| 14 | =134.39 * (1+3%) | 138.42 | =138.42 / (1+14%) ^ 14 | 22.11 |
| 15 | =138.42 * (1+3%) | 142.57 | =142.57 / (1+14%) ^ 15 | 19.97 |
| 16 | =142.57 * (1+3%) | 146.85 | =146.85 / (1+14%) ^ 16 | 18.05 |
| 17 | =146.85 * (1+3%) | 151.26 | =151.26 / (1+14%) ^ 17 | 16.31 |
| 18 | =151.26 * (1+3%) | 155.80 | =155.80 / (1+14%) ^ 18 | 14.73 |
| 19 | =155.80 * (1+3%) | 160.47 | =160.47 / (1+14%) ^ 19 | 13.31 |
| 20 | =160.47 * (1+3%) | 165.28 | =165.28 / (1+14%) ^ 20 | 12.03 |
| 21 | =165.28 * (1+3%) | 170.24 | =170.24 / (1+14%) ^ 21 | 10.87 |
| 22 | =170.24 * (1+3%) | 175.35 | =175.35 / (1+14%) ^ 22 | 9.82 |
| 23 | =175.35 * (1+3%) | 180.61 | =180.61 / (1+14%) ^ 23 | 8.87 |
| 24 | =180.61 * (1+3%) | 186.03 | =186.03 / (1+14%) ^ 24 | 8.01 |
| 25 | =186.03 * (1+3%) | 191.61 | =191.61 / (1+14%) ^ 25 | 7.24 |
| 25 | =191.61 * (1+3%) / (14% - 3%) | 1794.17 | =1794.17/ (1+14%) ^ 25 | 67.80 |
| Total present value | 825.71 | |||
| NPV (Total PV - Initial cost) | =825.71 - 500 | |||
| NPV | 325.71 |
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