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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

jeff jeffy answered 2 years ago
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