Homework SourseA project has annual cash flows of 8000 for the next 10 year
A project has annual cash flows of $8,000 for the next 10 years and then $8,500 each year for the following 10 years. The IRR of this 20-year project is 8.39%. If the firm\'s WACC is 8%, what is the project\'s NPV? Round your answer to the nearest cent. Do not round your intermediate calculations.
Solution
At IRR, Sum of (All present value of cash flows) = Investment or Initial cash outflow
Let’s calculate investment value by discounting cash inflows at IRR = 8.39%:
Year
Inflows
Df = Discounting factor = 1/(1+8.39%)^Year
PV= Inflows x Df
1
8000
0.922594
7380.75
2
8000
0.851180
6809.44
3
8000
0.785294
6282.35
4
8000
0.724508
5796.06
5
8000
0.668427
5347.42
6
8000
0.616687
4933.49
7
8000
0.568952
4551.61
8
8000
0.524912
4199.29
9
8000
0.484281
3874.24
10
8000
0.446795
3574.36
11
8500
0.412210
3503.79
12
8500
0.380303
3232.57
13
8500
0.350865
2982.35
14
8500
0.323706
2751.50
15
8500
0.298649
2538.52
16
8500
0.275532
2342.02
17
8500
0.254205
2160.74
18
8500
0.234528
1993.49
19
8500
0.216374
1839.18
20
8500
0.199625
1696.82
Total = Initial Investment
77790.01
Now, we can calculate NPV with by plotting investment and by discounting cash flows @8%:
Year
Inflows
Df = Discounting factor = 1/(1+8%)^Year
PV= Inflows x Df
0
-77790.01
1.000000
-77790.01
1
8000
0.925926
7407.41
2
8000
0.857339
6858.71
3
8000
0.793832
6350.66
4
8000
0.735030
5880.24
5
8000
0.680583
5444.67
6
8000
0.630170
5041.36
7
8000
0.583490
4667.92
8
8000
0.540269
4322.15
9
8000
0.500249
4001.99
10
8000
0.463193
3705.55
11
8500
0.428883
3645.50
12
8500
0.397114
3375.47
13
8500
0.367698
3125.43
14
8500
0.340461
2893.92
15
8500
0.315242
2679.55
16
8500
0.291890
2481.07
17
8500
0.270269
2297.29
18
8500
0.250249
2127.12
19
8500
0.231712
1969.55
20
8500
0.214548
1823.66
Total = Net Present Value
2309.20
| Year | Inflows | Df = Discounting factor = 1/(1+8.39%)^Year | PV= Inflows x Df |
| 1 | 8000 | 0.922594 | 7380.75 |
| 2 | 8000 | 0.851180 | 6809.44 |
| 3 | 8000 | 0.785294 | 6282.35 |
| 4 | 8000 | 0.724508 | 5796.06 |
| 5 | 8000 | 0.668427 | 5347.42 |
| 6 | 8000 | 0.616687 | 4933.49 |
| 7 | 8000 | 0.568952 | 4551.61 |
| 8 | 8000 | 0.524912 | 4199.29 |
| 9 | 8000 | 0.484281 | 3874.24 |
| 10 | 8000 | 0.446795 | 3574.36 |
| 11 | 8500 | 0.412210 | 3503.79 |
| 12 | 8500 | 0.380303 | 3232.57 |
| 13 | 8500 | 0.350865 | 2982.35 |
| 14 | 8500 | 0.323706 | 2751.50 |
| 15 | 8500 | 0.298649 | 2538.52 |
| 16 | 8500 | 0.275532 | 2342.02 |
| 17 | 8500 | 0.254205 | 2160.74 |
| 18 | 8500 | 0.234528 | 1993.49 |
| 19 | 8500 | 0.216374 | 1839.18 |
| 20 | 8500 | 0.199625 | 1696.82 |
| Total = Initial Investment | 77790.01 |
