In: Finance
Consider cash flows for projects A and B
Year: 0, 1, 2, 3, 4, 5
Project A: -$1000, 375, 375, 375, 375,-100
Project B: -$1000, 900, 700, 500, -200, 200
The cost of capital for both projects is 10%
1. Find the NPV and MIRR of projects A and B. If project A and B are mutually exclusive.
2. Find the crossover rate for projects A and B.
3. What is the profitability index for projects A and B? How many IRRs exist for projects A and B?
1.
NPV OF PROJECT A:
Year | CF | PVF @ 10% | PV |
0 | -1000 | 1 | -1000 |
1 | 375 | 0.909090909 | 340.91 |
2 | 375 | 0.826446281 | 309.92 |
3 | 375 | 0.751314801 | 281.74 |
4 | 375 | 0.683013455 | 256.13 |
5 | -100 | 0.620921323 | -62.09 |
NPV | 126.61 |
NPV OF PROJECT B
Year | CF | PVF @ 10% | PV |
0 | -1000 | 1 | -1000 |
1 | 900 | 0.909090909 | 818.18 |
2 | 700 | 0.826446281 | 578.51 |
3 | 500 | 0.751314801 | 375.66 |
4 | -200 | 0.683013455 | -136.60 |
5 | 200 | 0.620921323 | 124.18 |
NPV | 759.93 |
The IRR is the interest rate that makes the NPV of the project equal to zero.
The equation to calculate the IRR of Project A is:
0 = –$1,000 + $375 / (1+ IRR) + $375 / (1+ IRR)2+ $375 / (1+ IRR)3 + $375 / (1+ IRR)4 - $100 / (1+ IRR)5
IRR = 16.09%
Similarly IRR of Project B is:
0 = –$1,000 + $900 / (1+ IRR) + $700 / (1+ IRR)2+ $500 / (1+ IRR)3 - $200 / (1+ IRR)4 - $200 / (1+ IRR)5
IRR = 54.40%
3.
Profitability Index of Project A : (initial investment + NPV) / Initial investment = 1000+126.61 / 1000 = 1.12661
Profitability Index of Project B: 1000 + 759.93 / 1000 = 1.75993