Question

In: Finance

Consider cash flows for projects A and B Year: 0, 1, 2, 3, 4, 5 Project...

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?

Solutions

Expert Solution

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


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