Question

A company is considering two mutually exclusive projects that have the following cash flows:

Year                       Project A Cash Flow                      Project B Cash Flow

0                              -$10,000                                             -$8,000

1                                   1000                                                7000

2                                   2000                                                1000            

3                                   6000                                                1000

4                                   6000                                                1000

If the company’s required rate of return is 10%, find the project’s NPV, IRR, PI, and payback period. Which project they should invest in?

Answer 1

Firstly we will calculate the NPV of both projects

Projects A NPV = (10,000) + 1000 / 1.10¹ + 2000 / 1.10² + 6000 / 1.10³ + 6000 / 1.10⁴

= $ 1,167.95

Projects B NPV = (8000) + 7000 / 1.10¹ + 1000 / 1.10² + 1000 / 1.10³ + 1000 / 1.10⁴

= $ 624.41

In order to compute the IRR the NPV of the projects shall be equal to zero.

IRR of project A:

Lets calculate the project NPV by taking a hypotheticaly rate of 12%

= (10,000) + 1000 / 1.12¹ + 2000 / 1.12² + 6000 / 1.12³ + 6000 / 1.12⁴

= $ 571.03

Now lets calculate the project NPV by taking a hypotheticaly rate of 15%

= (10,000) + 1000 / 1.15¹ + 2000 / 1.15² + 6000 / 1.15³ + 6000 / 1.15⁴

= ($ 242.53)

Now we can see that the IRR shall be in between these two rates since the projects NPV is zero between these two rates and we shall use the below formula in order to compute IRR.

= Lower Rate + Lower Rate NPV / ( Lower Rate NPV - Higher Rate NPV ) x (Higher Rate - Lower Rate)

By plugging the figures computed above in the formula we shall get:

= 12% + 571.03 / ( 571.03 - (242.53) ) x (15 -12)

= 12% + (571.03 / 813.56) x 3

= 14.10% Approximately

IRR of project B:

Lets calculate the project NPV by taking a hypotheticaly rate of 12%

= (8000) + 7000 / 1.12¹ + 1000 / 1.12² + 1000 / 1.12³ + 1000 / 1.12⁴

= $ 394.49

Now lets calculate the project NPV by taking a hypotheticaly rate of 16%

= (8000) + 7000 / 1.16¹ + 1000 / 1.16² + 1000 / 1.16³ + 1000 / 1.16⁴

= ($ 29.41)

Now we can see that the IRR shall be in between these two rates since the projects NPV is zero between these two rates and we shall use the below formula in order to compute IRR.

= Lower Rate + Lower Rate NPV / ( Lower Rate NPV - Higher Rate NPV ) x (Higher Rate - Lower Rate)

By plugging the figures computed above in the formula we shall get:

= 12% + 394.49 / ( 394.49 - (29.41) ) x (16 -12)

= 12% + (394.49 / 423.90) x 4

= 15.72% Approximately

PI of project A shall be computed by using the below formula

= Present Value of future cash flows / Initial Investment

= $ 11,167.95 / $ 10,000

= 1.17 Approximately

PI of project B shall be computed by using the below formula

= Present Value of future cash flows / Initial Investment

= $ 8,624.41 / $ 8,000

= 1.08 Approximately

Payback period of Project A can be computed as follows:

Year	Cash Flow	Cumulative Cash Flow
0	(10,000)	(10,000)
1	1000	(9000)
2	2000	(7000)
3	6000	(1000)

As we can see that at the end of year 3 in order to recover our initial investment we need $ 1000 more. So our payback period shall be

= 3 years + Balance amount to be recovered for our initial investment / Year 4 cash inflow

= 3 years + 1000 / 6000

= 3.17 years Approximately

Payback period of Project B can be computed as follows:

Year	Cash Flow	Cumulative Cash Flow
0	(8,000)	(8,000)
1	7000	(1000)
2	1000	0

As we can see that at the end of year 2, we have recovered our initial investment of $ 8,000 so our payback period shall be 2 years.

Since these two projects are mutually exclusive, we shall select only one project out of these on the basis of NPV criteria. So the project A shall be chosen since the NPV of project A is greater than the NPV of project B

Feel free to ask in case of any query relating to this question.