Question

Consider an investment project with net cash flows as follows.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             

EOY	Net Cash Flow
0	minus−​$117 comma 000117,000
1	19 comma 00019,000
2	33 comma 00033,000
3	25 comma 00025,000
4	34 comma 00034,000
5	38 comma 00038,000

The​ project's internal rate of return is closest to which choice​ below?

Choose the closest answer below.

A.The IRR for the project is

27.627.6​%

per year.

B.The IRR for the project is

4.74.7​%

per year.

C.The IRR for the project is

7.97.9​%

per year.

D.The IRR for the project is

11.811.8​%

per year

Answer 1

The correct answer is (C) The IRR for the project is 7.9​%

Internal rate of return is that discount rate at which Present value of the cash flow is equal to zero.

Present value of amount(A) received after n years is given by:

P = A/(1 + r)ⁿ where r = rate of return

Hence Net present Value is given by:

NPV = -117000/(1 + r)⁰ + 19000/(1 + r)¹ + 33000/(1 + r)² + 25000/(1 + r)³ + 34000/(1 + r)⁴ + 38000/(1 + r)⁵

This NP V = 0 when r = internal rate of return

=> -117000 + 19000/(1 + r)¹ + 33000/(1 + r)² + 25000/(1 + r)³ + 34000/(1 + r)⁴ + 38000/(1 + r)⁵ = 0

Let 1 + r = t

=> -117000 + 19000/t¹ + 33000/t² + 25000/t³ + 34000/t⁴ + 38000/t⁵ = 0

=> -117000t⁵ + 19000t⁴ + 33000t³ + 25000t² + 34000t + 38000 = 0

Solving it we get:

t = 1.079

=> r = t - 1 = 0.079 = 7.9%

So, Internal rate of return = 7.9%

Hence, the correct answer is (C) The IRR for the project is 7.9​%