Question

Consider a project with the following cash flows: 𝐶𝐶0 = −50, 𝐶𝐶1 = 175, 𝐶𝐶2 = −30.

(a) Calculate the positive IRR(s) for this project to the nearest percent.

(b) Would you accept this project if the opportunity cost of capital is 20%?

Answer 1

answer a)

As there are 2 sign changes in the cash flows, there are two IRR's associated with the cash flows. One is a negative interest rate and another is positive. We are interested to find the positive IRR.

The positive IRR is based on the present worth computation based on the following equation

0 = - 50 + 175 (P/F, i* % , 1 year ) - 30 (P/F, i*, 2 years)

The value of i is found by trial and error approach by substituting different values of interest rates.

50 + 30 (P/F, i*, 2 years)   = 175 (P/F, i* % , 1 year )

Let i = 20%

50 + 20.83 = 145.83

Let i = 100%

50 + 7.5 = 87.5

Let i = 200 %

50 + 3.33 = 58.33

Let i = 235%

52.67 = 52.24

Therefore the ositive IRR is between 234 % and 235 %

Positive IRR = 231.92 %

 

answer b)

The project is acceptable because the positive IRR is higher than the opportunity cost of capital of 20% .