Question

A company is considering a project with the following cash flows:

Time Cash Flow

0 -$100 <<<<<<< negative

1 $100

2 -$100 <<<<<<< negative

3 $120 At a cost of capital of 10%:

a. What is the NPV?

b. What is the Modified Internal rate of Return?

Should the company accept this project?

Answer 1

Given about a project,

Initial cost C0 = $100

CF1 = $100

CF2 = -$100

CF3 = $120

Cost of capital Kc = 10%

a). NPV of the project is Sum of PV of future cash flows minus initial investment

NPV = CF1/(1+Kc) + CF2/(1+Kc)^2 + CF3/(1+Kc)^3 - C0

=> NPV = 100/1.1 - 100/1.1^2 + 120/1.1^3 - 100 = -$1.58

b). MIRR = (FV of future positive cash flows/PV of negative cash flows)^(1/t) - 1

FV of future positive cash flows is calculated using ordinary annuity formula:

FV of future positive cash flows = CF1*(1+Kc)^2 + CF3

FV of future positive cash flows = 100*1.1^2 + 120 = $241

PV of negative cash flows = C0 + CF2/(1+Kc)^2 = 100 + 100/1.1^2 = $182.64

=> MIRR = (241/182.64)^(1/3) - 1 = 9.68%

c). Since NPV of the project is less than 0 and MIRR is also less than 10%, this project should not be accepted.