Question

Internal Rate of Return (IRR) can be understood as the discount rate that

should be applied to a project such that Net Present Value (NPV) = $0. If the

discount rate applied in a certain 5 year project is 10%,

the resultant NPV is $50K, and the cost is $100K, what is the IRR?

(Assume that all costs for the project are incurred at the start of the project,

and the payout for this project occurs in one payment

at the end of Year 5).

Answer 1

Let payout (income) from project at end of year 5 be $V. Then

NPV = $50,000

$50,000 = - $100,000 + V x P/F(10%, 5)

V x 0.6209** = $150,000

V = $241,584.80

If IRR be R%, then

$100,000 = V x P/F(R%, 5)

$100,000 = $241,584.80 x P/F(R%, 5)

(1 + R)^-5** = 0.4139

(1 + R)⁵ = 1/0.4139 = 2.4158

Taking 5th root,

1 + R = 1.1929

R = 0.1929

R = 19.29%

**From P/F Factor table

**P/F(R%, N) = (1 + R)^-N