Question

An investment provides annual cash flows of $1200 for 9 years at a cost today of $5200. If the company’s hurdle rate is 8% should they accept the project and why? And what if the hurdle rate is 24%? Calculate the project’s IRR

Answer 1

Let cash flows for year t be CFt

Given, CF0 = -5200
CF1 to CF9 = 1200

Hurdle Rate = r

NPV = ΣCFt/(1+r)^t

= -5200 + 1200/(1+r) + 1200/(1+r)² + ..... + 1200/(1+r)⁹

= -5200 + 1200[1- (1+r)^-9]/r

When r = 8%, NPV = -5200 + 1200[1- (1+0.08)^-9]/0.08 = $2296.27 => Accept the project since NPV > 0

When r = 24%, NPV = -5200 + 1200[1- (1+0.24)^-9]/0.24 = $-921.40 => Reject the project since NPV < 0

Let IRR = i

IRR is the rare at which NPV = 0

=> -5200 + 1200[1- (1+i)^-9]/i = 0

=> 1200[1- (1+i)^-9]/i = 5200

Using hit and trial, i = 0.2065 or 20.65%