Question

It’s time to build a new call center. It looks like the center will cost $10.5 million to build and generate cash flows of $2 million the first year, $3 million per year for the next two years, $4 million per year for the following two years, and $2 million in its final year of operation. If your required return is 12%, what is the IRR of building the new center?

Answer 1

The IRR is the rate at which NPV is zero.

Lets compute NPV at 17% as shown below:

= - $ 10.5 million + $ 2 million / 1.17 + $ 3 million / 1.17² + $ 3 million / 1.17³ + $ 4 million / 1.17⁴ + $ 4 million / 1.17⁵ + $ 2 million / 1.17⁶

= $ 0.012776018 million Approximately

Lets compute NPV at 18% as shown below:

= - $ 10.5 million + $ 2 million / 1.18 + $ 3 million / 1.18² + $ 3 million / 1.18³ + $ 4 million / 1.18⁴ + $ 4 million / 1.18⁵ + $ 2 million / 1.18⁶

= - $ 0.272183395 million Approximately

It means that the IRR lies between 17% and 18% and is computed as follows:

= Lower rate + [ Lower rate NPV / ( Lower rate NPV - Higher rate NPV ) ] x ( Higher rate - Lower rate)

= 17 + [ $ 0.012776018 million / ( $ 0.012776018 million - ( - $ 0.272183395 million) ] x ( 18 - 17)

= 17 + [ $ 0.012776018 million / $ 0.284959413 million] x 1

= 17 + 0.04

= 17.04% Approximately