Question

Project L costs $48,086.22, its expected cash inflows are $10,000 per year for 11 years, and its WACC is 10%. What is the project's IRR? Round your answer to two decimal places.

Answer 1

The IRR is the rate at which NPV is zero.

Lets compute NPV at 17% as shown below:

= - $ 48,086.22 + $ 10,000 / 1.17 + $ 10,000 / 1.17² + $ 10,000 / 1.17³ + $ 10,000 / 1.17⁴ + $ 10,000 / 1.17⁵ + $ 10,000 / 1.17⁶ + $ 10,000 / 1.17⁷ + $ 10,000 / 1.17⁸ + $ 10,000 / 1.17⁹ + $ 10,000 / 1.17¹⁰ + $ 10,000 / 1.17¹¹  

= $ 277.9135704 Approximately

Lets compute NPV at 18% as shown below:

= - $ 48,086.22 + $ 10,000 / 1.18 + $ 10,000 / 1.18² + $ 10,000 / 1.18³ + $ 10,000 / 1.18⁴ + $ 10,000 / 1.18⁵ + $ 10,000 / 1.18⁶ + $ 10,000 / 1.18⁷ + $ 10,000 / 1.18⁸ + $ 10,000 / 1.18⁹ + $ 10,000 / 1.18¹⁰ + $ 10,000 / 1.18¹¹  

= - $ 1,526.166653 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 + [ $ 277.9135704 / ( $ 277.9135704 - ( - $ 1,526.166653) ] x ( 18 - 17)

= 17 + [ $ 277.9135704 / $ 1,804.080223] x 1

= 17.15% Approximately

Feel free to ask in case of any query relating to this question