Question

Iron Works International is considering a project that will produce annual cash flows of $38,800, $47,500, $58,200, and $23,700 over the next four years, respectively. What is the internal rate of return if the project has an initial cost of $112,200?

Multiple Choice

• 19.14%

• 18.35%

• 15.95%

• 17.55%

• 17.02%

Answer 1

The IRR is the rate at which NPV is zero.

Lets compute NPV at 19% as shown below:

= - $ 112,200 + $ 38,800 / 1.19 + $ 47,500 / 1.19² + $ 58,200 / 1.19³ + $ 23,700 / 1.19⁴

= $ 303.1207064

Lets compute NPV at 20% as shown below:

= - $ 112,200 + $ 38,800 / 1.20 + $ 47,500 / 1.20² + $ 58,200 / 1.20³ + $ 23,700 / 1.20⁴

= - $ 1,770.601852

It means that the IRR lies between 19% and 20% and is computed as follows:

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

= 19 + [ $ 303.1207064 / ( $ 303.1207064 - ( - $ 1,770.601852) ] x ( 20 - 19)

= 19 + [ $ 303.1207064 / $ 2,073.722558] x 1

= 19 + 0.14

= 19.14% Approximately