MINDTAP Q Search this course Jeanelle v From Cengage Questio

MINDTAP Q Search this course Jeanelle v From Cengage Question 12 of 20 D QuestionsProblem 11.02 10. Check My Work (3 remaining) 12. Click here to read the eBook: Internal Rate of Return 13. (IRR) 15 16. 17 18. IRR Project L costs $50,966.31, its expected cash inflows are $11,000 per year for 10 years, and its WACC is 9%. what is the project\'s IRR? Round your answer to o two decimal places.

Solution

Cost of project = $50,966.31

Annual cash inflow = $11,000

Time = 10 years

WACC = 9%

Present value of cash inflows (at 9% discount rate) = Annual cash inflow x PVAF(_{9%, 10})

= 11,000 x 6.418

= $70,598

NPV (At 9%) = Present value of cash inflows - Present value of cash outflows

= 70,598 - 50,966.31

= $19,631.69

IRR is the rate at which NPV of the project is 0. Since at 9% discount rate, NPV is positive, IRR must be more than 9%.

Let us discount cash inflows at a higher discount rate, say 18%.

Present value of cash inflows (at 18% discount rate) = Annual cash inflow x PVAF(_{18%, 10})

= 11,000 x 4.494

= $49,434

NPV (At 18%) = Present value of cash inflows - Present value of cash outflows

= 49,434 - 50,966.31

= - $1,532.31

Since, at 18% discount rate, NPV has become negative, hence IRR must lie below 18%

Let us discount cash inflows at 17%.

Present value of cash inflows (at 17% discount rate) = Annual cash inflow x PVAF(_{17%, 10})

= 11,000 x 4.659

= $51,249

NPV (At 17%) = Present value of cash inflows - Present value of cash outflows

= 51,249 - 50,966.31

= $282.69

Hence, IRR must lie between 17% to 18%

IRR = Lower rate + [ (NPV at lower rate/NPV at lower rate - NPV at higher rate) ] x (Higher rate - Lower rate)

= 17% + [ (282.69/(282.69 + 1,532.31) ] x (18 - 17)

= 17% + [ 282.69/1,815 ] x 1

= 17% + 0.1557%

= 17.15%

Hence, IRR is 17.15%