Calculate the IRR of a 20-year project with a cost of $400,000 and annual cash ﬂows of $50,000 in years 1-10 and $25,000 in years 11-20. The company's required rate of return is 10%.
A) 4.53%
B) 6.53%
C) 8.53%
D) 10.53%
E) 12.53%

Question

Quizplus · Accepted Answer

To calculate the IRR, we need to find the discount rate at which the sum of the present values of all future cash flows equals the initial cost. Using the given cash flows and the required rate of return of 10%, we can calculate the present value of each cash flow as follows:

PV of cash flows in years 1-10 = $50,000 x [(1 - 1/(1 + 10%)^10)/10%] = $379,073.51
PV of cash flows in years 11-20 = $25,000 x [(1 - 1/(1 + 10%)^10)/10%] / (1 + 10%)^10 = $98,855.69
PV of project cost = $400,000

Total present value of cash flows = $379,073.51 + $98,855.69 = $477,929.20

We can now solve for the IRR by finding the discount rate that makes the present value of all cash flows equal to the initial cost:

$477,929.20 = $400,000 / (1 + IRR)^20

IRR = 8.53%

Therefore, the answer is C) 8.53%. This IRR is greater than the required rate of return of 10%, indicating that the project is expected to generate a return higher than the company's minimum acceptable rate of return.

Calculate the IRR of a 20-Year Project with a Cost