Question

Project A requires an initial outlay at t = 0 of $2,000, and its cash flows are the same in Years 1 through 10. Its IRR is 13%, and its WACC is 8%. What is the project's MIRR? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

To calculate the MIRR, we first need to find the terminal value of the cash flows at the end of year 10 using the IRR:

PV = -$2,000

PMT = C

N = 10

IRR = 13%

Using the formula for the present value of an annuity, we can solve for C:

PV = C * [(1 - (1 + r)^-n) / r]

$2,000 = C * [(1 - (1 + 0.13)^-10) / 0.13]

C = $383.14

Now we can calculate the future value of the cash flows at the end of year 10 using the WACC as the discount rate:

PV = -$2,000

PMT = $383.14

N = 10

WACC = 8%

Using the formula for the future value of an annuity, we can solve for FV:

PV = PMT * [(1 - (1 + r)^-n) / r] + FV / (1 + r)^n

-$2,000 = $383.14 * [(1 - (1 + 0.08)^-10) / 0.08] + FV / (1 + 0.08)^10

FV = $4,353.34

Now we can calculate the MIRR using the formula:

MIRR = [(FV / PV)^(1/n)] - 1

MIRR = [($4,353.34 / $2,000)^(1/10)] - 1

MIRR = 0.1165 or 11.65%

Therefore, the project's MIRR is 11.65%.