Houston Inc. is considering a project which involves building a new refrigerated warehouse which will cost $7,000,000 at t = 0 and which is expected to have operating cash flows of $500,000 at the end of each of the next 20 years. However, repairs which will cost $1,000,000 must be incurred at the end of the 10th year. Thus, at the end of Year 10 there will be a $500,000 operating cash inflow and an outflow of -$1,000,000 for repairs. If Houston's cost of capital is 12 percent, what is the project's MIRR? (Hint: Think carefully about the MIRR equation and the treatment of cash outflows.)
A) 7.75%
B) 8.29%
C) 9.81%
D) 11.45%
E) 12.33%

Question

Quizplus · Accepted Answer

Firstly, calculate the present value of the operating cash flows (OCF) without repairs using the formula:
PV of OCF = OCF × ((1 - (1 + r)^-n)/r)
where OCF = $500,000, r = 12%, and n = 20.
PV of OCF = $500,000 × ((1 - (1+0.12)^-20)/0.12) = $3,456,163.44

Next, calculate the present value of the repair cost using the same formula, but with n = 10 since the repairs are due at the end of Year 10:
PV of repair cost = -$1,000,000 × ((1 - (1+0.12)^-10)/0.12) = -$320,713.28

Then, calculate the future value (FV) of the remaining cash flows including the repair cost as a negative cash outflow at the end of Year 10 using the formula:
FV = PV × (1+r)^n
where PV = $3,456,163.44 - $320,713.28 = $3,135,450.16, r = 12%, and n = 10.
FV = $3,135,450.16 × (1+0.12)^10 = $8,483,310.25

Now, calculate the MIRR using the formula:
MIRR = ((FV/PV)^(1/n))-1
where PV = -$7,000,000, FV = $8,483,310.25, and n = 20 since there are 20 total periods.
MIRR = ((8,483,310.25/-7,000,000)^(1/20))-1 = 8.29%

Therefore, the project's MIRR is 8.29%, which is closest to answer choice B.