Houston Inc.is considering a project which involves building a new refrigerated warehouse which will cost R7,000,000 at t = 0 and which is expected to have operating cash flows of R500,000 at the end of each of the next 20 years.However, repairs which will cost R1,000,000 must be incurred at the end of the 10th year.Thus, at the end of Year 10 there will be a R500,000 operating cash inflow and an outflow of R1,000,000 for repairs.If Houston's required rate of return is 12 percent, what is the project's MIRR? (Hint: Think carefully about the MIRR equation and the treatment of cash outflows.)

Question

Quizplus · Accepted Answer

The MIRR (Modified Internal Rate of Return) is the discount rate that equates the present value of cash inflows to the future value of cash outflows. In this case, we have both positive and negative cash flows, so we need to use the MIRR equation to determine the rate that makes the sum of the present value of cash inflows and the terminal value of the cash outflows equal to the initial investment.

Step 1: Calculate the present value of cash inflows using the PV formula:
PV = CF / (1+r)^n

n = 1 to 9: PV = 500,000 / (1+0.12)^n = 500,000 / 1.12^n
n = 10: PV = (500,000 - 1,000,000) / (1+0.12)^10 = -148,627.12
n = 11 to 20: PV = 500,000 / (1+0.12)^n = 500,000 / 1.12^(n-10)

Total PV of cash inflows = PV1 + PV2 + PV3...+ PV20 = 4,761,073.23

Step 2: Calculate the terminal value of the cash outflows at the end of Year 20:
TV = CF / r = 1,000,000 / 0.12 = 8,333,333.33

Step 3: Calculate the MIRR by solving for r in the following equation:
PV of inflows + TV of outflows = PV of outflows

4,761,073.23 + TV = 7,000,000
TV = 2,238,926.77

4,761,073.23 + 2,238,926.77 = 7,000,000 / (1+r)^20

r = 8.29%

Therefore, the MIRR for the project is 8.29%. Option B is the correct answer.