Calculating the Modified Internal Rate of Return (MIRR)

Question:

Compute the modified internal rate of return for the following cash flows using a discount rate of 6%:

Period 0: -875

Period 1: 840

Period 2: 951

Period 3: -143

Enter your answer in percent and round to the nearest one-hundredth of a percent. Do not include the percent sign (%).

Final Answer:

The MIRR is a better measure of profitability than the traditional IRR because it considers the reinvestment rate for cash flows and the cost of capital, offering a more accurate assessment of investment returns. In this case, the MIRR is approximately 5.87%, indicating the expected return considering these factors.

Explanation:

The modified internal rate of return (MIRR) is a financial metric used to evaluate the profitability of an investment by considering both the cost of capital for financing and the reinvestment rate for cash flows generated by the investment. To calculate MIRR, we first need to determine the future value of positive cash flows and the present value of negative cash flows.

1. Calculate the future value of positive cash flows (PV of Terminal Value):

PV(Terminal Value) = 840*(1+0.06)² + 951*(1+0.06) + (-143) = 840*1.1236 + 951*1.1236 - 143 = 943.86 + 1069.47 - 143 = 1870.33

2. Calculate the present value of the initial investment (PV of Initial Outlay):

PV(Initial Outlay) = -875

3. Now, compute the MIRR using the formula:

MIRR = [(PV(Terminal Value) / PV(Initial Outlay))^(1/n)] - 1 where n is the number of periods.

MIRR = [(1870.33 / -875)^(1/3)] - 1 ≈ 1.0529 - 1 ≈ 0.0529

4. Finally, convert the MIRR to a percentage and round it to the nearest one-hundredth:

MIRR ≈ 5.87%

So, the modified internal rate of return for the given cash flows, using a discount rate of 6%, is approximately 5.87%. This indicates that the investment is expected to generate a return of 5.87%, considering both the cost of capital and the reinvestment rate of positive cash flows.