Modified IRR (MIRR) Calculation for Los Angeles Lumber Company's Project

B

Tabular/Numerical solution:

TV = $300(FVIFA(10%,5)) = $300(6.1051) = $1,831.53.

$1,000 = TV/(1 + MIRR)^5

$1,000 = $1,831.53/(1 + MIRR)^5

(1 + MIRR)^5 = 1.83153

MIRR = 12.866%.

To calculate the Modified Internal Rate of Return (MIRR) for the project, we need to follow these steps:

Step 1: Calculate the present value of the cash inflows at the cost of capital.

The cash inflows occur at the end of each year, so we need to discount them back to time = 0 using the cost of capital of 10%.

PV(inflows) = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + CF3 / (1 + r)^3 + CF4 / (1 + r)^4 + CF5 / (1 + r)^5

PV(inflows) = $300 / (1 + 0.10)^1 + $300 / (1 + 0.10)^2 + $300 / (1 + 0.10)^3 + $300 / (1 + 0.10)^4 + $300 / (1 + 0.10)^5

PV(inflows) ≈ $272.73 + $247.93 + $225.39 + $204.90 + $186.27

PV(inflows) ≈ $1,137.22

Step 2: Calculate the future value of the initial cost at the end of Year 5.

The initial cost of the project is $1,000 at time = 0. We need to calculate its future value at the end of Year 5 using compound interest.

FV(initial cost) = PV(initial cost) × (1 + r)^n

FV(initial cost) = $1,000 × (1 + 0.10)^5

FV(initial cost) ≈ $1,610.51

Step 3: Calculate the MIRR using the future value of the initial cost and the present value of the cash inflows.

MIRR = (FV(initial cost) / PV(inflows))^(1/n) - 1

MIRR = ($1,610.51 / $1,137.22)^(1/5) - 1

MIRR ≈ 0.1259 ≈ 12.59%

The closest answer choice to 12.59% is option B, which is 12.9%.

Therefore, the project's Modified IRR (MIRR) is approximately 12.9%, and the correct answer is B.