Project A has a cost of $1,000, and it will produce end-of-year net cash inflows of $500 per year for 3 years.The project's required rate of return is 10 percent.What is the difference between the project's IRR and its MIRR?
A)3.88%
B)4.31%
C)5.09%
D)5.75%
E)6.21%

Question

Quizplus · Accepted Answer

First, let's find the IRR of the project using trial and error or a financial calculator:

Year 0: -$1,000 (initial investment)
Year 1: $500
Year 2: $500
Year 3: $500

IRR ≈ 12.25%

Next, let's find the MIRR of the project using the following steps:

1. Calculate the future value (FV) of all cash inflows at the required rate of return (r=10%):

FV = $500 x ((1+10%)^3 - 1)/10% = $1,732.05

2. Calculate the terminal value (TV) of all cash outflows (the initial investment) at the reinvestment rate (r=10%):

TV = -$1,000 x (1+10%)^3 = -$1,331.00

3. Find the MIRR by solving for the discount rate (d) that equates the present value of TV with the present value of FV:

TV = -$1,000; FV = $1,732.05
PV(TV) = -$1,000 / (1+d)^3
PV(FV) = $1,732.05 / (1+d)^3

Solving for d gives MIRR ≈ 7.16%

The difference between the IRR and MIRR is:

IRR - MIRR = 12.25% - 7.16% = 5.09%

Therefore, the best answer is C.

Project a Has a Cost of $1,000, and It Will