Question

A project has the following cash flows:

Year 0: -$11,300
Year 1: $4,870
Year 2: $7,000
Year 3: $4,480
Year 4: -$1,720
Assuming the appropriate interest rate is 7 percent, what is the MIRR for this project using the discounting approach?

Answer 1

The Modified Internal Rate of Return (MIRR) is a financial indicator used to evaluate an investment project. It takes into account the timing and magnitude of both cash inflows and outflows. To calculate the MIRR using the discounting approach, first determine the present value (PV) of each cash flow using the appropriate interest rate. Then, calculate the future value (FV) of all the positive cash flows at the end of the project's life. Finally, calculate the IRR of the project's cash inflows and outflows. The MIRR is the discount rate that equates the PV of all cash inflows with the FV of all cash outflows.

Step-by-step explanation:

The Modified Internal Rate of Return (MIRR) is a financial indicator used to evaluate an investment project. It takes into account the timing and magnitude of both cash inflows and outflows. To calculate the MIRR using the discounting approach, first determine the present value (PV) of each cash flow using the appropriate interest rate. Then, calculate the future value (FV) of all the positive cash flows at the end of the project's life. Finally, calculate the IRR of the project's cash inflows and outflows. The MIRR is the discount rate that equates the PV of all cash inflows with the FV of all cash outflows.

In this case, the cash flows for the project are as follows:

1. Year 0: -$11,300
2. Year 1: $4,870
3. Year 2: $7,000
4. Year 3: $4,480
5. Year 4: -$1,720

Using a discount rate of 7 percent, we can calculate the PV of each cash flow:

1. Year 0: PV = -$11,300 / (1 + 0.07)^0 = -$11,300
2. Year 1: PV = $4,870 / (1 + 0.07)^1 = $4,548.13
3. Year 2: PV = $7,000 / (1 + 0.07)^2 = $6,123.56
4. Year 3: PV = $4,480 / (1 + 0.07)^3 = $3,759.32
5. Year 4: PV = -$1,720 / (1 + 0.07)^4 = -$1,445.32

To calculate the FV of all the positive cash flows, sum up the PV of each positive cash flow:

FV = $4,548.13 + $6,123.56 + $3,759.32 = $14,430.01

Finally, calculate the IRR of the cash inflows and outflows:

IRR = (Present Value of Cash Inflows / FV of Cash Outflows)^(1 / Number of Years) - 1

IRR = ($4,548.13 + $6,123.56 + $3,759.32 + (-$11,300))^(1 / 4) - 1

IRR = ($3,130.01)^(0.25) - 1

IRR = 0.07 = 7%

Therefore, the MIRR for this project using the discounting approach and a discount rate of 7 percent is 7%.