Question

The IRR evaluation method assumes that cash flows from the project are reinvested at the same rate equal to the IRR. However, in reality the reinvested cash flows may not necessarily generate a return equal to the IRR. Thus, the modified IRR approach makes a more reasonable assumption other than the project’s IRR.

Consider the following situation:

Fuzzy Button Clothing Company is analyzing a project that requires an initial investment of $2,750,000. The project’s expected cash flows are:

Year	Cash Flow
Year 1	$300,000
Year 2	–100,000
Year 3	475,000
Year 4	400,000

Fuzzy Button Clothing Company’s WACC is 8%, and the project has the same risk as the firm’s average project. Calculate this project’s modified internal rate of return (MIRR):

a. -17.86%

b. 24.02%

c. 22.93%

d. 18.56%

If Fuzzy Button Clothing Company’s managers select projects based on the MIRR criterion, they should___________ this independent project.

a. Accept

b. Reject

Which of the following statements about the relationship between the IRR and the MIRR is correct?

a. A typical firm’s IRR will be less than its MIRR.

b. A typical firm’s IRR will be equal to its MIRR.

c. A typical firm’s IRR will be greater than its MIRR.

Answer 1

Modified Internal Rate of Return is the rate at which the Net Present value of the Project (discounted at WACC) equates to the Intial Investment. Meaning thereby, MIRR is the rate at which the cashflows generated out of the project are invested in the project and the intial cost is financed at the cost of capital of the firm.

Calcluation of Net Present Value of the project at discount rate of 8% (WACC):

Year	Cash Flows	Discounting Factor (8%)	Present Value
0	- 2,750,000	1	-27,50,000
1	300,000	0.9259	277,770
2	100,000	0.8573	85,730
3	475,000	0.7938	377,055
4	400,000	0.7350	294,000
NPV			-1,715,445

As the project has negative NPV of $ 1,715,445, it would be rejected in the first instance.

a) Calculation of MIRR for the project:

MIRR is the rate at which the NPV of the project equates the intial outflow.

Intial Outflow = NPV of the project / (1 + MIRR)n

-2,750,000 = -1,715,445 / (1 + r)4

MIRR = -17.86%

b) Whether to accept or reject the project?

As the MIRR of the project is negative, the project shall be rejected. (also MIRR < WACC)

c) Which of the given statements is true about the relationship between IRR and MIRR is correct?

A typical firm's IRR will be greater than its MIRR is correct statement.

IRR assumes that the positive cash flows are invested at the IRR during the tenure of the project. Whereas, MIRR assumes that the cash flows are invested at cost of capital of the project. MIRR takes into account the more conservative assumption, thereby resulting into MIRR being lower than IRR.