# MIRR and IRR

I am an investor in a company. We are considering a project which involves opening a new store at a cost of $10,000,000 at t = 0. The project is expected to have operating cash flows of $5,000,000 at the end of each of the next 4 years. However, the facility will have to be repaired at a cost of $6,000,000 at the end of the second year. Thus, at the end of Year 2 there will be a $5,000,000 operating cash inflow and an outflow of -$6,000,000 for repairs. The company's cost of capital is 15 percent. What is the difference between the project's MIRR and its regular IRR?

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#### Solution Preview

The first thing to do is to put down the cash flows.

Year 0 Cash outflow = -10,000,000

Year 1 Cash inflow = 5,000,000

Year 2 Cash inflow = 5,000,000 and cash outflow = 6,000,000 and so the net in -1,000,000

Year 3 Cash inflow = 5,000,000

Year 4 Cash inflow = 5,000,000

We can use excel to calculate the IRR and MIRR and find the difference. Using excel the IRR comes to 13.78% and MIRR comes to 14.29% and the difference is 0.51%.

If you wish to do manually

IRR is the rate that will make the PV of cash flows equal ...

#### Solution Summary

The solution explains how to calculate the MIRR and IRR for a project.

10 Finance multiple choice questions: project payback period, IRR, WACC, MIRR, NPV

1. Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows.

a. The longer a project's payback period, the more desirable the project is normally considered to be by this criterion.

b. One drawback of the payback criterion for evaluating projects is that this method does not properly account for the time value of money.

c. If a project's payback is positive, then the project should be rejected because it must have a negative NPV.

d. The regular payback ignores cash flows beyond the payback period, but the discounted payback method overcomes this problem.

e. If a company uses the same payback requirement to evaluate all projects, say it requires a payback of 4 years or less, then the company will tend to reject projects with relatively short lives and accept long-lived projects, and this will cause its risk to increase over time.

2. Assume a project has normal cash flows. All else equal, which of the following statements is CORRECT?

a. The project's IRR increases as the WACC declines.

b. The project's NPV increases as the WACC declines.

c. The project's MIRR is unaffected by changes in the WACC.

d. The project's regular payback increases as the WACC declines.

e. The project's discounted payback increases as the WACC declines.

3. Which of the following statements is CORRECT?

a. For a project to have more than one IRR, then both IRRs must be greater than the WACC.

b. If two projects are mutually exclusive, then they are likely to have multiple IRRs.

c. If a project is independent, then it cannot have multiple IRRs.

d. Multiple IRRs can only occur if the signs of the cash flows change more than once.

e. If a project has two IRRs, then the smaller one is the one that is most relevant, and it should be accepted and relied upon.

4. Which of the following statements is CORRECT?

a. The MIRR and NPV decision criteria can never conflict.

b. The IRR method can never be subject to the multiple IRR problem, while the MIRR method can be.

c. One reason some people prefer the MIRR to the regular IRR is that the MIRR is based on what is generally a more reasonable assumption about the reinvestment rate than the regular IRR.

d. The higher the WACC, the shorter the discounted payback period.

e. The MIRR method assumes that cash flows are reinvested at the crossover rate.

5. Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows.

a. A project's MIRR is always greater than its regular IRR.

b. A project's MIRR is always less than its regular IRR.

c. If a project's IRR is greater than its WACC, then the MIRR will be less than the IRR.

d. If a project's IRR is greater than its WACC, then the MIRR will be greater than the IRR.

e. To find a project's MIRR, we compound cash inflows at the IRR and then discount the terminal value back to t = 0 at the WACC.

6. Edmondson Electric Systems is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that if a project's projected NPV is negative, it should be rejected.

WACC:

10.00%

Year:

0

1

2

3

Cash flows:

-$1,000

$500

$500

$500

a. $243.43

b. $255.60

c. $268.38

d. $281.80

e. $295.89

7. Tucker Corp. is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be negative, in which case it will be rejected.

Year:

0

1

2

3

Cash flows:

-$1,000

$450

$450

$450

a. 15.82%

b. 16.65%

c. 17.48%

d. 18.36%

e. 19.27%

8. ZumBahlen Inc. is considering the following mutually exclusive projects:

Project A

Project B

Year

Cash Flow

0

-$5,000

-$5,000

1

200

3,000

2

800

3,000

3

3,000

800

4

5,000

200

At what cost of capital will the net present value of the two projects be the same? (That is, what is the "crossover" rate?)

a. 15.68%

b. 16.15%

c. 16.74%

d. 17.33%

e. 17.80%

9. Suppose Tapley Corporation uses a WACC of 8% for below-average risk projects, 10% for average-risk projects, and 12% for above-average risk projects. Which of the following independent projects should Tapley accept, assuming that the company uses the NPV method when choosing projects?

a. Project A, which has average risk and an IRR = 9%.

b. Project B, which has below-average risk and an IRR = 8.5%.

c. Project C, which has above-average risk and an IRR = 11%.

d. Without information about the projects' NPVs we cannot determine which one or ones should be accepted.

e. All of the projects should be accepted.

10. Langston Labs has an overall (composite) WACC of 10%, which reflects the cost of capital for its average asset. Its assets vary widely in risk, and Langston evaluates low-risk projects with a WACC of 8%, average projects at 10%, and high-risk projects at 12%. The company is considering the following projects:

Project

Risk

Expected Return

A. High

15%

B.

Average

12

C

High

11

D

Low

9

E

Low

6

Which set of projects would maximize shareholder wealth?

a.

A and B.

b.

A, B, and C.

c.

A, B, and D.

d.

A, B, C, and D.

e.

A, B, C, D, and E.

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