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Chapter 26: Q27RQ (page 1464)

How is IRR calculated with unequal net cash inflows?

Short Answer

Expert verified

The after-tax cash flow for each period at time t is divided by some rate, r. The initial investment is then subtracted from the total of these discounted cash flows, yielding the present NPV. It is important to "reverse engineer" the value of r needed to make the NPV equal zero in order to determine the IRR.

Step by step solution

01

Example

years

Net PV Present

Cash factor value

Inflow (i=16%)

Net PV Present

Cash factor value

Inflow (i=18%)

PV of each year’s inflow:

1 (n=1)

2 (n=2)

3 (n=3)

4 (n=4)

5 (n=5)

Total PV of cash inflows 0 Initial investment

NPV

$500,000 0.862 $431,000

350,000 0.743 260,000

300,000 0.641 192,300

250,000 0.552 138,000

40,000 0.476 19,000

(1,040,390)

1,000,000)

$40,390

$500,000 0.847 $431,000

350,000 0.718 251,300

300,000 0.609 182,700

250,000 0.516 129,000

40,000 0.437 17,000

(1,003,980)

(1,000,000)

$3,980

In this example for 1,000,000 initial investment in a project and these irregular cashflows we can conclude that IRR for this project is 18%.

02

IRR advantage over NAV

NPV will be negative when IRR <cost of capital. Benefits: Since this strategy is expressed in percentage form, it is simple for financial managers to compare it to the necessary cost of capital.

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Most popular questions from this chapter

Using ARR to make capital investment decisions Refer to the Henry Hardware information in Exercise E26-20. Assume the project has no residual value. Compute the ARR for the investment. Round to two places.

Henry Hardware is adding a new product line that will require an investment of \(1,512,000. Managers estimate that this investment will have a 10-year life and generate net cash inflows of \)310,000 the first year, \(270,000 the second year, and \)240,000 each year thereafter for eight years.

You are planning for a very early retirement. You would like to retire at age 40 and have enough money saved to be able to withdraw \(215,000 per year for the next 40 years (based on family history, you think you will live to age 80). You plan to save by making 10 equal annual installments (from age 30 to age 40) into a fairly risky investment fund that you expect will earn 10% per year. You will leave the money in this fund until it is completely depleted when you are 80 years old.

Requirements

1. How much money must you accumulate by retirement to make your plan work? (Hint:Find the present value of the \)215,000 withdrawals.)

2. How does this amount compare to the total amount you will withdraw from the investment during retirement? How can these numbers be so different?

Suppose Hunter Valley is deciding whether to purchase new accounting software. The payback for the $30,050 software package is two years, and the software’s expected life is three years. Hunter Valley’s required rate of return for this type of project is 10.0%. Assuming equal yearly cash flows, what are the expected annual net cash savings from the new software?

S26-6 Using the ARR method to make capital investment decisions Refer to the Hunter Valley Snow Park Lodge expansion project in Short Exercise S26-4. Calculate the ARR. Round to two decimal places.

Refer to Short Exercise S26-4. Continue to assume that the expansion has no residual value. What is the project’s IRR? Is the investment attractive? Why or why not?
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