Chapter 5: Net present value and other investment rules

Corporate Finance

Ross, Westerfield, and Jaffe

Outline

1. Net present value (NPV)

2. The payback period method

3. The discounted payback period method

4. The Internal rate of return (IRR)

5. The profitability index

Good decision criteria

Does the rule take the time value of money into consideration?

Does the rule adjust for risk? Does the rule tell us whether and by how

much the project add value to the firm?

A proposed project

Your company is looking at a new project that has the following cash flows.

Year 0: initial cost, C0 = $100,000.

Year 1: CF1 = $30,000.

Year 2: CF2 = $50,000.

Year 3: CF3 = $60,000. The applicable discount rate is 10%.

1st method: the NPV rule

NPV = PV – C0: the difference between the present value of the investment’s future net cash flows, i.e., benefits, and its initial cost.

Ideas: (1) an investment is worth undertaking if it creates value for its owners, and (2) an investment creates value if it worth more than it costs within the time value of money framework (Chapter 4).

Decision rule

If NPV > = 0, accept the project. If NPV < 0, reject the project. A positive NPV suggests that the project is expected

to add value to the firm, and the project should improve shareholders’ wealth.

Because the goal of financial management is to increase shareholders’ wealth, NPV is a good measure of how well this project will meet this goal.

Project NPV

Year CF C(0) PV NPV0 100000 136741 30000 27272.7 >02 50000 41322.3 Accept!3 60000 45078.9

113674Discount rate 0.1

Judging the NPV rule

Does the NPV rule take the time value of money into consideration?

Does the NPV rule adjust for risk? Does the NPV rule tell us whether and by

how much the project add value to the firm?

Finally, they listen

CFOs are using what academics consider better measures in their capital-budgeting analysis. According to a recent survey, more than 85 percent say they use net present value (NPV) analysis in at least three out of four decisions…."Finance textbooks have taught for years that NPV is superior, but this is the first known survey to show it's the preferred tool," says co-author Patricia A. Ryan, a professor of corporate finance at Colorado State University.

Source: CFO.com.

2nd method: payback period

Payback period: the amount of time required for an investment to generate after-tax cash flows sufficient to recover its initial cost.

Decision rule

An investment is accepted (rejected), if payback period < (>) some specified number of time period.

The cutoff is arbitrarily chosen by the manager or the entrepreneur.

Project payback period

Year CF C(0) Accu. CF $ to be recoved Payback period0 1000001 30000 30000 700002 50000 80000 20000 >23 60000 140000 -40000 <3

To be exact,2+(20000/60000)2.33 years

The decision

The payback period is longer than 2 years and shorter than 3 years.

If the cutoff is 2 years, we’d reject the project. If the cutoff is 3 years, we’d accept the

project.

Judging the payback period rule

Does the payback period rule take the time value of money into consideration?

Does the payback period rule adjust for risk? Does the payback period rule tell us whether

and by how much the project add value to the firm?

The good and the bad

Advantage:– Easy to understand and communicate.

Disadvantages:– Ignores the time value of money.– Fail to consider the riskness of the project, no i.– Requires an arbitrary cutoff point.– Ignores cash flows beyond the cutoff.– Biased against long-term projects, such as R&Ds.

3rd method: discounted payback period

Discounted payback period: the length of time required for an investment’s discounted cash flows to equal its initial cost.

Decision rule

An investment is accepted (rejected), if discounted payback period < (>) some specified number of time period.

Again, the cutoff is arbitrarily chosen.

Project discounted payback period

Year CF C(0) PV Accu. PV To be recovered Dis. Payback0 1000001 30000 27272.7 27272.727 72727.272732 50000 41322.3 68595.041 31404.95868 >23 60000 45078.9 113673.93 -13673.92938 <3

Discount rate 0.1 2+ (31404/45079)

2.70 years

The decision

The discounted payback period is longer than 2 years and shorter than 3 years.

If the cutoff is 2 years, we’d reject the project. If the cutoff is 3 years, we’d accept the

project.

Judging discounted payback period

Does the payback period rule take the time value of money into consideration?

Does the payback period rule adjust for risk? Does the payback period rule tell us whether

and by how much the project add value to the firm?

The good and the bad

Advantage:– Still fairly easy to understand and communicate.– Take TVM into consideration.

Disadvantages:– Requires an arbitrary cutoff point.– Ignores cash flows beyond the cutoff.– Biased against long-term projects, such as R&Ds.

4th method: IRR

IRR: the discounted rate that makes the NPV of an investment zero.

Decision rule

An investment is accepted (rejected), if the IRR > (<) the required rate.

Project IRR

Year CF C(0) IRR-CF IRR PV0 100000 -100000 17%1 30000 30000 256862 50000 50000 366543 60000 60000 37660

100000

The decision

The computed IRR is 17%, which is higher than the 10% required rate. Thus, we accept the project.

Judging the IRR

Does the IRR rule take the time value of money into consideration?

Does the IRR rule adjust for risk? Does the IRR rule tell us whether and by how

much the project add value to the firm?

NPV vs. IRR

For most projects, NPV and IRR lead to the same conclusion.

Practitioners really like to use IRR because this measure gives practitioners a good idea about at what rate they are able to earn. Knowing a return is intuitively appealing.

IRR provides a measure about the value of a project to someone who doesn’t know all the estimation details.

If the IRR is high enough, one may not need to estimate the required return at all.

A warning

Typical IRR calculations build in reinvestment assumptions.

This makes projects look better than they actually are.

But, non-unique IRR solutions

Year Costs CF IRR-CF IRR But, how about: NPV0 100 -100 10% 20% -1001 230 230 191.672 132 -132 -91.67

0

Lesson

Before you use your IRR estimate, always verify the result with the NPV result.

In real life, NPV and IRR are the 2 most popular decision rules used by modern (big) U.S. corporations. And, they tend to be used together.

5th method: the profitability index

Profitability index (PI) = PV / C0. Often used for government or other non-for-

profit investments. Measures the benefit per unit cost, based on

the time value of money. A profitability index of 1.2 suggests that for

every $1 of initial investment, we create an additional $0.20 in value.

Decision rule

For a project, we accept the project only if PI > 1.

For mutually exclusive projects, practitioners sometimes choose the project with the highest PI. However, this approach is problematic.

If there is no capital constraint, one should choose the project with the highest NPV from the mutually exclusive pool.

Project PI

Year CF C(0) PV PI0 100000 1.13671 30000 27272.73 >12 50000 41322.31 Accept!3 60000 45078.89

113673.9Discount rate 0.1

The good and the bad

Advantages:– Related to NPV, generally leading to identical

decisions.– Easy to understand and communicate.

Disadvantage:– Should not be used for making mutually exclusive

decisions.

Real options

So far, you know that NPV is the best criterion; IRR is another almost equally good and important one.

But these analyses mainly address independent projects whose acceptance or rejection has no implications on the acceptance or rejection of other projects.

When projects have (real) options, NPV and IRR may perform poorly.

An example: timing option

Suppose that the NPV for a developer to built a building on a vacant land now is positive. The simple version of the NPV rule would lead to the conclusion that the developer should build the building now.

In real life, the developer may choose to wait. For instance, the developer may believe that this is not the best timing (although the NPV is positive). The developer may want to wait for another few years when the real estate market is stronger to realize a much larger NPV at that time.

More real options

In real life, there are several more types of real options that will make capital budgeting a even more complex task.

Chapter 7, pp. 221-224 has an introduction to another two types of real options: (1) the option to expand, and (2) the option to abandon.

I bet these will be treated in your intermediate corporate finance course.

Assignment

The ABC Co. is considering expanding its production capacity by 30%. The expansion will require $20 million initially. The net cash flow from this expansion is $4 million for the first year. The net cash flows are expected to grow at a rate of 5% each year for 4 years, but then slow to a 3% growth thereafter. The ABC Co. estimates that the cost of capital (i.e., required return) for this expansion is 8%.

Task: write a report answering (1) should ABC Co. expand? Why? (2) If the market interest rate increases and thus the cost of capital for this expansion increases to 12%, would your recommendation change?

Due in a week.

End-of-chapter

Concept questions: 1-11, 13, and 14. Questions and problems: 1-4, 7-9, 12, 14(a),

14(b), 15, 16(a), 16(b), 17, 18(a), and 18(b).