NPV and Other Investment Criteria

P.V. Viswanath

For an Introductory Course in Finance

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Key Concepts and Skills

The NPV Rule Understand the payback rule and its shortcomings Understand accounting rates of return and their

problems Understand the internal rate of return and its

strengths and weaknesses Understand the net present value rule and why it is

the best decision criteria

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Chapter Outline

Net Present Value The Payback Rule The Average Accounting Return The Internal Rate of Return The Profitability Index The Practice of Capital Budgeting

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Sources of Investment Ideas

Three categories of projects: New Products Cost Reduction Replacement of Existing assets

Sources of Project Ideas: Existing customers R&D Department Competition Employees

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Good Decision Criteria

We need to ask ourselves the following questions when evaluating decision criteria Does the decision rule adjust for the time value of

money? Does the decision rule adjust for risk? Does the decision rule provide information on whether

we are creating value for the firm? The Net Present Value rule satisfies these three

criteria, and is, therefore, the preferred decision rule.

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Net Present Value

The difference between the market value of a project and its cost

How much value is created from undertaking an investment? The first step is to estimate the expected future cash flows. The second step is to estimate the required return for projects of this

risk level. The third step is to find the present value of the cash flows and

subtract the initial investment.

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NPV Decision Rule

If the NPV is positive, accept the project A positive NPV means that the project is expected to add

value to the firm and will therefore increase the wealth of the owners.

Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.

NPV is an additive measure: If there are two projects A and B, then NPV(A and B) = NPV(A) +

NPV(B).

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Project Example Information

You are looking at a new project and you have estimated the following cash flows: Year 0:CF = -165,000 Year 1:CF = 63,120; NI = 13,620 Year 2:70,800; NI = 3,300 Year 3:91,080; NI = 29,100 Average Book Value = 72,000

Your required return for assets of this risk is 12%.

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Computing NPV for the Project

Using the formulas: NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 –

165,000 = 12,627.42

Do we accept or reject the project?

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Estimating Project Cashflows

Before the NPV decision rule can be applied, we need project cashflow forecasts for each year.

These are built up from estimates of incremental revenues and associated project costs.

Cash Flow = Revenues – Fixed Costs – Variable Costs – Taxes – Long-term Investment Outlays – Changes in Working Capital

An equivalent formula is: Cashflow = Net Income + Noncash expenses (that were included in

the Net Income computation) +(1-tax rate)Interest – Long-term Investment Outlays – Changes in Working Capital

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Cost of Capital

The cost of capital is the opportunity cost of capital for the firm’s investors and is used to discount the project cashflows.

The cost of capital is also called the WACC and is computed as the firm’s after-tax weighted cost of debt and equity

WACC = (E/V)Re + (D/V)Rd(1-), where E, D are market values of the firm’s equity and debt; V = D+E is the

total value of the firm; and is the firm’s corporate tax rate The cost of debt Rd is multiplied by (1-) because interest payments on

debt are deductible for tax purposes. Since the tax advantage of debt is taken into account in the

denominator, we do not include it in the numerator as well, thus avoiding double counting.

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Sensitivity Analysis

Since the firm will not know the future level of output, or the other cost parameters with certainty, it is important to know how the value of the project changes as these parameters are varied.

This is called sensitivity analysis If the final decision on the project is very sensitive to a

particular parameter, it would be more valuable to expend resources on obtaining more precise estimates of that parameter.

The break-even point is the point of indifference between accepting and rejecting the project.

With respect to sales, this is the number of units that have to be sold in order for the project to be in the black.

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Issues to keep in mind

Sunk costs should be ignored. These costs have already been incurred and cannot be undone whatever the decision that is going to be currently taken.

Only incremental cashflows should be considered. Hence if a machine is to be replaced by a new machine, only the additional flows implied by the new machine should be considered to make the decision of whether to buy the new machine.

Only cashflows must be considered; allocated expenses, such as depreciation are to be ignored because they reflect capital expenditures already made and are a kind of sunk cost.

Of course, if there are any tax implications related to depreciation computations, these must be taken into account.

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Projects with Unequal Lives

Suppose we have to choose between the following two machines, L and S to replace an existing machine.

Machine L costs $1000 and needs to be replaced once every four years, while machine S costs $600 a unit and must be replaced every two years.

The flows C1-C4 represent cost savings over the current machine, for the next four years.

The discount rate is 10 percent. Project C0 C1 C2 C3 C4 NPV----------------------------------------------------------------------------L -1000 500 500 500 500 584.93S -600 500 500 267.77

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Projects with Unequal Lives

Treating this problem as a simple present value problem, we would choose machine L, since the present value of L is greater than that of S.

However, choosing S gives us additional flexibility because we are not locked into a four-year cycle. Perhaps better alternatives may be available in year 3.

Furthermore, the present comparison is not appropriate because even if no better alternatives are available because we have not considered the tax savings in years 3 and 4 if we go with machine S – we can always buy a second S-type machine at the end of year two!

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Projects with Unequal Lives

Consider the modified alternatives:

Project C0 C1 C2 C3 C4 NPV-------------------------------------------------------------------------------------------L -1000 500 500 500 500 584.93S -600 500 500 267.77Second S -600 500 500 220.66Combination S -600 500 -100 500 500 488.43

We see that the combination of two S-type machines are not as disadvantageous compared to one L-type machine, though the L-type machine still wins out.

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Projects with Unequal Lives

Alternatively, we can convert the flows for the machines into equivalent equal annual flows.

Thus, we find X, such that the present value of L and L1 are equal.

Project C0 C1 C2 C3 C4 NPV----------------------------------------------------------------------------L -1000 500 500 500 500 584.93L1 0 X X X X 584.93

This is obtained as the solution to the equation PV(Annuity of $X for 4 years at 10%) = $584.93 and works out to $184.53

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Projects with Unequal Lives

Similarly, we convert the flows for machine S into equivalent equal annual flows.

Thus, we find X, such that the present value of S and S1 are equal.

Project C0 C1 C2 C3 C4 NPV----------------------------------------------------------------------------S -600 500 500 267.77S1 0 Y Y 267.77

This is obtained as the solution to the equation PV(Annuity of $Y for 2 years at 10%) = $267.77 and works out to $154.29

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Projects with Unequal Lives

The values X and Y can simply be compared and the project with the lower equivalent annual flow is chosen.

We are effectively making the choice betweenthe following two projects

Project C0 C1 C2 C3 C4----------------------------------------------------------------------------L1 0 X X X XS1 0 Y Y Y Y The advantage of this approach is that we don’t need to

explicitly construct two projects with the same project lives.

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Internal Rate of Return

This is the most important alternative to NPV It is often used in practice and is intuitively

appealing It is based entirely on the estimated cash flows and

is independent of interest rates found elsewhere

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IRR – Definition and Decision Rule

Definition: IRR is the return that makes the NPV = 0 Decision Rule: Accept the project if the IRR is

greater than the required return

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Computing IRR For The Project

If you do not have a financial calculator, then this becomes a trial and error process In the case of our problem, we can find that the IRR =

16.13%. Note that the IRR of 16.13% > the 12% required return

Do we accept or reject the project?

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NPV Profile

To understand what the IRR is, let us look at the NPV profile.

The NPV profile is the function that shows the NPV of the project for different discount rates.

Then, the IRR is simply the discount rate where the NPV profile intersects the X-axis.

That is, the discount rate for which the NPV is zero.

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NPV Profile For The Project

-20,000

-10,000

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

Discount Rate

NP

V

IRR = 16.13%

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Decision Criteria Test - IRR

Does the IRR rule account for the time value of money?

Does the IRR rule account for the risk of the cash flows?

Does the IRR rule provide an indication about the increase in value?

Should we consider the IRR rule for our primary decision criteria?

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Advantages of IRR

Knowing a return is intuitively appealing It is a simple way to communicate the value of a

project to someone who doesn’t know all the estimation details

If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task

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NPV Vs. IRR

NPV and IRR will generally give us the same decision

Exceptions Non-conventional cash flows – cash flow signs change

more than once Mutually exclusive projects

Initial investments are substantially different Timing of cash flows is substantially different

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IRR and Nonconventional Cash Flows

When the cash flows change sign more than once, there is more than one IRR

When you solve for IRR you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation

If you have more than one IRR, which one do you use to make your decision?

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Another Example – Nonconventional Cash Flows

Suppose an investment will cost $90,000 initially and will generate the following cash flows: Year 1: 132,000 Year 2: 100,000 Year 3: -150,000

The required return is 15%. Should we accept or reject the project?

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NPV Profile

($10,000.00)

($8,000.00)

($6,000.00)

($4,000.00)

($2,000.00)

$0.00

$2,000.00

$4,000.00

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

Discount Rate

NP

V

IRR = 10.11% and 42.66%

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Summary of Decision Rules

The NPV is positive at a required return of 15%, so you should Accept

If you compute the IRR, you could get an IRR of 10.11% which would tell you to Reject

You need to recognize that there are non-conventional cash flows and look at the NPV profile.

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IRR and Mutually Exclusive Projects

Mutually exclusive projects If you choose one, you can’t choose the other Example: You can choose to attend graduate school next

year at either Harvard or Stanford, but not both

Intuitively you would use the following decision rules: NPV – choose the project with the higher NPV IRR – choose the project with the higher IRR

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Example With Mutually Exclusive Projects

Period Project A Project B

0 -500 -400

1 325 325

2 325 200

IRR 19.43% 22.17%

NPV 64.05 60.74

The required return for both projects is 10%.

Which project should you accept and why?

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NPV Profiles

($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

$140.00

$160.00

0 0.05 0.1 0.15 0.2 0.25 0.3

Discount Rate

NP

V AB

IRR for A = 19.43%

IRR for B = 22.17%

Crossover Point = 11.8%

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Conflicts Between NPV and IRR

NPV directly measures the increase in value to the firm

Whenever there is a conflict between NPV and another decision rule, you should always use NPV

IRR is unreliable in the following situations Non-conventional cash flows Mutually exclusive projects

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Additional Decision Rules

In addition to the NPV and IRR rules, there are some other decision rules that are popularly used.

These are conceptually flawed, but have the advantage of being easy to compute and use.

They may, therefore, be used if a quick decision is necessary and not a lot is riding on the decision.

Two examples of these alternative decision rules are the payback rule and the accounting rate of return.

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Payback Period

How long does it take to get the initial cost back in a nominal sense?

Computation Estimate the cash flows Subtract the future cash flows from the initial cost until

the initial investment has been recovered

Decision Rule – Accept if the payback period is less than some preset limit

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Computing Payback For The Project

Assume we will accept the project if it pays back within two years. Year 1: 165,000 – 63,120 = 101,880 still to recover Year 2: 101,880 – 70,800 = 31,080 still to recover Year 3: 31,080 – 91,080 = -60,000 project pays back in

year 3

Do we accept or reject the project?

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Decision Criteria Test - Payback

Does the payback rule account for the time value of money?

Does the payback rule account for the risk of the cash flows?

Does the payback rule provide an indication about the increase in value?

Should we consider the payback rule for our primary decision criteria?

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Advantages and Disadvantages of Payback

Advantages Easy to understand Adjusts for uncertainty of

later cash flows Biased towards liquidity

Disadvantages Ignores the time value of money Requires an arbitrary cutoff point Ignores cash flows beyond the

cutoff date Biased against long-term projects,

such as research and development, and new projects

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Justifying the Payback Period Rule

We usually assume that the same discount rate is applied to all cash flows. Let di be the discount factor for a cash flow at time i, implied by a constant discount rate, r, where . Then di+1/di = 1+r, a constant. However, if the riskiness of successive cash flows is greater, then the ratio of discount factors would take into account the passage of time as well as this increased riskiness.

In such a case, the discount factor may drop off to zero more quickly than if the discount rate were constant. Given the simplicity of the payback method, it may be appropriate in such a situation.

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Justifying the Payback Period Rule

Discount factor

Timing of cash flow

0

Discount factor function implied bythe payback period rule

True discount factor function

Discount factor function implied bya constant discount rate

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Average Accounting Return

There are many different definitions for average accounting return

The one used in the book is: Average net income / average book value Note that the average book value depends on how the

asset is depreciated.Need to have a target cutoff rateDecision Rule: Accept the project if the AAR is

greater than a preset rate.

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Computing AAR For The Project

Assume we require an average accounting return of 25%

Average Net Income: (13,620 + 3,300 + 29,100) / 3 = 15,340

AAR = 15,340 / 72,000 = .213 = 21.3% Do we accept or reject the project?

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Decision Criteria Test - AAR

Does the AAR rule account for the time value of money?

Does the AAR rule account for the risk of the cash flows?

Does the AAR rule provide an indication about the increase in value?

Should we consider the AAR rule for our primary decision criteria?

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Advantages and Disadvantages of AAR

Advantages Easy to calculate Needed information will

usually be available

Disadvantages Not a true rate of return;

time value of money is ignored

Uses an arbitrary benchmark cutoff rate

Based on accounting net income and book values, not cash flows and market values

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Summary of Decisions For The Project

Summary

Net Present Value Accept

Payback Period Reject

Average Accounting Return Reject

Internal Rate of Return Accept

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Profitability Index

Measures the benefit per unit cost, based on the time value of money

A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value

This measure can be very useful in situations where we have limited capital

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Advantages and Disadvantages of Profitability Index

Advantages Closely related to NPV,

generally leading to identical decisions

Easy to understand and communicate

May be useful when available investment funds are limited

Disadvantages May lead to incorrect

decisions in comparisons of mutually exclusive investments

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Capital Budgeting In Practice

We should consider several investment criteria when making decisions

NPV and IRR are the most commonly used primary investment criteria

Payback is a commonly used secondary investment criteria

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Quick Quiz

Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years.

What is the payback period? What is the NPV? What is the IRR? Should we accept the project?

What decision rule should be the primary decision method? When is the IRR rule unreliable?