Chapter 7

Semih Yildirim ADMS 3530

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Chapter 7NPV and Other Investment Criteria

Chapter Outline Net Present Value (NPV) Other Investment Criteria

IRR (Internal Rate of Return)Payback and Discounted Payback Book Rate of Return

Investment Criteria When Projects Interact Pitfalls with IRR Capital Rationing


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Net Present Value• Capital Budgeting Decision

Central to the success of any company is the investment decision, also known as the capital budgeting decision.

Assets acquired as a result of the capital budgeting decision can determine the success of the business for many years.

It is extremely important that we ensure that the correct capital budgeting decision is made!


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Suppose you had the opportunity to buy a Tbill (Treasury Bill) which would be worth $400,000 one year from today.

Interest rates on Tbills are a risk free 7%. What would you be willing to pay for this

investment?

$400,000 / (1.07) = $373,832

PV today:0 1 2

-$400,000


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You would be willing to pay $373,382 for a risk free $400,000 a year from today.

Suppose this were, instead, an opportunity to construct a building, which you could sell in a year for $400,000 with certainty (That means the project is risk free.)

Since this investment has the same risk and promises the same cash flows as the Tbill, it is also worth the same amount to you:

$373,282


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Now, assume you could buy the land for $50,000 and construct the building for $300,000. Is this a good deal?

Sure! If you would be willing to pay $373,382 for this investment and can acquire it for only $350,000, you have found a very good deal!

You are better off by:$373,382 - $350,000 = $23,832


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We have just developed a way of evaluating an investment decision which is known as Net Present Value (NPV).

NPV is defined as the PV of the cash flows from an investment minus the initial investment.

NPV = PV – Required Investment (C0)= [$400,000/(1+.07)] - $350,000= $23,832


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This discount rate is known as the opportunity cost of capital.

It is called this because it is the return you give up by investing in the project.

In this case, you give up the money you could have used to buy a 7% tbill so that you can construct a building.

But, a Tbill is risk free! A construction project is not! We should use a higher opportunity cost of capital.


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Net Present Value• Risk and Net Present Value

Suppose instead you believe the building project is as risky as a stock which is yielding 12%.

Now your opportunity cost of capital would be 12% and the NPV of the project would be:

NPV = PV – IC0= [$400,000/(1+.12)] -

$350,000= $357,143 - $350,000 =

$7,142.86 The project is significantly less attractive once you take

account of risk. This leads to a basic financial principal: A risky dollar is

worth less than a safe one.


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Net Present Value• Valuing long lived projects

The NPV rule works for projects of any duration: Simply discount the cash flows at the appropriate opportunity cost of

capital and then subtract the cost of the initial investment.

The critical problems in any NPV problem are to determine: The amount and timing of the cash flows. The appropriate discount rate.

NPV Rule: Accept Projects with Positive NPVs


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Net Present Value


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Other Investment Criteria• Net Present Value vs Other Criteria

Use of the NPV criterion for accepting or rejecting investment projects will maximize the value of a firm’s shares.

Other criteria are sometimes used by firms when evaluating investment opportunities.

Some of these criteria can give wrong answers! Some of these criteria simply need to be used with

care if you are to get the right answer!


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Other Investment Criteria• Internal Rate of Return (IRR)

IRR is simply the discount rate at which the NPV of the project equals zero.

You can calculate the rate of return on a project by:1. Setting the NPV of the project to zero.

2. Solving for “r”. Unless you have a financial calculator, this calculation must be

done by using trial and error!


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To go back to our office example, we discovered the following:

Discount Rate NPV of Project

7% $23,382

12% $7,143

At what rate of return will the NPVof this project be equal to zero?


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If we solve for “r” in the equation below, we find the IRR for this project is 14.29%:

• IRR Decision Rule: Accept Projects with IRR which exceeds the opportunity cost of capital

r


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Another way of solving for IRR is to graph the NPV at various discount rates.

The point where this NPV profile crosses the “x” axis will be the IRR for the project.


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IRR BY GRAPH

NPV Profile for this Project

($20,000)

($10,000)

$0

$10,000

$20,000

$30,000

$40,000

$50,000

$60,000

5% 10% 15% 20%

Discount Rate

NP

V (

$)

IRR = 14.3%(occurs where NPV = 0)


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Other Investment Criteria• Internal Rate of Return (IRR) vs NPV:

The NPV Rule states that you invest in any project which has a positive NPV when its cash flows are discounted at the opportunity cost of capital.

The Rate of Return Rule states that you invest in any project offering a rate of return which exceeds the opportunity cost of capital.

i.e., if you can earn more on a project than it costs to undertake, then you should accept it!

The NPV and IRR rules will give the same accept/reject answer about a project as long as the NPV of a project declines smoothly as the discount rate increases.

Do not confuse IRR and the opportunity cost of capital


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Other Investment Criteria• Payback

Payback is the time period it takes for the cash flows generated by the project to recover the initial investment in the project.

Example: You are paying $150 a month to park a car in your apartment’s garage. You can purchase a parking spot for $5,400. What is the payback for this “project”?

3 years $5,400 / (12 * $150) The Payback Rule states that a project should be accepted if its

payback is less than a specified cutoff period. For example, if your cutoff were 4 years to payback, then you would

buy the parking spot. If it were 2 years, you wouldn’t buy the parking spot:

3 years is longer than you consider desirable to get your money out of a project.


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Other Investment Criteria• Payback

Payback is a very poor way of determining a project’s acceptability:

It ignores all cashflows after your cutoff date. It ignores TVM principle: it does not discount CFs

Calculate the payback and NPV for the following projects if the discount rate is 10%:

a

Cash Flows in Dollars

Project: C0 C1 C2 C3

A -2,000 +1,000 +$1,000 +10,000

B -2,000 +1,000 +$1,000 -

C -2,000 - +$2,000 -


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Other Investment Criteria

• Payback vs NPV … what to do? Under NPV, only project A is acceptable. B and C

have negative NPV’s and are thus both unacceptable. But if your payback period is 2 years, then all the

projects are acceptable.

NPV and payback disagree … what is the correct answer?

Project: Payback (years) NPV @ 10%

A 2 $7,248.69

B 2 - 264.46

C 2 - 347.11


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Other Investment Criteria• Payback vs NPV … what to do?

Payback gives the same weight to all CFs which occur before the cutoff period, while it completely ignores the CFs after the cutoff

The firm decision will be biased towards too many short term lived projects

And against some long-lived projects. NPV gives the correct answer:

Only project A will increase shareholder value. Therefore, it should be the only project accepted.

Lesson: Use NPV if you want to make the correct

investment decision!


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Other Investment Criteria• Discounted Payback

Discounted payback is the time period it takes for the discounted cash flows generated by the project to cover the initial investment in the project.

It offers an important advantage over Payback: if a project is acceptable with the Discounted Payback, it must have a positive NPV (if the ignored Cashflows are all positive!)

Although better than payback, it still ignores all cash flows after an arbitrary cutoff date.

Therefore it will reject some positive NPV projects. NPV is thus always preferable to discounted payback

in evaluating projects!

a


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Discounted Payback Example (OCC=10%, cut-off = 4 years)


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Other Investment Criteria• Book Rate of Return

Book rate of return equals the company’s accounting income divided by its assets.

a

Book Rate of Return = Book Income / Book Assets

Managers rarely use thismeasurement to make decisions:

The components reflect historic costs andaccounting income, not market

values and cash flows.

a


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Project Interactions• Investment Criteria When Projects Interact

NPV has proven to be the only reliable measure of a project’s acceptability.

But, what happens when we must choose among projects which interact?

The NPV rule can be adapted to deal with the following situations:

Mutually Exclusive Projects The Investment Timing Decision Long- vs Short-Lived Equipment (Unequal Lives) Replacing an Old Machine


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Project Interactions• Mutually Exclusive Projects

Most projects you deal with will be either-or propositions. For example, you own a vacant piece of land. You have many either-or choices:

You could construct a townhouse or a condo. You could heat it with oil or with natural gas.

If you choose one of the options, you cannot pursue the other. They cannot be realized simultaneously. Calculate the NPV of each project From those, chose the project with the highest (positive) NPV.


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Project Interactions• Mutually Exclusive Projects

In Example 7.4, you are going to replace your office network. You can choose between a cheaper, slower package or a more

expensive, faster option. Calculate the NPV for the two projects if the discount rate is 7%:

Both projects have a positive NPV, thus both are acceptable. However, you cannot do both of the these projects!

Since the faster system would make a greater contribution to the value of the firm, it should be your preferred choice.

a


Project: C0 C1 C2 C3 NPV @7%

Faster $ (800) $ 350 $ 350 $ 350 $ 118.50

Slower $ (700) $ 300 $ 300 $ 300 $ 87.30


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Project Interactions• The Investment Timing Decision

Sometimes your choice is start a project now or wait and do it at a later date.

In Example 7.1, you looked at purchasing a new computer system.

Its cost today was $50,000 and its NPV was $19,740.

However, you know that these systems are dropping in price every year.

From the numbers on the next slide, when should you purchase the computer?


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Project Interactions

Year of Purchase Cost

PV of Savings

NPV at Year of

PurchaseNPV

Todayt = 0 $50 $70 $20 $20.0t = 1 $45 $70 $25 $22.7t = 2 $40 $70 $30 $24.8t = 3 $36 $70 $34 $25.5t = 4 $33 $70 $37 $25.3t = 5 $31 $70 $39 $24.2

The decision rule for investment timing is tochoose the investment date which resultsin the highest net present value today.


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Project Interactions• Long- vs Short-Lived Equipment

Suppose you must choose between buying Machine D and E.

The two machines are designed differently, but have identical capacity and do the same job.

The difference? Machine D costs $15,000 and lasts 3 years. It

costs $4,000 per year to operate. Machine E costs $10,000 and lasts 2 years. It costs

$6,000 per year to operate.

Which machine should the firm acquire?


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Project Interactions• Long- vs Short-Lived Equipment

So far, this looks like a mutually exclusive choice like problem 7.4

Calculate PV of the costs for the projects if the discount rate is 6%:

a

Cash OutFlows in Dollars

Project: C0 C1 C2 C3 PV @ 6%

Machine D 15000 4000 4000 4000 $25,692.5

Machine E 10000 6000 6000 - $21,000

Should you accept Machine Ebecause the PV of its costs are lower?

.


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Project Interactions• Long- vs Short-Lived Equipment• Choosing Machine E may not be the best decision. Why not?

All we know is that Machine E costs less to run over 2 years than Machine D does over 3 years.

D is being penalized by having one extra year of costs charged against it!

What we should be asking is: How much would it cost per year to use Machine E as versus Machine D?

• We solve this problem by calculating the Equivalent Annual Cost (EAC) of the two machines.

• The EAC is the cost per period with the same PV as the cost of the machine.

Think of it as calculating the annual rental charge for the machine. There will be equal annual payments (an annuity). The PV of these payments must equal the PV of the cost of the

machine.

a

.


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Project Interactions• Calculating Equivalent Annual Cost:


Project: C0 C1 C2 C3 PV @ 6%

Machine D 15000 4000 4000 4000 $25,692.5

EquivalentAnnual cost: ? ? ? $25,692.5

The equivalent annual cost is calculated as follows:

.

Equivalent Annual Cost = PV of Costs / Annuity Factor

= $25,692.5 / 3 Year Annuity Factor

= $25,692.5 / 2.673

= $9,611.5 per year

9,611.5 9,611.5 9,611.5


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Project Interactions

• Long- vs Short-Lived Equipment We see from the equivalent annual costs that D is

actually the better choice because its annual cost is lower than for Machine E.

If mutually exclusive projects have unequal lives, then you should calculate the equivalent annual cost of the projects.

This will allow you to select the project which will maximize the value of the firm.


Project: PV @ 6% Equivalent Annual Cost

D $25,692.5 $9,611.50

E $21,000 $11,454.37


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Project Interactions• Replacing an old machine

When should existing equipment be replaced?

For example: You are operating an old machine which will last 2

more years. It costs $12,000 per year to operate. A new machine costs $25,000 to buy, but is more

efficient and can be operated for $8,000 per year. It will last for 5 years.

.

Should you replace the old machine?


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Project Interactions• Replacing an old machine

Solve these problems by calculating for the new machine the PV of the cash flows and its equivalent annual cost:


Project: C0 C1 C2 C3 C4 C5 PV @ 6%

New Machine 25 8 8 8 8 8 $58.70

EquivalentAnnual cost: ? ? ? ? ? $58.70

Your choice: pay $12,000 per year to run the oldmachine or $13,930 per year for the new machine.

.

13.93 13.93 13.93 13.93 13.93

Obviously, it’s cheaper to keep your old machine!


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Project Interactions• Pitfalls with IRR: 1-Mutually Exclusive Projects

IRR can mislead you when choosing among mutually exclusive projects.

Calculate the IRR and NPV for the following projects:


Project: C0 C1 C2 C3 IRR NPV @ 7%

H -350 400 - -

I -350 16 16 466

Project H has a higher IRR …but Project I contributes more to the value of the firm.

.

Obviously, you should prefer Project I!

14.29% $24,000

12.96% $59,000


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Project Interactions• Pitfalls with IRR

Remember: a high IRR is not an end in itself! Higher IRR for a project does not necessarily

mean a higher NPV. You goal should be to maximize the value of

the firm. Remember:

NPV is the most reliable criterion for project evaluation.

Only NPV measures the amount by which a project would increase the value of the firm.

.


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Project Interactions• Pitfalls with IRR: 2 – Lending vs Borrowing

Calculate the IRR and NPV for the projects below:


Project: C0 C1 IRR NPV @ 10%

J -100 +150

K +100 -150

Both projects have the same IRR …but Project J contributes more to the value of the firm.

.

Obviously, you should prefer Project J!

50% + $36.4

50% - $36.4


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Project Interactions• Pitfalls with IRR – Lending vs Borrowing

Project J involves lending $100 at 50% interest. Project K involves borrowing $100 at 50% interest.

Which option should you choose? Remember:

When you lend money, you want a high rate of return. When you borrow money, you want a low rate of return.

The IRR calculation shows that both projects have a 50% rate of return and are equally desirable.

You should see that this is a trap! The NPV rule correctly warns you away from a project

which involves borrowing money at 50%.

.


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Project Interactions• Other Pitfalls with IRR

3. Some projects will generate multiple internal rates of return.

Look at Figure 7.4 on page 218 for an example.

4. Some projects have no internal rate of return. Look at Footnote #6 on page 219 for an example.

How should you evaluate a project in cases like this?

.

You should calculate NPV!


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Capital Rationing• Capital Rationing

Occurs when a limit is set on the amount of funds available to a firm for investment.

• Soft Rationing Occurs when these limits are imposed by

senior management.

• Hard Rationing Occurs when these limits are imposed by the

capital markets.


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Capital Rationing• Rules for Project Selection

A firm maximizes its value by accepting all positive NPV projects.

With capital rationing, you need to select a group of projects which is within the company’s resources and gives the highest NPV.

This is done with the Profitability Index (PI) pick the projects that give the highest NPV per

dollar of investment.

PI = NPV / Initial Investment (C0)


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Capital Rationing• Profitability Index (PI)

For example: Suppose your firm had the following projects and only $20 million to spend:

Which Projects should your firm select?

Project C0 C1 C2

NPV @ 10%

L -3.00 2.20 2.42 1.00M -5.00 2.20 4.84 1.00N -7.00 6.60 4.84 3.00O -6.00 3.30 6.05 2.00P -4.00 1.10 4.84 1.00

Budget -25.00


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Capital Rationing• Profitability Index

Project C0

NPV @ 10% PI

L 3.00 1.00 1/3 = 0.33M 5.00 1.00 1/5 = 0.20N 7.00 3.00 3/7 = 0.43O 6.00 2.00 2/6 = 0.33P 4.00 1.00 1/4 = 0.25

ACCEPT

ACCEPT

ACCEPT

ACCEPT


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Summary of Chapter 6 NPV is the only measure which always gives

the correct decision when evaluating projects. The other measures can mislead you into

making poor decisions if used alone. The other measures are:

IRR Payback Discounted Payback Book Rate of Return Profitability Index (PI)

See the next slide for a summary.


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Summary of Chapter 6

Independent Projects

Mutually Exclusive Projects *

Capital Rationing

NPV

IRR

Payback

Discounted Payback

Book Rate of Return

Profitability Index

Type of Decision:

* Includes: Investment Timing Decision, Unequal Livesand Replacement Decision


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Summary of Chapter 6 It should be noted that when capital rationing

is in place, NPV by itself, cannot lead you to the correct decision.

You must combine NPV with the Profitability Index. Ranking the projects this way will allow you to

choose the package of projects which will offer the highest NPV per dollar of investment.

In summary:

NPV should always be used when evaluating project acceptability!

Chapter 7

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