Copyright © 2003 McGraw Hill Ryerson Limited 6-1 prepared by: Carol Edwards BA, MBA, CFA...

copyright © 2003 McGraw Hill Ryerson Limited

6-16-1

prepared by:Carol EdwardsBA, MBA, CFA

Instructor, FinanceBritish Columbia Institute of Technology

Fundamentals

of Corporate

Finance

Second Canadian Edition


6-26-2

Chapter 6NPV and Other Investment Criteria

Chapter Outline Net Present Value (NPV) Other Investment Criteria Investment Criteria When Projects Interact 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.

How do we ensure that the correct capital budgeting decision is made?


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Suppose you had the opportunity to buy a tbill 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 (guaranteed).

Since this investment has the same risk and 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?

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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Notice that the cash flows are discounted at 7%, which is the cost of the tbill.

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.


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Net Present Value• Risk and Net Present Value

You have assumed the building project is risk free.

This is an unreasonable assumption. Suppose instead you believe the building project is

as risky as the stock market which is yielding 12%. Now your opportunity cost of capital would be

12% and the NPV of the project would be:

NPV = PV – C0

= [$400,000/(1+.12)] - $350,000= $357,143 - $350,000 = $7,143


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Net Present Value• Risk and Net Present Value

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 thana 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.


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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 14.3%:

NPV = [C1/(1+r)] - C0

0 = [$400,000/(1+r)] - 350,000

r = 14.3% 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 GRAPHNPV 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!


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

The rate of return rule and NPV rule will give the same answer as long as the NPV of the project declines as the discount rate increases.

In other words, a project’s NPV profile should look similar to the NPV profile on Slide #17.

It should be sloping smoothly downwards to the right.


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Other Investment Criteria• Payback

Payback is the time period it takes for the cash flows generated by the project to cover 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)


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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:

The project takes 3 years to payback, which is longer than you consider desirable to get your money out of a project.


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

It often leads to nonsensical decisions. 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 $7,249

B 2 - 264

C 2 - 347


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

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.

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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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


6-286-28

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 2 storey building or a 50 storey one.

You could heat it with oil or with natural gas. If you choose one of the options, you cannot

pursue the other.


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Mutually exclusive projects are two or more projects which cannot be pursued simultaneously.

When choosing among mutually exclusive projects:

1. Calculate the NPV of each project.

2. From those projects which have a positive NPV, select the one whose NPV is highest.


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In Example 6.4, you were told that 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%:

a


Project: C0 C1 C2 C3

Faster -800 +350 +350 +350

Slower -700 +300 +300 +300


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Project Interactions

• Mutually Exclusive Projects 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.

Project: NPV @ 7%

Faster $118.5

Slower $ 87.3


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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 6.1, you looked at purchasing a new computer system.

Its cost today was $50,000 and its NPV was about $20,000.

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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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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So far, this looks like a mutually exclusive choice like problem 6.4 on Slide #30 …

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 15 4 4 4 $25.69

Machine E 10 6 6 - $21.00

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

.


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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:

a

How much would it cost per year touse Machine E as versus Machine D?

.


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We solve this problem by calculating the Equivalent Annual Cost of the two machines.

The Equivalent Annual Cost 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 15 4 4 4 $25.69

EquivalentAnnual cost: ? ? ? $25.69

The equivalent annual cost is calculated as follows:

.

Equivalent Annual Cost = PV of Costs / Annuity Factor

= $25.69 / 3 Year Annuity Factor

= $25.69 / 2.673

= $9.61 per year

9.61 9.61 9.61


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• 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 $25.69 $9.61

E $21.00 $11.45


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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

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 @ 6%

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 – Lending vs Borrowing

Calculate the IRR and NPV for the projects below:


Project: C0 C1 IRR NPV @ 6%

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 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.

.


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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

Some projects will generate multiple internal rates of return.

Look at Figure 6.5 on page 191 for an example. Some projects have no internal rate of return.

Look at Footnote #7 on page 191 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

How is this done?

is within the company’s resources and

gives the highest NPV.

Key Question:


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Capital Rationing• Profitability Index (PI)

The solution is to pick the projects that give the highest NPV per dollar of investment.

We do this by calculating the Profitability Index:

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!

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