The theory and practice of corporate

The Theory and Practice of The Theory and Practice of Corporate Corporate

Some alternative investment rules

From this handout we will start learning “capital budgeting”, the decision-making process of accepting or rejecting project.

The most useful decision rule is the net present value (NPV) rule where project is accepted when the net present value of the cash flow of the project is positive, and rejected if it is negative.

See next page

Some alternative investment rules (contd)

Although NPV rule is our preferred rule, there are other investment rules that are used in practices. These alternative investment rules had been used for several reasons: These alternative rules may be easy to calculate, may be easy to understand, or may be used simply because it have been conventionally used.

Some alternative investment rules (contd)

In this handout, we will learn some alternative investment rules.

- First, this handout summarizes some reason we may prefer NPV rules. Then, it will explain

1. Payback Period Rule

2. Average accounting return rule

3. The internal rate of return

4. Profitability Index

Why use Net Present Value?

A basic investment rule is to

Accept the project if the NPV is greater than zero

Reject the project if NPV is less than zero.

Why use Net Present Value? (Contd)

• First reason we prefer NPV rule is that accepting positive NPV projects benefits the stockholders. Suppose that a firm has a productive asset worth $V and has $100 of cash. Consider the following two strategies. The market interest rate is 0.06

(1) Use $100 of corporate cash to invest in the project. The $107 dividend will be paid as a dividend in one year.

(2) Forgo the project and pay the $100 of corporate cash as a dividend today.

See next slide


If the firm takes strategy (1), the value of the firm today will be

$V+$107/1.06=$V+$100.94

If the firm takes the strategy (2), the value of the firm today will be

$V+$100 Clearly the firm value for strategy (1) is greater than

the firm value for strategy (2) by the amount equal to the net present value of the project ($0.94). Thus, accepting the positive NPV project will benefit the shareholder.


Second reason we prefer the NPV rule is that, the firm value will increase by the NPV. This can be seen from the example in the previous slides. The firm value for strategy (1) was higher than the firm value for strategy (2) by the amount equal to the NPV of the project.

Thus, if the goal of the firm is to maximize its value, NPV rule gives clearer guidance than other alternative investment rules.

Alternative Investment rule

Although NPV method is our preferred method for capital budgeting, it is worthwhile to learn other alternative methods. It is worthwhile, first because learning other methods highlights, and second because these alternative methods are used in the real world.

Next slides shows the extent to which these alternative methods are used in the real world.

The practice of capital budgeting

According Graham, Campbell and Harvey “The Theory and Practice of Corporate Finance: Evidence from the Field” Journal of Financial Economics 2000, the practice of capital financing decision of majority of the US and Canadian companies are given by the following table.

% of CFOs who always or almost always use a given technique

% of almost always

Internal Rate of Return 75.6%

NPV 74.9%

Payback method 56.7%

Discounted payback 29.5%

Accounting rate of return 30.3%

Profitability index 11.9%

Alternative Investment rule (1): The Payback Period Rule

“Payback period” rule is the decision rule where you accept the project if the initial investment can be paid back within pre-determined criteria period. For example, if the predetermined criteria period is 4 years, then you will accept the investment project if the initial investment can be paid back within 4 years.

There are certain problem with this “payback method”1. When the payback period is computed (number of years

to recover initial costs), typically the cash flow is not discounted

2. Minimum Acceptance Criteria (criteria period) is set arbitrary by management

3. There may be several projects that can be accepted. Then criteria to rank amount these project is set arbitrary by the management.

Payback Period RuleExample

Year Cash flow

0 -100

1 20

2 30

3 50

4 60

: :

• Consider a project with the following cash flow.

•If the minimum criteria for payback period is 3 years, is this project accepted?

•You could see that payback period rule gives an easy-to-understand, and easy-to-compute investment decision rule: You do not have to consider the cash flow after the criteria period.

•However, this also causes a problem.

See next page.

Example 2Year Project

AProject B

Project C

0 -100 -100 -100

1 20 50 50

2 30 30 30

3 50 20 10

4 60 60 60000

: : : :

• Now consider the three project given in the table.

Exercise

If the minimum criteria is 3 years, which project will be accepted?

•This example shows some disadvantages of the payback period rule.

The Payback Period Rule (continued)

Disadvantages: Ignores the time value of money Ignores cash flows after the payback period Biased against long-term projects Requires an arbitrary acceptance criteria A project accepted based on the payback criteria

may not have a positive NPV Advantages:

Easy to understand

Alternative investment rule (2)The Discounted Payback Period Rule

Since one of the problems with the payback method is that it does not discount the cash flow, one way to modify the method is to discount the cash flow and find out the payback period.

However, major problems still remain: You still have to arbitrarily set the criteria periods; the decision still have a bias against long term project since it still ignores the cash flow after the criteria period.

Also, by the time you have discounted the cash flows, you might as well calculate the NPV.

Alternative investment rule 3Average accounting return

Investent of ValueBook Average

IncomeNet AverageAAR

• The procedure of the AAR method is to accept the project if AAR is greater than a target return.

•Although this procedure has several problems (which will be described later), this method provides a percentage return of the investment. Thus, this method provides an easy-to-understand decision rule.

•Another popular alternative investment method is the average accounting return (AAR) method. 　 The average accounting return (AAA) is given by the following.

Average Accounting Return RuleExample

Consider a company that is evaluating whether to buy a new store in a new mall. The purchase price is $500,000. We will assume that the store has an estimated life of 5 years. We assume that the store will worth nothing at the end of the lifetime.

Excel Sheet “Average accounting return example” shows the estimated cash revenue and expenses for each of the 5 periods.

Use the file to compute the cash flow for each period by filling Table 1. Use straight line depreciation.

Average Accounting Return RuleExample (contd)

Table 1 Year 1 Year 2 Year 3 Year 4 Year 5Revenue 433,333 450,000 266,667 200,000 133,333

Expense 200,000 150,000 100,000 100,000 100,000

Before tax

Cash flow

233,333 300,000 166,667 100,000 33,333

Depreciation 100,000 100,000 100,000 100,000 100,000

Earning before tax

133,333 200,000 66,667 0 -66,667

tax 33,333 50,000 16,667 0 -16,667

Net Income 100,000 150,000 50,000 0 -50,000

Then, the average net income is given by

Average Net Income =(100,000+150,000+50,000+0-50,000)/5=50,000


Now, compute the average investment of this project by filling Table 2 of “Average Accounting Return exercise”.


Table　2 Year　0 Year　1 Year2 Year3 Year4 Year5

Value　of　the　investment　

$500,000$400,00

0$300,00

0$200,00

0$100,00

0$0

We simply take the average of the investment. Notice that investment occurs at date 0. Therefore, there are 6 periods in this table. The average investment is then determined by

Average Investment =(500,000+400,000+300,000+200,000+100,000+0)/6=250,000


Thus, the average accounting return of this example is given by %20

000,250$

000,50$AAR

If the company has a target average accounting return smaller than 20% (say 15%), the project will be accepted. If the company had a target AAR greater than 20%, the project will be rejected.

Problems with Average Accounting Return

AAR uses accounting number. Since the decision to depreciate or expense a certain item depends on accountant judgment, the computed AAR is influenced by accountant judgment.

Minimum acceptance criteria is set arbitrarily by management.

AAR does not take into account the time value of money.

Alternative Investment rule 4Internal Rate of Return

Similar to average accounting return, internal rate of return provides a single number (in percentage) summarizing the merit of the project. Thus, this method provides an easy-to-understand decision rule for investment.

Internal Rate of Return, however, has several problems. These problems will be discussed later in this handout.

Internal Rate of Return (IRR) Example

To see the basic idea of IRR decision rule, consider a project that generates one time cash flow of $110 thousand dollars next year. Initial cost of this investment is $100 thousand dollars, which will occur at today. Then, what is the return on this investment. See next Page

Internal Rate of Return (IRR) Example, Contd

To answer the question, we will solve the following equation for y.

01

110100

y

Solution to y is called the Internal Rate of Return.Internal rate of return for this example is 10%. This means that if the discount rate is lower than 10% (say 8%), it makes sense for the firm to invest in the project; the project provides a higher return than if the firm invests the money elsewhere.

Thus, the basic IRR rule of investment is to accept the project if the IRR is greater than the discount rate.

Internal Rate of Return -Decision Rule-

Consider an investment project with the following cash flow.

Period 0 1 2 ··· T

Cash flow ‒C0 C1 C2 ··· CT

Internal rate of return (IRR) is the solution to the following equation.

0)1()1(1 2

210

TT

IRR

C

IRR

C

IRR

CC

Decision rule: The decision rule is to accept the project if IRR is greater than discount rate, and reject if IRR is smaller than the discount rate.

Internal Rate of Return: Example

Let us consider another example given in the graph below.

0 1 2 3

$50 $100 $150

-$200

• Although we can compute IRR by using excel function IRR(:), let us find IRR manually.

See next page.

Exercise

To compute the IRR, consider to compute Z, which is defined in the following equation, for many different value of y.

32 )1(

150$

)1(

100$

)1(

50$200

yyyZ

Notice that IRR is the value of y that makes Z equal to zeroUse “Internal Rate of Return Exercise”, fill the table, and graph Z against y to find the IRR.

AnswerFinding　IRR

- 60

- 40

- 20

0

20

40

60

80

100

120

0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00%

r

Z

IRR=19.44%

•IRR is computed as 19.44%. Therefore, if the discount rate is smaller than 19.44%, the project is accepted.

Internal Rate of Return

• As can be seen from the example in the previous slides, internal rate of return provides a single number that summarizes the merit of the project.

• Since the IRR does not depend on the discount rate, this is called “internal rate of return”; the number that is intrinsic to the project.

• Although IRR is attractive decision rule, it has several problems, which are summarized in the following slides.

Problems with IRR approach (1)Multiple solutions

Consider the　following case.Period 0 1 2

Cash flow

-100 230 -132

Exercise: Use “problem with IRR 1”. Compute Z for each value of y, and graph Z against y.

AnswerProblems　with　IRR　(Multiple　Solution)

- 1

- 0.8

- 0.6

- 0.4

- 0.2

0

0.2

0.4

0.6

0.8

1

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0%

r

Z

Two　solutions

• There are two solutions to IRR. This typically occurs when negative cash flow occurs sometime after the initial period.

•Although such cash flow seems strange, it is not uncommon. For example, strip-mining project requires the excavation of the earth at the initial period. When all the mineral is extracted, the company will have to reclaim the land causing cash outflow. .

Problems with IRR approach (1)Multiple solutions, Contd

When cash flow exhibits “flip-flop” pattern, (the project has negative cash flow, positive cash flow, and then negative cash flow), the multiple solution is likely to occur.

“Modified IRR” method can be used for such a case. Consider the same example. The cash flow is [-$100, $230, -$132]

Modified IRR combines the second cash flow ($230) and the third cash flow (-$132) using a discount rate so that there is only one change in sign.

See next page

Problems with IRR approach (1)Multiple solutions, (modified IRR, contd)

Suppose that the discount rate is 14%. Then, modified IRR combines the second cash flow and the third cash flow by

$230‒$132/(1+0.14)=$114.21 After combining the second and third cash flow, the

modified cash flow of the project looks like [-$100, $114.21]

Finally, you compute the IRR using the modified cash flow. If the resulting IRR is greater than the discount rate you used (14%), the project is accepted.

In this example, modified IRR is 14.21%. Since this is greater than the discount rate 14%, this project will be accepted.

Problems with IRR approach (1)Multiple solutions, (modified IRR, contd)

The modified IRR may solve the problem. But this method violates the fundamental spirit of IRR that it does not depend on the discount rate.

Also, if there are several negative cash flows, this modified IRR becomes difficult to implement.

This problem shows one of the reasons why we prefer the net present value method over IRR rule.

Problems with IRR approach (2)-Two period cash flow, with negative cash outflow coming

in second period-

Suppose a company conduct a seminar. The participants pay the fees in advance. Therefore, the cash inflow occurs at date 0 (today). The large expense occurs at the seminar date. Therefore, the negative cash flow occurs at date 1 (1 period from today). See Next Page


in second period- Contd

Suppose that the cash flow of the project is given by the following.Period 0 1

Cash flow

100 -130

Suppose that the cash flow of the project is given by the following.

If you compute the IRR of this project, it will be 30%

See next page



This particular case gives rise to the following unusual decision making rule.　 The decision making rule when the data 0 cash

flow is positive and date 1 cash flow is negative is to accept the project if IRR is less than the discount rate, and reject if IRR is greater than the discount rate.

The intuitive reason for this unusual decision rule is the following.



Investing in this seminar project is like borrowing $100 at data 0, and paying back $130 at date 1. Internal rate of return on 30% is like borrowing $100 at 30% interest rate.

Therefore, if the discount rate (market interest rate) is smaller than the IRR, (say 25%), it makes more sense to borrow from the bank than investing in the project. This leads to the decision rule to reject the project when IRR is greater than the discount rate.

As can be seen, this could cause a confusion for the decision making. This is another reason we prefer net present value method over IRR method.

Problem with IRR (3)-Scale Problem-

Another problem of IRR is that it does not take into account the scale of the project. For example, consider two projects, project A and project B. Project A is a small project (initial cost of $10,000) with 20% internal rate of return. Project B is large project (initial cost of $100 million) with 10% internal rate of return.

Although the project B will bring larger cash flows, IRR decision rule would falsely make the project A appear more attractive. This is the basic illustration of scale problem. See next page.

Problem with IRR (3)-Scale Problem-

Scale problem becomes a problem when there are two mutually exclusive projects.

Mutually exclusive projects: Project A and B are called mutually exclusive if you cannot accept both project at the same time.

If two projects are not mutually exclusive, you can accept both projects as long as both projects have IRRs greater than the discount rate.

However, if two projects are mutually exclusive, you have to choose either project A or B. If IRR method is used for this purpose, scale problem may occurs.

See the example in the next slide,

Problem with IRR (3)-Scale Problem- Example

Consider you produce a movie on either a small budget or a big budget. Then two plans are mutually exclusive.

Exercise: Fill in the blanks.

Cash Flow at date 0

Cash flow at date 1

IRR NPV at 25% discount rate

Small budget

-10 million $40 million

Big budget -25 million $65million

Problem with IRR (3)-Scale Problem- Example

IRR for small budget movie is 300%, while IRR for a big budget movie is 160%. However, net present value of the project B is greater.

If we blindly apply IRR method to the decision to choose between small budget and large budget movies, we would choose low budget movie since it has higher IRR. However, it has a smaller net present value. This is the problem of scale problem in IRR method, and is one of the reasons NPV method is preferred over IRR method.

We can somehow remedy this problem by using incremental IRR. See next page.

Problem with IRR (3)-Scale Problem- Example contd

Incremental IRR: First you compute the incremental (or additional) cash flow from choosing small budget instead of large budget. Then compute incremental IRR.

Period 0 1 IRR

Small budget ‒$10m $40m 300%

Large budget ‒$25m $65m 160%

Incremental cash flow from choosing large budget instead of small budget

‒$25m ‒(‒$10m)= ‒$15m

$65m ‒ $40m=$25m

Incremental IRR=66.67%

Problem with IRR (3)-Scale Problem- Example contd

In the previous slide, incremental IRR is 66.67%. This means that choosing large budget movie instead of small budget move will brings additional return of 66.67%. Put differently, increasing the budget from small to large will bring additional return of 66.67%.

Therefore, if 66.67% is greater than the discount rate, large budget movies should be accepted because 66.67% is the additional return from increasing the size of the project.

Alternative Investment Rule 5-Profitability Index (PI)-

Profitability index also provides a single number that summarizes the merit of a project.

Profitability Index is computed as

investment Initial

investment initial tosubsequent flowscash of PV Index ity Profitabil

Alternative Investment Rule 5-Profitability Index Example-

Consider a project with the following cash flows. Assume the discount rate of 12%.

Period 0 1 2

Cash flow

-20 70 10

Using this example, the profitability Index is computed in the following ways. See next slides.

Alternative Investment Rule 5-Profitability Index Example-

5.70$)12.1(

10$

12.1

70$2

First, you compute the present discount value of cash flows subsequent to the initial investment with discount rate of 12%. This is given by

Then, the profitability index is computed by dividing the above number ($70.5) by the initial investment ($20). Therefore, the Profitability Index (PI) for this example is given by

53.320$

5.70$PI

Decision to accept or reject an independent project is given by the following.

Decision rule: Accept the project if PI >1. Reject if PI<1.

Alternative Investment Rule 5-Profitability Index Decision rules-

A problem with the profitability index

A problem occurs when we consider two mutually exclusive project. As was the case in the IRR method, profitability method does not take the size of the project into account.

To illustrate the problem, consider the following two mutually exclusive project.

Period 0 1 2

Project 1

-20 70 10

Project 2

-10 15 40

A problem with the profitability index, Contd

As an exercise, compute profitability index for both projects. Assume the discount rate of 12%

Period 0 1 2

Project 1 -20 70 10

Project 2 -10 15 40

A problem with the profitability index, contd

Period 0 1 2 PI

Project 1 -20 70 10 3.53

Project 2 -10 15 40 4.53

•As can be seen, project 2 has greater PI. However, since profitability index is the ratio, PI misses out the fact that project 2 is a smaller project.

•Therefore, if the size of the projects are different, it is not necessarily the case that project with greater profitability index is more attractive project.

•We can remedy this weakness by using incremental cash flow.

See next page.


Exercise: Profitability index for incremental cash folow: Complete the following table

Period 0 1 2 PI

Project 1 -20 70 10 3.53

Project 2 -10 15 40 4.53

Incremental cash flow (1-2)

PI for the incremental cash flow=


The profitability index for the incremental cash flow was 2.52. This means that choosing project 1 instead of project 2 will still increase profit. Put differently, increasing the size of the project from project 2 to project 1 will bring additional profit. Thus, project 1 is preferred.

As can be seen, scale problem can be remedied by computing the PI for incremental cash flow. However, net present value method is more straightforward when choosing between mutually exclusive projects.

The practice of capital budgeting

According Graham, Campbell and Harvey “The Theory and Practice of Corporate Finance: Evidence from the Field” Journal of Financial Economics 2000, the practice of capital financing decision of majority of the US and Canadian companies are given by the following table.

% of CFOs who always or almost always use a given technique

% of almost always

IRR 75.6%

NPV 74.9%

Payback method 56.7%

Discounted payback 29.5%

Accounting rate of return 30.3%

Profitability index 11.9%

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