Portfolio funding

Slide 1

8-1

Capital Budgeting

• Analysis of potential projects

• Long-term decisions

• Large expenditures

• Difficult/impossible to reverse

• Determines firm’s strategic direction

When a company is deciding whether to invest in a new project, large sums of money can be at stake. For

example, the Artic LNG project would build a pipeline from Alaska’s North Slope to allow natural gas to

be sent from the area. The cost of the pipeline and plant to clean the gas of impurities was expected to be

$45 to $65 billion. Decisions such as these long-term investments, with price tags in the billions, are

obviously major undertakings, and the risks and rewards must be carefully weighed. We called this the

capital budgeting decision. This module introduces you to the practice of capital budgeting. We will

consider a variety of techniques financial analysts and corporate executives routinely use for the capital

budgeting decisions.

1. Net Present Value (NPV) 2. Payback Period 3. Average Accounting Rate (AAR) 4. Internal Rate of Return (IRR) or Modified Internal Rate of Return (MIRR) 5. Profitability Index (PI)

Slide 2

8-2

• All cash flows considered?

• TVM considered?

• Risk-adjusted?

• Ability to rank projects?

• Indicates added value to the firm?

Good Decision Criteria

All things here are related to maximize the stock price. We need to ask ourselves the following

questions when evaluating capital budgeting decision rules:

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?

Slide 3

8-3

Net Present Value

• The difference between the market value of a

project and its cost

• How much value is created from undertaking

an investment?

Step 1: Estimate the expected future cash flows.

Step 2: Estimate the required return for projects of

this risk level.

Step 3: Find the present value of the cash flows and

subtract the initial investment to arrive at the Net

Present Value.

Net present value—the difference between the market value of an investment and its cost.

The NPV measures the increase in firm value, which is also the increase in the value of what the

shareholders own. Thus, making decisions with the NPV rule facilitates the achievement of our

goal – making decisions that will maximize shareholder wealth.

Slide 4

8-4

Net Present Value Sum of the PVs of all cash flows

Initial cost often is CF0 and is an outflow.

NPV =∑ n

t = 0

CFt

(1 + R)t

NPV =∑ n

t = 1

CFt

(1 + R)t - CF0

NOTE: t=0

Up to now, we’ve avoided cash flows at time t = 0, the summation begins with cash flow zero—

not one.

The PV of future cash flows is not NPV; rather, NPV is the amount remaining after offsetting the

PV of future cash flows with the initial cost. Thus, the NPV amount determines the incremental

value created by undertaking the investment.

Slide 5

8-5

NPV – Decision Rule

• If NPV is positive, accept the project

• NPV > 0 means:

– Project is expected to add value to the firm

– Will increase the wealth of the owners

• NPV is a direct measure of how well this

project will meet the goal of increasing

shareholder wealth.

Slide 6

8-6

Rationale for the NPV Method

• NPV = PV inflows – Cost

NPV=0 → Project’s inflows are “exactly sufficient to repay the invested capital and provide the required rate of return”

Conceptually, a zero-NPV project earns exactly its required return. Assuming that risk has been

adequately accounted for, investing in a zero-NPV project is equivalent to purchasing a financial

asset in an efficient market. In this sense, one would be indifferent between the capital expenditure

project and the financial asset investment. Further, since firm value is completely unaffected by

the investment, there is no reason for shareholders to prefer either one.

In practice, financial managers are rarely presented with zero NPV projects for at least two reasons.

First, in an abstract sense, zero is just another of the infinite number of values the NPV can take;

as such, the likelihood of obtaining any particular number is small. Second, and more pragmatically,

in most large firms, capital investment proposals are submitted to the finance group from other

areas for analysis. Those submitting proposals recognize the ambivalence associated with zero

NPVs and are less likely to send them to the finance group in the first place.

Slide 7

8-7

Sample Project Data

• You are looking at a new project and have estimated the following cash flows, net income and book value data:

– Year 0: CF = -165,000

– Year 1: CF = 63,120 NI = 13,620

– Year 2: CF = 70,800 NI = 3,300

– Year 3: CF = 91,080 NI = 29,100

– Average book value = $72,000

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

• This project will be the example for all problem exhibits in this module.

This example will be used for each of the decision rules so that we can compare the different rules

and see that conflicts can arise. This illustrates the importance of recognizing which decision rules

provide the best information for making decisions that will increase owner wealth.

Slide 8

8-8

Display You Enter CF, 2nd,CLR WORK

CF0 -165000 Enter, Down C01 63120 Enter, Down F01 1 Enter, Down C02 70800 Enter, Down F02 1 Enter, Down C03 91080 Enter, Down F03 1 Enter, NPV I 12 Enter, Down NPV CPT

12,627.41

Cash Flows:

CF0 = -165000

CF1 = 63120

CF2 = 70800

CF3 = 91080

Computing NPV for the Project Using the TI BAII+

Do we accept or reject the project? Accept

Again, the calculator used for the illustration is the TI BA-II plus. The basic procedure is the same;

you start with the year 0 cash flow and then enter the cash flows in order. F01, F02, etc. are used

to set the frequency of a cash flow occurrence. Many calculators only require you to use this

function if the frequency is something other than 1.

Using the formulas:

NPV = -165,000 + 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 = 12,627.41

Using the calculator (details):

Press the following keys: 2nd, CF, 2nd, Clear.

Calculator displays CF0, 165,000 +|– key, press the Enter key.

Press down arrow, enter 63,120, and press Enter.

Press down arrow, enter 1, and press Enter.

Press down arrow, enter 70,800, and press Enter.

Press down arrow, enter 1, and press Enter.

Press down arrow, enter 91,080, and press Enter.

Press down arrow, enter 1, and press Enter.

Press NPV; calculator shows I = 0; enter 12 and press Enter.

Press down arrow; calculator shows NPV = 0.00.

Press CPT; calculator shows NPV = 12,627.41.

Slide 9

8-9

• Does the NPV rule account for the time value of money?

• Does the NPV rule account for the risk of the cash flows?

• Does the NPV rule provide an indication about the increase in value?

• Should we consider the NPV rule for our primary decision rule?

Decision Criteria Test – NPV

The answer to all of these questions is yes. The risk of the cash flows is accounted for through

the choice of the discount rate.

NPV meets all desirable criteria

 Considers all CFs

 Considers TVM

 Adjusts for risk

 Can rank mutually exclusive projects

Mutually exclusive investment decisions – taking one project means another cannot be taken. An

excellent example of mutually exclusive projects is the choice of which college or university to

attend. Many students apply and are accepted to more than one college, yet they cannot attend

more than one at a time. Consequently, they have to decide between mutually exclusive projects.

Slide 10

8-10

Payback Period

• How long does it take to recover the initial cost of a project?

• Computation

– Estimate the cash flows

– Subtract the future cash flows from the initial cost until initial investment is recovered

– A “break-even” type measure

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

Payback period—length of time until the accumulated cash flows equal or exceed the original

investment, i.e., how fast you recover your initial investment.

Payback period rule – investment is acceptable if its calculated payback is less than some

prespecified number of years.

Slide 11

8-11

Computing Payback for the Project

• Do we accept or reject the project?

Capital Budgeting Project

Year CF Cum. CFs

0 (165,000)$ (165,000)$

1 63,120$ (101,880)$

2 70,800$ (31,080)$

3 91,080$ 60,000$

Payback = year 2 +

+ (31080/91080)

Payback = 2.34 years

Assume we will accept the project if it pays back within two years.

Year 1: 165,000 – 63,120 = 101,880 still to recoup

Year 2: 101,880 – 70,800 = 31,080 still to recoup

Year 3: 31,080 – 91,080 = -60,000

If we assume that the cash flows occur evenly throughout the year, which is typical for this method,

then the project pays back in 2.34 years. The payback rule would say to reject the project.

Slide 12

8-12

• 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 rule?

Decision Criteria Test – Payback

The answer to all of these questions is no.

Decision Criteria Test – Payback

• -No discounting involved • -Doesn’t consider risk differences • -How do we determine the cutoff point • -Biased toward short-term investments

Real-World Tip: Interestingly, the payback period technique is used quite heavily in determining

the viability of certain investment projects in the health care industry. Why? Consider the nature

of the health care industry: the technology is rapidly changing, some of the equipment tends to be

extremely expensive, and the industry itself is increasingly competitive. What this means is that, in

many cases, an equipment purchase is complicated by the fact that, while the machine may be able

to perform its function for, say, 6 years or more, new and improved equipment is likely to be

developed that will supersede the “old” equipment long before its useful life is over. Demand from

patients and physicians for “cutting-edge technology” can drive a push for new investment. In the

face of such a situation, many hospital administrators then focus on how long it will take to recoup

the initial outlay, in addition to the NPV and IRR of the equipment.

Slide 13

8-13

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

Slide 14

8-14

Average Accounting Return

• Many different definitions for average accounting

return (AAR)

• In this module, we will use the following specific

definition:

– Note: Average book value depends on how the asset is depreciated.

• Requires a target cutoff rate

• Decision Rule: Accept the project if the AAR is greater than target rate.

Value Book Average

IncomeNet Average AAR 

Average accounting return = measure of accounting profit / measure of average accounting

value. In other words, it is a benefit/cost ratio that produces a pseudo rate of return. However,

due to the accounting conventions involved, the lack of risk adjustment and the use of profits

rather than cash flows, it isn’t clear what is being measured.

Slide 15

8-15

• 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?

Computing AAR

Sample Project Data:

Year 0: CF = -165,000

Year 1: CF = 63,120 NI = 13,620

Year 2: CF = 70,800 NI = 3,300

Year 3: CF = 91,080 NI = 29,100

Average book value = $72,000

You may ask where you came up with the 25%. Note that this is one of the drawbacks of this

rule. There is no good theory for determining what the return should be. We generally just use

some rule of thumb. This rule would indicate that we reject the project.

- Another example

You are deciding whether to open a store in a new shopping mall. The required investment in

improvements is $500,000. The store would have a five-year life because everything reverts to the

mall owners after that time. The required investment would be 100 percent depreciated (straight-

line) over five years, so the depreciation would be $500,000 / 5 = $100,000 per year. Net income

is $100,000 in the first year, $150,000 in the second year, $50,000 in the third year, $0 in Year 4,

and -$50,000 in Year 5. AAR?

To calculate the average book value for this investment, we note that we started out with a book

value of $500,000 (the initial cost) and ended up at $0 (i.e., we need to consider six book values).

The average book value during the life of the investment is thus ($500,000 + 0) / 2 = $250,000. As

long as we use straight-line depreciation, the average investment will always be one-half of the

initial investment. We could, of course, calculate the average of the six book values directly. In

thousands, we would have ($500 + 400 + 300 + 200 + 100 + 0) / 6 = $250. The average net income

is [$100,000 + 150,000 + 50,000 + 0 + (-50,000)] / 5 = $50,000. Thus, AAR = $50,000 / $250,000

= 20%

Slide 16

8-16

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?

The answer to all of these questions is NO. In fact, this rule is even worse than the payback rule in

that it doesn’t even use cash flows for the analysis. It uses net income and book value. It isn’t clear

what is being measured. Thus, it is not surprising that most surveys indicate that few large firms

employ the payback and/or AAR methods exclusively.

Slide 17

8-17

Advantages and Disadvantages of AAR

• Advantages

– Easy to calculate

– Needed information usually available

• Disadvantages

– Not a true rate of return

– Time value of money ignored

– Uses an arbitrary benchmark cutoff rate

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

-Since it involves accounting figures rather than cash flows, it is not comparable to returns in

capital markets

-It treats money in all periods as having the same value

-There is no objective way to find the cutoff rate

Slide 18

8-18

• 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.

Internal Rate of Return

Internal rate of return (IRR)—the rate that makes the present value of the future cash flows equal

to the initial cost or investment. In other words, the discount rate that gives a project a $0 NPV.

The IRR rule is very important. Management, and individuals in general, often have a much better

feel for percentage returns, and the value that is created, than they do for dollar increases. A dollar

increase doesn’t appear to provide as much information if we don’t know what the initial

expenditure was. Whether or not the additional information is relevant is another issue.

Slide 19

8-19

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

The goal of IRR is not to find zero NPV projects, but rather to find a range of discount rates for

which the project is acceptable.

Slide 20

8-20

NPV vs. IRR

NPV )R1(

CFn

0t t

t  

 

IRR: Enter NPV = 0, solve for IRR.

NPV: Enter r, solve for NPV

Slide 21

8-21

Display You Enter CF, 2nd, CLR WORK

CF0 -165000 Enter, Down C01 63120 Enter, Down F01 1 Enter, Down C02 70800 Enter, Down F02 1 Enter, Down C03 91080 Enter, Down F03 1 Enter, IRR IRR CPT

16.1322

Cash Flows:

CF0 = -165000

CF1 = 63120

CF2 = 70800

CF3 = 91080

Computing IRR for the Project Using the TI BAII

IRR = 16.13% > 12% required return

Do we accept or reject the project?

Internal rate of return (IRR) – the rate that makes the present value of the future cash flows equal

to the initial cost or investment. In other words, the discount rate that gives a project a $0 NPV.

IRR decision rule – the investment is acceptable if its IRR exceeds the required return

If you do not have a financial calculator, then this becomes a trial and error process.

Enter the cash flows as you did with NPV.

Using the calculator (details):

Press the following keys: 2nd, CF, 2nd, Clear.

Calculator displays CF0, 165,000 +|– key, press the Enter key.

Press down arrow, enter 63,120, and press Enter.

Press down arrow, enter 1, and press Enter.

Press down arrow, enter 70,800, and press Enter.

Press down arrow, enter 1, and press Enter.

Press down arrow, enter 91,080, and press Enter.

Press down arrow, enter 1, and press Enter.

Press IRR; calculator shows IRR = 0.00

Press CPT; calculator shows IRR = 16.132.

Slide 22

8-22

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

N P

V IRR = 16.13%

Note that the NPV profile is also a form of sensitivity analysis—the slope of the NPV profile

indicates how much a project’s estimated NPV is affected by a change in the discount rate used

to compute it.

Slide 23

8-23

• 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?

Decision Criteria Test - IRR

The answer to all of these questions is yes, although it is not always as obvious.

The IRR rule accounts for time value because it is finding the rate of return that equates all of the

cash flows on a time value basis. The IRR rule accounts for the risk of the cash flows because you

compare it to the required return, which is determined by the risk of the project. The IRR rule

provides an indication of value because we will always increase value if we can earn a return

greater than our required return. We could consider the IRR rule as our primary decision criteria,

but as we will see, it has some problems that the NPV does not have. That is why we end up

choosing the NPV as our ultimate decision rule.

Slide 24

8-24

• 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.

Advantages of IRR

• Considers all cash flows • Considers time value of money • Provides indication of risk

However, if you get a very large IRR then you should go back and look at your cash flow estimates

again. In competitive markets, extremely high IRRs should be rare. Also, since the IRR calculation

assumes that you can reinvest future cash flows at the IRR, a high IRR may be unrealistic.

Slide 25

8-25

NPV vs. IRR

• NPV and IRR will generally give the same decision

• Exceptions

– Non-conventional cash flows

• Cash flow sign changes more than once

– Mutually exclusive projects

• Initial investments are substantially different

• Timing of cash flows is substantially different

NPV and IRR comparison: If a project’s cash flows are conventional (costs are paid early and

benefits are received over the life), and if the project is independent, then NPV and IRR will give

the same accept or reject decision.

There are situations where NPV and IRR will give conflicting answers. Non-conventional cash

flows – the sign of the cash flows changes more than once or the cash inflow comes first and

outflows come later.

Slide 26

8-26

• 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?

IRR and Nonconventional Cash Flows

Nonconventional cash flows means the sign of the cash flows changes more than once or the cash

inflow comes first and outflows come later. If this occurs, you will have multiple internal rates of

return. This is problematic for the IRR rule; however, the NPV rule still works correctly.

Nonconventional cash flows and multiple IRRs occur when there is a net cost to shutting down a

project. The most common examples deal with collecting natural resources. After the resource has

been harvested, there is generally a cost associated with restoring the environment.

Mutually exclusive investment decisions – taking one project means another cannot be taken. An

excellent example of mutually exclusive projects is the choice of which college or university to

attend. Many students apply and are accepted to more than one college, yet they cannot attend

more than one at a time. Consequently, they have to decide between mutually exclusive projects.

Slide 27

8-27

Non-Conventional 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?

NPV = – 90,000 + 132,000 / 1.15 + 100,000 / (1.15)2 – 150,000 / (1.15)3 = 1,769.54

Calculator: CF0 = -90,000; C01 = 132,000; F01 = 1; C02 = 100,000; F02 = 1; C03 = -150,000;

F03 = 1; I = 15; CPT NPV = 1769.54

If you compute the IRR on the calculator, you get 10.11% because it is the first one that you come

to. So, if you just blindly use the calculator without recognizing the uneven cash flows, NPV would

say to accept and IRR would say to reject.

Another type of nonconventional cash flow involves a “financing” project, where there is a positive

cash flow followed by a series of negative cash flows. This is the opposite of an “investing” project.

In this case, our decision rule reverses, and we accept a project if the IRR is less than the cost of

capital, since we are borrowing at a lower rate.

Slide 28

8-28

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

N P

V

IRR = 10.11% and 42.66%

When you cross the x-axis more than once, there will

be more than one return that solves the equation

You should accept the project if the required return is between 10.11% and 42.66%.

This provides a good visual of the 2 IRRs.

Slide 29

8-29

• Mutually exclusive projects

 If you choose one, you can’t choose the other.

 Example: You can choose to attend graduate school 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

IRR and Mutually Exclusive Projects

Mutually exclusive investment decisions – taking one project means another cannot be taken. An

excellent example of mutually exclusive projects is the choice of which college or university to

attend. Many students apply and are accepted to more than one college, yet they cannot attend

more than one at a time. Consequently, they have to decide between mutually exclusive projects.

Slide 30

8-30

Example of 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?

This is a simple example of two mutually exclusive projects that result in conflicting signals

from NPV and IRR.

The important point is that we DO NOT use IRR to choose between projects.

Slide 31

8-31

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, always use NPV

• IRR is unreliable in the following situations:

– Non-conventional cash flows

– Mutually exclusive projects

Slide 32

8-32

Modified Internal Rate of Return (MIRR)

• Controls for some problems with IRR

• Three Methods:

1.Discounting Approach = Discount future outflows (negative CF) to present and add to CF0

2. Reinvestment Approach = Compound all CFs except CF0 forward to end

3. Combination Approach – Discount outflows to present; compound inflows to end

– MIRR will be unique number for each method

FR = Finance rate (discount)

RR = Reinvestment rate (compound)

let’s go back to the cash flows in Figure 8.5: −$60, +$155, and −$100. As we saw, there are two

IRRs, 25 percent and 33⅓ percent. We next illustrate three different MIRRs, all of which have the

property that only one answer will result, thereby eliminating the multiple IRR problem.

1. With the discounting approach, the idea is to discount all negative cash flows back to the present

at the required return and add them to the initial cost. Then, calculate the IRR. Because only the

first modified cash flow is negative, there will be only one IRR.

2. We compound all cash flows (positive and negative) except the first out to the end of the

project’s life and then calculate the IRR. In a sense, we are “reinvesting” the cash flows and not

taking them out of the project until the very end.

3. As the name suggests, the combination approach blends our first two methods. Negative cash

flows are discounted back to the present, and positive cash flows are compounded to the end of

the project.

Slide 33

8-33

MIRR Method 1 Discounting Approach

Method 1: Discounting Approach

R = 20%

Yr CF ADJ MCF

0 -60 -69.444 -129.44444

1 155 155

2 -100 0

IRR= 19.74%

Step 1: Discount future outflows (negative

cash flows) to present and add to CF0

Step 2: Zero out negative cash flows which

have been added to CF0.

Step 3: Compute IRR normally

1. With the discounting approach, the idea is to discount all negative cash flows back to the present

at the required return and add them to the initial cost. Then, calculate the IRR. Because only the

first modified cash flow is negative, there will be only one IRR.

Slide 34

8-34

MIRR Method 2 Reinvestment Approach

Step 1: Compound ALL cash flows (except CF0) to end of project’s life

Step 2: Zero out all cash flows which have been

added to the last year of the project’s life.

Step 3: Compute IRR normally

Method 2: Reinvestment Approach

R = 20%

Yr CF ADJ MCF

0 -60 -60

1 155 0

2 -100 186 86

IRR= 19.72%

We compound all cash flows (positive and negative) except the first out to the end of the project’s

life and then calculate the IRR. In a sense, we are “reinvesting” the cash flows and not taking them

out of the project until the very end.

The MIRR on this set of cash flows is 19.72 percent, or a little lower than we got using the

discounting approach.

Slide 35

8-35

MIRR Method 3 Combination Approach

Step 1: Discount all outflows (except CF0) to

present and add to CF0.

Step 2: Compound all cash inflows to end of

project’s life

Step 3: Compute IRR normally

Method 3: Combination Approach

R = 20%

Yr CF ADJ MCF

0 -60 -69.444 -129.44444

1 155 0

2 -100 186 186

IRR= 19.87%

The combination approach blends our first two methods. Negative cash flows are discounted back

to the present, and positive cash flows are compounded to the end of the project.

Slide 36

8-36

MIRR versus IRR

• MIRR correctly assumes reinvestment at opportunity cost = WACC

• MIRR avoids the multiple IRR problem

• Managers like rate of return comparisons, and MIRR is better for this than IRR

As our example makes clear, one problem with MIRRs is that there are different ways of

calculating them, and there is no clear reason to say one of our three methods is better than any

other. The differences are small with our simple cash flows, but they could be much larger for a

more complex project.

Slide 37

8-37

Profitability Index

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

• If a project costs $200 and the present value of its future cash flows is $220. (PI: 220/200=1.1)

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

• Can be very useful in situations of capital rationing

• Decision Rule: If PI > 1.0  Accept

Another method used to evaluate projects involves the profitability index (PI), or benefit-cost ratio.

This index is defined as the present value of the future cash flows divided by the initial investment.

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Profitability Index

• For conventional CF Projects:

PV(Cash Inflows)

Absolute Value of Initial Investment0

n

1t t

t

CF

)r1(

CF

PI   

This index is defined as the present value of the future cash flows divided by the initial investment.

If a project has a positive NPV, then the PI will be greater than 1.

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Advantages and Disadvantages of Profitability Index

• Advantages

– Closely related to NPV, generally leading to identical decisions

• Considers all CFs

• Considers TVM

– Easy to understand and communicate

– Useful in capital rationing

• Disadvantages

– May lead to incorrect decisions in comparisons of mutually exclusive investments (can conflict with NPV)

– Eg. Project A vs B A: Cost: 5, PV of CF: 10

B: Cost: 100, PV of CF: 150

A: NPV 5, PI 2

B: NPV 50, PI 1.5

The PI is obviously very similar to the NPV. If a project has a positive NPV, then the present value

of the future cash flows must be bigger than the initial investment. The profitability index would

thus be bigger than 1.00

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Capital Budgeting In Practice

• Consider all investment criteria when making decisions

• NPV and IRR are the most commonly used primary investment criteria

• Payback is a commonly used secondary investment criteria

Even though payback and AAR should not be used to make the final decision, we should consider

the project very carefully if they suggest rejection. There may be more risk than we have

considered or we may want to pay additional attention to our cash flow estimations. The fact that

payback is commonly used as a secondary criterion may be because short paybacks allow firms to

have funds sooner to invest in other projects without going to the capital markets.

It is common among large firms to employ a discounted cash flow technique such as IRR or NPV

along with payback period or average accounting return. It is suggested that this is one way to

resolve the considerable uncertainty over future events that surrounds the estimation of NPV.

Why are smaller firms more likely to use payback as a primary decision criterion?

• Small firms don’t have direct access to the capital markets and therefore find it more difficult to estimate discount rates based on funds cost; the AAR is the project-level equivalent to the

ROA measure used for analyzing firm profitability; and some small firm decision-makers

may be less aware of DCF approaches than their large firm counterparts.

When managers are judged and rewarded primarily on the basis of periodic accounting figures,

there is an incentive to evaluate projects with methods such as payback or average accounting

return. On the other hand, when compensation is tied to firm value, it makes more sense to use

NPV as the primary decision tool.

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Capital Budgeting In Practice

There have been a number of surveys conducted asking firms what types of investment criteria

they actually use

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• Net present value  Difference between market value and cost  Take the project if the NPV is positive.  Has no serious problems  Preferred decision criterion

• Internal rate of return  Discount rate that makes NPV = 0  Take the project if the IRR is greater than the required return.  Same decision as NPV with conventional cash flows  IRR is unreliable with nonconventional cash flows or mutually exclusive

projects.

• Profitability Index  Benefit-cost ratio  Take investment if PI > 1  Cannot be used to rank mutually exclusive projects  May be used to rank projects in the presence of capital rationing

Summary – DCF Criteria

For IRR, we assume a conventional investment project. For a financing project, we accept if the

IRR is less than the “required” rate.

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• Payback period  Length of time until initial investment is recovered

 Take the project if it pays back within some specified period.

 Doesn’t account for time value of money, and there is an arbitrary cutoff period

• Discounted payback period  Length of time until initial investment is recovered on a

discounted basis

 Take the project if it pays back in some specified period.

 There is an arbitrary cutoff period.

Summary – Payback Criteria

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• Average Accounting Return

 Measure of accounting profit relative to book value

 Similar to return on assets measure

 Take the investment if the AAR exceeds some specified return level.

 Serious problems and should not be used

Summary – Accounting Criterion

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• An investment project has the following cash flows: CF0 = -1,000,000; C01 – C08 = 200,000 each

• If the required rate of return is 12%, what decision should be made using NPV?

• How would the IRR decision rule be used for this project, and what decision would be reached?

• How are the above two decisions related?

Comprehensive Problem

NPV

Press the following keys: 2nd, CF, 2nd, Clear.

Calculator displays CF0, 1000,000 +|– key, press the Enter key.

Press down arrow, enter 200,000, and press Enter.

Press down arrow, enter 8, and press Enter.

Press NPV; calculator shows I = 0; enter 12 and press Enter.

Press down arrow; calculator shows NPV = 0.00.

Press CPT; calculator shows NPV = -6,472.

 NPV = -$6,472; reject the project since it would lower the value of the firm.

IRR (Don’t need to repeat above since the data is already in the calculator, but just hit IRR after

computing NPV)

Press IRR; calculator shows IRR = 0.00

Press CPT; calculator shows IRR = 16.132.

 IRR = 11.81%, so reject the project since it would tie up investable funds in a project that will provide insufficient return.

The NPV and IRR decision rules will provide the same decision for all independent projects with

conventional/normal cash flow patterns. If a project adds value to the firm (i.e., has a positive NPV), then

it must be expected to provide a return above that which is required. Both of those justifications are good

for shareholders.