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.
Slide 38
8-38
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.