Slide 1 8-1Capital Budgeting• Analysis of potent.docx

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:
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.

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.

8-8
Display You Enter
CF, 2nd,CLR WORK
CF0 -165000 Enter, Down
C01 63120 Enter, Down
F01 1 Enter, Down
F02 1 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 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
TVM
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.

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.

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
• 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
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.

8-15
• Assume we require an average accounting return
of 25%.
• Average Net Income:
• 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
• 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
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.

8-19
IRR
Definition and Decision Rule
• Definition:
• Decision Rule:
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
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
F01 1 Enter, Down
F02 1 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 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.

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.

Slide 27
8-27
Non-Conventional Cash Flows
• Suppose an investment will cost $90,000
initially and will generate the following cash
flows:
-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
either Harvard or Stanford, but not both.
• Intuitively, you would use the following decision
rules:
– choose the project with the higher NPV
– choose the project with the higher IRR
IRR and 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.

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.
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

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
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.

8-39
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
Slide 40
8-40
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.
Slide 41
8-41
Capital Budgeting In Practice
There have been a number of surveys conducted asking firms
what types of investment criteria

they actually use
Slide 42
8-42
• Net present value
criterion
• Internal rate of return
mutually exclusive
projects.
• Profitability Index
-cost ratio
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.
Slide 43
8-43
• Payback period
within some specified period.
arbitrary cutoff period
• Discounted payback period
discounted basis
ck in some specified period.

Summary – Payback Criteria
Slide 44
8-44
• Average Accounting Return
e investment if the AAR exceeds some
specified return level.
Summary – Accounting Criterion

8-45
• 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 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.
-$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.
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.

11-1
Return, Risk, and The Security Market Line
We have to define risk and then discuss how to measure it. We
then must quantify the relationship
between an asset’s risk and its required return.
There are two types of risk: systematic and unsystematic. This
distinction is crucial because, as we
will see, systematic risk affects almost all assets in the
economy, at least to some degree, while
unsystematic risk affects at most a small number of assets. We
then develop the principle of
diversification, which shows that highly diversified portfolios
will tend to have almost no
unsystematic risk.

11-2
• Expected returns are based on the probabilities of
possible outcomes.
• In this context, “expected” means average if the
process is repeated many times.
• The “expected” return does not even have to be a
possible return.
Where:
pi = the probability of state “i” occurring
Ri = the expected return on an asset in state i
Expected Returns
=
=
n
i
ii RpRE
1

)(
Slide 3
11-3
Example: Expected Returns
Stock C Stock T
State (i) Probability (Pi) (Ri) (Ri) ___
Boom 0.3 0.15 0.25
Normal 0.5 0.10 0.20
Recession ??? 0.02 0.01
1.00
• E(RC) = .3(.15) + .5(.1) + .2(.02) = 0.099
• E(RT) = .3(.25) + .5(.2) + .2(.01) = 0.177
13-3
• Suppose you have predicted the following
returns for stocks C and T in three possible

states of the economy. What are the
expected returns?
What is the probability of a recession? 1- 0.3 - 0.5 = 0.2
Or work in the percentage terms.
E(RC) = .3(15%) + .5(10%) + .2(2%) = 9.9%
E(RT) = .3(25%) + .5(20%) + .2(1%) = 17.7%
Slide 4
11-4
Variance and Standard Deviation
the volatility of returns
• Variance = Weighted average of squared
deviations
• Standard Deviation = Square root of variance

=
−=
n
i
ii RERp
1
22 ))((σ
Variance measures the dispersion of points around the mean of a
distribution. In this context, we
are attempting to characterize the variability of possible future
security returns around the expected
return. In other words, we are trying to quantify risk and return.
Variance measures the total risk
of the possible returns.
Slide 5
11-5

Variance and Standard Deviation
• Consider the previous example. What are the variance
and standard deviation for each stock?
Stock C Stock T
State (i) Probability (Pi) (Ri) (Ri) ___
Boom 0.3 0.15 0.25
Normal 0.5 0.10 0.20
Recession 0.2 0.02 0.01
E(RC) = 0.099 E(RT) = 0.177
• Stock C
-0.099)2 + .5(0.10-0.099)2 + .2(0.02-0.099)2 =
0.002029
• Stock T
-0.177)2 + .5(0.20-0.177)2 + .2(0.01-0.177)2 =
0.007441
13-5

11-6
Another Example
• Consider the following information:
State(i) Probability (Pi) ABC, Inc. Return
Boom .25 0.15
Normal .50 0.08
Slowdown .15 0.04
Recession .10 -0.03
• What is the expected return?
• E(R) = .25(0.15) + .5(0.08) + .15(0.04) + .1(-0.03) = 8.05%
• What is the variance?
• Variance = .25(.15-0.0805)2 + .5(0.08-0.0805)2 + .15(0.04-
0.0805)2 +
• .1(-0.03-0.0805)2 = 0.00267475
• What is the standard deviation?
• Standard Deviation = 5.17%
13-6

⚫ E(R) = .25(0.15) + .5(0.08) + .15(0.04) + .1(-0.03) = 0.0805
(=8.05%)
⚫ Variance = .25(.15-0.0805)2 + .5(0.08-0.0805)2 + .15(0.04-
0.0805)2 + .1(-0.03-0.0805)2 =
0.00267475
⚫ Standard Deviation = 0.0517 (=5.17%)
You may experience confusion in understanding the
mathematics of the variance calculation. You may
have the feeling that you should divide the variance of an
expected return by (n−1). Note that the
probabilities account for this division. We divide by n−1 in the
historical variance because we are looking
at a sample. If we looked at the entire population (which is what
we are doing with expected values), then
we would divide by n (or multiply by 1 ⁄ n) to get our historical
variance. This is the same as saying that the
“probability” of occurrence is the same for all observations and
is equal to 1 ⁄ n.
Slide 7

11-7
Portfolios
• Portfolio = collection of assets
• An asset’s risk and return impact how the
stock affects the risk and return of the
portfolio
• The risk-return trade-off for a portfolio is
measured by the portfolio expected return
and standard deviation, just as with
individual assets
Each individual has their own level of risk tolerance. Some
people are just naturally more inclined
to take risk, and they will not require the same level of
compensation as others for doing so. Our
risk preferences also change through time. We may be willing to
take more risk when we are young
and without a spouse or kids. But, once we start a family, our
risk tolerance may drop.

11-8
Portfolio Expected Returns
• Expected return for an asset:
• The expected return of a portfolio is the
weighted average of the expected returns
for each asset in the portfolio
• Weights (wj) = % of portfolio invested in
each asset
=
=
m
1j
jjP )R(Ew)R(E
=
=
n
1i
iiRp)R(E

The expected return on a portfolio is the sum of the product of
the expected returns on the
individual securities and their portfolio weights. Let wj be the
portfolio weight for asset j and m
be the total number of assets in the portfolio.
You can also find the expected return by finding the portfolio
return in each possible state and
computing the expected value as we did with individual
securities.
Slide 9
11-9
Example: Portfolio Weights
• Suppose you have $15,000 to invest and you have
purchased securities in the following amounts. What
are your portfolio weights in each security?

▪ $2000 of C
▪ $3000 of KO
▪ $4000 of INTC
▪ $6000 of BP
▪ C: 2000/15000 = .133
▪ KO: 3000/15000 = .2
▪ INTC: 4000/15000 = .267
▪ BP: 6000/15000 = .4
13-9
Weights (wj) ?
C – Citigroup
KO – Coca-Cola
INTC – Intel
BP – BP
Note that the sum of the weights = 1 (=100%).
A portfolio is a collection of assets, such as stocks and bonds,
held by an investor. Portfolios can

be described by the percentage investment in each asset. These
percentages are called portfolio
weights.
Example: If two securities in a portfolio have a combined value
of $10,000 with $6000 invested
in IBM and $4000 invested in GM, then the weight on IBM =
6000 ⁄ 10000 = .6 (=60%) and the
weight on GM = 4000 ⁄ 100000 = .4 (=40%) or we can simply
calculate the weight on GM by 1 –
0.6 = 0.4 (=40%) since the sum of the weights equals 1
(=100%).
Slide 10
11-10
Expected Portfolio Returns
• Consider the portfolio weights computed
previously. If the individual stocks have the
following expected returns, what is the

expected return for the portfolio?
•
▪ C: 19.69%
▪ KO: 5.25%
▪ INTC: 16.65%
▪ BP: 18.24%
• E(RP) = .133(0.1969) + .2(0.0525)
+ .267(0.1665) + .4(0.1824) = 0.1541
13-10
▪ C: 2000/15000 = .133
▪ KO: 3000/15000 = .2
▪ INTC: 4000/15000 = .267
▪ BP: 6000/15000 = .4
Weights (wj) Expected Return E(Rj)
Slide 11

11-11
Portfolio Variance
• Compute portfolio return for each state:
RP,i = w1R1,i + w2R2,i + … + wmRm,i
• Compute the overall expected portfolio
return using the same formula as for an
individual asset
• Compute the portfolio variance and standard
deviation using the same formulas as for an
individual asset
The calculation of portfolio variance requires three steps:
1. Compute the portfolio return for each state of the economy.
2. Compute the overall expected return of the portfolio.
3. Compute portfolio variance and standard deviation using the
same formulas as for an
individual asset.
Unlike expected return, the variance of a portfolio is NOT the
weighted sum of the individual

security variances. Combining securities into portfolios can
reduce the total variability of returns.
Slide 12
11-12
Example: Portfolio Variance
• Consider the following information on returns and
probabilities:
▪ Invest 50% of your money in Asset A
State Probability A B
Boom .4 30% -5%
Bust .6 -10% 25%
• What are the expected return and standard
deviation for each asset?
deviation for the portfolio?
13-12

11-13
• Invest 50% of your money in Asset A
State Probability A B
Boom .4 30% -5%
Bust .6 -10% 25%
deviation for each asset?
Asset A: E(RA) = .4(0.3) + .6(-0.1) = 0.06 (=6%)
Variance(A) = .4(0.3-0.06)2 + .6(-0.1-0.06)2 = 0.0384
Std. Dev.(A) = 0.196 (=19.6%)

Asset B: E(RB) = .4(-0.05) + .6(0.25) = 0.13 (=13%)
Variance(B) = .4(-0.05-0.13)2 + .6(0.25-0.13)2 = 0.0216
Std. Dev.(B) = 0.147 (=14.7%)
• What are the expected return for the portfolio?
E(Rp) = .5(0.06) + .5(0.13) = 0.095 (=9.5%)
13-13
Expected return and standard deviation for each asset
Asset A: E(RA) = .4(30%) + .6(-10%) = 6%
Variance(A) = .4(30%-6%)2 + .6(-10%-6%)2 = 384
Std. Dev.(A) = √384 =19.6%
Asset B: E(RB) = .4(-5%) + .6(25%) = 13%
Variance(B) = .4(-5%-13%)2 + .6(25%-13%)2 = 216

Std. Dev.(B) = √216 =14.7%
Expected return for the portfolio (1)
The expected return on a portfolio is the sum of the product of
the expected returns on the
individual securities and their portfolio weights. Weights (wj) =
% of portfolio invested in each
asset. There are two stocks in your portfolio and you invest 50%
of your money in Asset A.
What percent are you investing in Asset B? 50% (= (100% -
50%)). Thus, WA = 0.5, and WB = 0.5
E(Rp) = .5(6%) + .5(13%) = 9.5%
Slide 14
11-12
• Consider the following information on returns and
probabilities:
State Probability A B Portfolio

Boom .4 30% -5% 12.5% = RP,Boom
Bust .6 -10% 25% 7.5% = RP,Bust
E(RA) = 6% E(RB) = 13% E(Rp)
13-12
(1)
(2)
To compute the standard deviation for the portfolio, we need to
follow three steps (See Slide 11)
1. Compute the portfolio return for each state of the economy.
There are two stocks in your portfolio and you invest 50% of
your money in Asset A. What
percent are you investing in Asset B? 50% (= (100% - 50%)).
Thus, WA = 0.5, and WB = 0.5
Portfolio return in boom: RP,Boom = 0.5(0.3) + 0.5(-0.05) =
0.125 (=12.5%)
Portfolio return in bust: RP,Bust = 0.5(-0.1) + 0.5(0.25) = 0.075
(=7.5%)

RP,Boom = 0.5(30%) + 0.5(-5%) = 12.5%
RP,Bust = 0.5(-10%) + 0.5(25%) =7.5%
2. Compute the overall expected return of the portfolio.
In Slide 13, we computed E(Rp) = .5(6%) + .5(13%) = 9.5%
- (1)
You can also find the expected return for the portfolio by
finding the portfolio return in each
possible state and computing the expected value as we did with
individual securities.
E(Rp) = .4(12.5%) + .6(7.5%) = 9.5% - (2)
Slide 15
11-14
State Probability A B Portfolio

Boom .4 30% -5% 12.5%
Bust .6 -10% 25% 7.5%
Portfolio return in boom (RP,Boom) = .5(.3) + .5(-.05) = .125
Portfolio return in bust (RP,Bust) = .5(-.1) + .5(.25) = .075
Expected return for portfolio E(RP) = .5(.06) + .5(.13) = .095 or
.4(.125) + .6(.075) = .095
Variance of portfolio = .4(.125-.095)2 + .6(.075-.095)2 = .06
Standard deviation = .0245
13-14
3. Compute portfolio variance and standard deviation using the
same formulas as for an individual
asset.
Expected return = .5(6%) + .5(13%) = 9.5% or
Expected return = .4(12.5%) + .6(7.5%) = 9.5%
Variance of portfolio = .4(12.5%-9.5%)2 + .6(7.5%-9.5%)2 =
6%

Standard deviation = 2.45%
Unlike expected return, the variance of a portfolio is NOT the
weighted sum of the individual
security variances. Combining securities into portfolios can
reduce the total variability of returns.
• Note that the variance is NOT equal to .5(384) + .5(216) = 300
and
• Standard deviation is NOT equal to .5(19.6) + .5(14.7) =
17.17%
To compute variance of portfolio, follow the direction of (2) in
the previous slide.
Slide 16
11-15
• Realized returns are generally not equal to
expected returns.
• There is the expected component and the
unexpected component.
▪ At any point in time, the unexpected return can be

either positive or negative.
▪ Over time, the average of the unexpected component is
zero.
Expected vs. Unexpected Returns
Expected vs. Unexpected Returns
Total return = Expected return + Unexpected return
Total return differs from expected return because of surprises,
or “news.” This is one of the
reasons that realized returns differ from expected returns.
Slide 17
11-16
Announcements and News
• Announcements and news contain both an expected
component and a surprise component

• It is the surprise component that affects a stock’s
price and therefore its return
• This is very obvious when we watch how stock prices
move when an unexpected announcement is made
or earnings are different than anticipated
13-16
Announcement—the release of information not previously
available. Announcements have two
parts: the expected part and the surprise part. The expected part
is “discounted” information used
by the market to estimate the expected return, while the surprise
is news that influences the
unexpected return.
Slide 18
11-17
Announcements and News

• On November 17, 2004 it was announced that K-
Mart would acquire Sears in an $11 billion deal.
Sears’ stock price jumped from a closing price of
$45.20 on November 16 to a closing price of $52.99
(a 7.79% increase) and K-Mart’s stock price jumped
from $101.22 on November 16 to a closing price of
$109.00 on November 17 (a 7.69% increase). Both
stocks traded even higher during the day.
• Why the jump in price?
13-17
It is easy to see the effect of unexpected news on stock prices
and returns. Consider the following
two cases:
(1) On November 17, 2004 it was announced that K-Mart would
acquire Sears in an $11 billion
deal. Sears’ stock price jumped from a closing price of $45.20
on November 16 to a closing price
of $52.99 (a 7.79% increase) and K-Mart’s stock price jumped
from $101.22 on November 16 to
a closing price of $109.00 on November 17 (a 7.69% increase).
Both stocks traded even higher
during the day. Why the jump in price? Unexpected news, of
course.

(2) On November 18, 2004, Williams-Sonoma cut its sales and
earnings estimates for the fourth
quarter of 2004 and its share price dropped by 6%. There are
plenty of other examples where
unexpected news causes a change in price and expected returns.
Slide 19
11-18
Efficient Markets
• Efficient markets are a result of investors
trading on the unexpected portion of
announcements
• The easier it is to trade on surprises, the more
efficient markets should be
• Efficient markets involve random price
changes because we cannot predict surprises
13-18

11-19
Systematic Risk
• Risk factors that affect a large number of assets
• Also known as non-diversifiable risk or market risk.
• Examples: changes in GDP, inflation, interest rates,
etc.
Risk consists of surprises. There are two kinds of surprises:
Systematic Risk & Unsystematic
Risk
• Systematic risk is a surprise that affects a large number of
assets, although at varying
degrees. It is sometimes called market risk.
• Example: Changes in GDP, interest rates, and inflation are
examples of systematic risk.

11-20
Unsystematic Risk
• = Diversifiable risk
• Risk factors that affect a limited number of assets
• Also known as unique risk or asset-specific risk.
• Risk that can be eliminated by combining assets
into portfolios
• Examples: labor strikes, part shortages, etc.
• Unsystematic risk is a surprise that affects a small number of
assets (or one). It is
sometimes called unique or asset-specific risk.
• Example: Strikes, accidents, and takeovers are examples of
unsystematic risk.

11-21
Diversification
• Portfolio diversification is the investment in
several different asset classes or sectors
• Diversification is not just holding a lot of assets
• For example, if you own 50 Internet stocks, you
are not diversified
• However, if you own 50 stocks that span 20
different industries, then you are diversified
13-21
Portfolio diversification can substantially reduce risk without
an equivalent reduction in expected
returns
• Reduces the variability of returns

Minimum level of risk that cannot be diversified away =
systematic portion
Slide 23
11-22
• Diversification can substantially reduce the
variability of returns without an equivalent
reduction in expected returns.
• This reduction in risk arises because worse than
expected returns from one asset are offset by
better than expected returns from another.
• However, there is a minimum level of risk that
cannot be diversified away and that is the
systematic portion.
The Principle of Diversification
Principle of Diversification – States that combining imperfectly
correlated assets can produce a
portfolio with less variability than the typical individual asset.

The portion of variability present in a single security that is not
present in a portfolio of securities
is called diversifiable risk. The level of variance that is present
in portfolios of assets is non-
diversifiable risk.
Slide 24
11-23
Standard Deviations of Annual Portfolio Returns
Table 13.7
A typical single stock on the NYSE has a standard deviation of
annual returns around 49%, while
the typical large portfolio of NYSE stocks has a standard
deviation of around 20%.

11-24
• The risk that can be eliminated by combining
assets into a portfolio.
• Often considered the same as unsystematic,
unique or asset-specific risk
• If we hold only one asset, or assets in the same
industry, then we are exposing ourselves to risk
that we could diversify away.
Diversifiable Risk
When securities are combined into portfolios, their unique or
unsystematic risks tend to cancel out,
leaving only the variability that affects all securities to some
degree. Thus, diversifiable risk is
synonymous with unsystematic risk. Large portfolios have little
or no unsystematic risk.

11-25
Total Risk = Stand-alone Risk
• Total risk = Systematic risk + Unsystematic risk
– The standard deviation of returns is a measure of
total risk
• For well-diversified portfolios, unsystematic risk
is very small
– Total risk for a diversified portfolio is essentially
equivalent to the systematic risk
– The expected return (market required return) on an
asset depends only on that asset’s systematic or
market risk.
Systematic risk cannot be eliminated by diversification since it
represents the variability due to
influences that affect all securities to some degree. Therefore,
systematic risk and non-
diversifiable risk are the same.

Total risk = Non-diversifiable risk + Diversifiable risk
= Systematic risk + Unsystematic risk
Slide 27
11-26
Market Risk for Individual Securities
• Measures the stock’s volatility relative to the
market
While the standard deviation of returns is a measure of total
risk, the beta coefficient measures
how much systematic risk an asset has relative to an asset of
average risk.
Beta measures the volatility of an individual asset or portfolio
relative to the market as a whole.

11-27
Measuring Systematic Risk
• How do we measure systematic risk?
▪ We use the beta coefficient
• What does beta tell us?
▪ A beta = 1 implies the asset has the same systematic
risk as the overall market
▪ A beta < 1 implies the asset has less systematic risk
than the overall market
▪ A beta > 1 implies the asset has more systematic risk
than the overall market
▪ Most stocks have betas in the range of 0.5 to 1.5
▪ Beta of a T-Bill = 0
13-27
Robert Hamada derived the following equation to reflect the

relationship between levered and
unlevered betas (excluding tax effects):
where:
D/E = debt-to-equity ratio
Slide 29
11-28
Beta Coefficients for Selected Companies
Table 13.8

11-29
• Consider the following information:
Standard Deviation Beta
Security C 20% 1.25
Security K 30% 0.95
• Which security has more total risk?
• Which security has more systematic risk?
• Which security should have the higher expected return?
Total vs. Systematic Risk
Security K has the higher total risk.
Security C has the higher systematic risk.
Security C should have the higher expected return.
• When securities are combined into portfolios, their unique or
unsystematic risks tend to
cancel out, leaving only the variability that affects all securities
to some degree. Thus,

Total risk for a diversified portfolio is essentially equivalent to
the systematic risk. The
expected return (market required return) on an asset depends
only on that asset’s
systematic or market risk.
Slide 31
11-30
Portfolio Beta
βp = Weighted average of the Betas of the
assets in the portfolio
Weights (wj)= % of portfolio invested in asset j
=
=
n
j
jjp w
1

The beta of the portfolio is simply a weighted average of the
betas of the securities in the
portfolio.
Slide 32
11-31
• Consider the previous example with the
following four securities.
Security Weight Beta
C .133 1.685
KO .2 0.195
INTC .267 1.161
BP .4 1.434
• What is the portfolio beta?
• .133(1.685) + .2(.195) + .267(1.161) + .4(1.434) = 1.147
Example: Portfolio Betas

Which security has the highest systematic risk?
C
Which security has the lowest systematic risk?
KO
Is the systematic risk of the portfolio more or less than the
market?
more
Slide 33
11-32
Example: Portfolio Expected Returns
and Betas
0%
5%
10%
15%

20%
25%
30%
0 0.5 1 1.5 2 2.5 3
E
x
p
ec
te
d
R
et
u
rn
Beta
Rf
E(RA)
There is a linear relationship between beta and expected return.

combined with a riskless asset, the
resulting expected return is the weighted sum of the expected
returns, and the portfolio beta is the
weighted sum of the betas. By varying the amount invested in
each asset, we can get an idea of the
relation between portfolio expected returns and betas. This
relationship is illustrated in this figure.
As can be seen, all of the risk-return combinations lie on a
straight line. The equation for a line is:
Y = mx + b
where: y = expected return
x = beta
m = slope = risk-premium per unit of beta
b = y-intercept = risk-free rate
E(R) = slope (Beta) + y-intercept
The y-intercept is = the risk-free rate, so all we need is the
slope

11-33
Reward-to-Risk Ratio: Definition and
Example
• The reward-to-risk ratio is the slope of the line
illustrated in the previous example
▪ Slope = (E(RA) – – 0)
▪ Reward-to-risk ratio for previous example =
(20 – 8) / (1.6 – 0) = 7.5
• What if an asset has a reward-to-risk ratio of 8
(implying that the asset plots above the line)?
• investors will want to buy the asset.
• What if an asset has a reward-to-risk ratio of 7
(implying that the asset plots below the line)?
• investors will want to sell the asset
13-33
The Reward-to-Risk Ratio is the expected return per unit of

systematic risk. In other words, it is
the ratio of risk premium to systematic risk.
If the reward-to-risk ratio = 8, then investors will want to buy
the asset. This will drive the price
up and the expected return down (remember time value of
money and valuation). When will the
flurry of trading stop? When the reward-to-risk ratio reaches
7.5.
If the reward-to-risk ratio = 7, then investors will want to sell
the asset. This will drive the price
down and the expected return up. When will the flurry of
trading stop? When the reward-to-risk
ratio reaches 7.5.
Slide 35
11-34
Beta and the Risk Premium

• Risk premium = E(R ) – Rf
• The higher the beta, the greater the risk
premium should be
• Can we define the relationship between the
risk premium and beta so that we can
estimate the expected return?
– YES!
The risk premium—the excess return of an asset above the risk-
free rate.
Slide 36
11-35
Security Market Line
• The security market line (SML) is the
representation of market equilibrium
• The slope of the SML = reward-to-risk ratio
= (E(RM) –

• But since the beta for the market is always
equal to one, the slope can be rewritten
• Slope = E(RM) – Rf = market risk premium
The line that gives the expected return/systematic risk
combinations of assets in a well-functioning,
active financial market is called the security market line.
Market Portfolios: Consider a portfolio of all the assets in the
market and call it the market portfolio.
This portfolio, by definition, has “average” systematic risk with
a beta of 1. Since all assets must
lie on the SML when appropriately priced, the market portfolio
must also lie on the SML. Let the
expected return on the market portfolio = E(RM). Then, the
slope of the SML = reward-to-risk ratio

11-36
Market Equilibrium
• In equilibrium, all assets and portfolios must
have the same reward-to-risk ratio
• Each ratio must equal the reward-to-risk
ratio for the market
M
fM
A
fA )RR(ER)R(E
−
=
−
The basic argument is that since systematic risk is all that
matters in determining expected return,
the reward-to-risk ratio must be the same for all assets. If it
were not, people would buy the asset
with the higher reward-to-risk ratio (driving the price up and

the return down).
The fundamental result is that in a competitive market where
only systematic risk affects E(R),
the reward-to-risk ratio must be the same for all assets in the
market. Consequently, the expected
returns and betas of all assets must plot on the same straight
line.
E.g., Amazon (Asset j =A)
We can solve for � ��
E RA Rf
βA
E RM Rf
βM
[E RA Rf] x βM = βA x [E RM Rf ]
Since the market beta, βM = 1 (Wee Slide 28),
E RA Rf = βA [E RM Rf ]
E RA = Rf + βA [E RM Rf ]

Since E(Rf) = Rf,
E RA = Rf + βA [E RM Rf]
This is called the capital asset pricing model (CAPM)
Slide 38
11-37
SML and Equilibrium
The Capital Asset Pricing Model (CAPM):
We can get an idea of the relationship between portfolio
expected returns and betas.

11-38
The SML and Required Return
• The Security Market Line (SML) is part of the
Capital Asset Pricing Model (CAPM)
Rf = Risk-free rate (T-Bill or T-Bond)
RM = Market return ≈ S&P 500
RPM = Market risk premium = E(RM) – Rf
E(Rj) = “Required Return of Asset j”
( )
( ) jMfj
jfMfj
RPRRE
RRERRE
+=
−+=

)(
)()(
Slide 40
11-39
Capital Asset Pricing Model
• The capital asset pricing model (CAPM)
defines the relationship between risk and
return
E(Rj) = Rf + βj(E(RM) – Rf)
• If an asset’s systematic r
CAPM can be used to determine its expected
return
Slide 41

11-40
Factors Affecting Required Return
• Rf measures the pure time value of money
• E(RM)-Rf measures the reward for bearing
systematic risk
amount of systematic risk
The CAPM states that the expected return for an asset depends
on:
-The time value of money, as measured by Rf
-The reward per unit risk, as measured by E(RM) − Rf
-The asset’s systematic risk,
Slide 42

11-41
Quick Quiz
Consider an asset with a beta of 1.2, a risk-free rate of
5%, and a market return of 13%.
– What is the reward-to-risk ratio in equilibrium?
– What is the expected return on the asset?
• E(R) = 5% + (13% - 5%)* 1.2 = 14.6%
Reward-to-risk ratio = 13 – 5 = 8%
Expected return = 5 + 1.2(8) = 14.6%

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