CORPORATE
FINANCIAL
THEORY
Lecture 1
Corporate Financial Theory
•
Introductions
•
•
•
Faculty
Students
Syllabus & Website
•
•
•
Tests
Homework (CONNECT)
Supplements
Course Goals






Put meanings to words
Transform the complex into the simple
Make HBR readable
Make WSJ readable
Allow you to identify “BS”
Improve critical thinking skills
What is “Finance”
Economics
Theoretical
Economics
Microeconomics
Macroeconomics
Applied
Economics
Financial
Economics
( “Finance” )
Classical
Economics
Supply
Econometrics
Adam Smith
Capital
Markets
Investments
Demand
Monetary Policy
Karl Marx
Corporate
Finance
Asset
Valuation
Consumer
Fiscal Policy
John Keynes
Risk
Management
Financial
Institutions
The Firm
Milton Friedman
What is “Finance”
Economic
Level

The Role of Finance in Society
Corporate
Level
Individual
Level
Same
Principles
apply to all
Create
value
by…
Grows the
Efficiently economic
Allocating pie
Resources
which …
What is “Finance”
Population
Unemployed
1970 = 203 mil
2007 = 301 mil
Employed
What is “Finance”
Goal of Finance
Maximize the value of the firm
What is “Finance”
Accounting
Accountin
g
Finance
Statistics
Economics
What is “Finance”

Finance uses …
 Accounting
data
 Statistics
 Economic
principles

For purposes of …
 Critical
Thinking
 Analysis
 Decision making
Statistics

Accounting
Finance is not …
 Math
Economics
 Regurgitation
Critical Thinking & Analysis
Other
* Identifying
relevant
information
* Data
interpretation
* NOT plug
and chug
How to Teach Critical Thinking
DOES NOT WORK





Memorization
Root practice
Pattern matching
Examples
Formulas
TECHNIQUES



See numerous new
situations
Learning via different
methods
Non-repetitive
practice
Review CONNECT
MBA 680 Homework
Frequently Asked Questions
1. What is the purpose of homework?
Answer:
The goal of the homework is to help you develop analysis and critical thinking skills.
2. How does the homework help develop analysis and
critical thinking skills?
Answer:
MBA 680 homework requires you to “figure it out.” The technique employed is to
give you questions you have never seen. Unlike the homework assignments in
almost every other class you have ever taken, the homework in this class is not
merely pattern matching. Traditional pattern matching eliminates critical thinking
and analysis skills, by teaching you to look for familiar patterns and then apply
them.
MBA 680 Homework
Frequently Asked Questions
3. How can I answer the question if I have never
seen the type of problem before?
Answer:
That is the challenge. You must determine alternative approaches to
traditional looking problems. Someone who has never seen a Delorean
might spend all day trying to open the door and never succeed. Yet, once
you realize the door opens up, instead of out, it seems so simple. A
Chinese Finger Trap illustrates the same situation. The solution is
impossible, counter intuitive and almost impossible to figure out, using
traditional logic. Yet, when solved, it seems so simple. This is what you will
experience in the homework.
MBA 680 Homework
Frequently Asked Questions
4. How does the homework align with the lectures and why does it not
match what we cover in class?
Answer:
The homework is a supplemental learning tool. That means it is not a repeat and practice of
what we covered in class. It is additional learning. Traditional homework is designed to be
“repeat and practice” of what you covered in class. The homework in this course is designed
TO BE DIFFERENT than what we covered in class. Development of critical thinking and analysis
skills could not occur if the homework merely copied what was done in class.
5. How do I get help during an assignment?
Answer:
Send me a spreadsheet of your work. I will review it and send feedback. Since the online
homework assignments are computational, you should do your work in a spreadsheet. Please
do not wait until the due date to ask for help, as I may not be available to reply in sufficient
time. If you are stuck at “I don’t know where to start,” read the chapter. While each problem
is creative, they all originate from concepts presented in the book.
MBA 680 Homework
Frequently Asked Questions
6. I have spent many hours on one problem and cannot figure it out.
What should I do?
Answer:
You should take a break long before spending hours on one problem. As you will see, the
answers are relatively simple, yet creative. Thus, brute force is not always the answer.
Sometimes, walking away and starting fresh is the best approach. When you return, however,
read the questions SLOWLY and try a completely different approach. Often reading the
question is the key, as nuances are sometimes buried in the question.
7. How much time should the homework take?
Answer:
It depends on the person. This is the most time consuming course for many students in the
MBA program. Thus, you need to allocate considerable time outside of class. The first
homework assignment is the most difficult and time consuming. Thus, students should start
early. Since taking breaks and starting fresh sometimes works, starting near the due date
reduces the chance to step away and return to the homework.
MBA 680 Homework
Frequently Asked Questions
8. Will you go over the homework answers in class?
Answer:
No. But, I will schedule a meeting to review it, individually. Once the homework due date has
passed, you may see the answers and methods for solving the problems online. Almost always,
the answer is creative, yet simple. Students often say “I can’t believe it was that easy.” If upon
review of the answers, you still cannot figure out how the answer was calculated, contact me
to schedule an appointment or visit me during my office hours. I am happy to review the
homework with you, individually.
9. Will the test be like the homework?
Answer:
Mostly, No. The same concepts will be covered on the exam, but you will not be required to
“figure it out,” as in the homework. Instead, you will be asked to apply what you have learned.
If you have developed analysis skills, however, the test will be easier. The challenge on the test
is to match the data provided with the finance technique required. Beyond this, the math is
relatively easy.
Time Value of Money
Q: Which is greater?
$100 today or $110 next year
A: It Depends on Inflation.
Example
Bike Cost (today) = B0 = $100
Bike Cost (next year) = B1 = $110
B0 = B 1
$100 (today) = $110 (next year)
110
100 =
1.10
Time Value of Money
C1
PV0 
(1  r )
Example
Bike Cost (today) = B0 = $100
Bike Cost (next year) = B1 = $110
B0 = B1
$100 (today) = $110 (next year)
100 =
10
1+.10
Time Value of Money
C1
PV0 
(1  r )
Modified formula for unknown time frame:
Ct
PV0 
(1  r )t
Net Present Value
Example
Q:Suppose we can invest $50 today & receive $60 later today.
What is our profit?
A: Profit = - $50 + $60
= $10
Net Present Value
Example
Suppose we can invest $50 today and receive $60
in one year. Assuming 10% inflation, what is our
profit?
60
NPV = -50 +
 $4.55
1.10
Net Present Value
NPV0  C0  (1 r )t
Ct
For multiple periods we have the
Discounted Cash Flow (DCF) formula
NPV0  C0  (1 r )1  (1 r ) 2  ....
C1
C2
Net Present Value
Terminology
C = Cash Flow
t = time period
r = “discount rate” or “cost of capital”
Notes
C is not an accounting number
r is not inflation
r is the cost at which you can raise capital. The cost depends on the risk.
Net Present Value
Example
If you can invest $50 today and get $60 in return
one year from now. What is your profit? (assume
you can borrow money at 12%)
60
NPV = -50 +
 $3.57
1.12
Valuing an Office Building
Step 1: Forecast cash flows
Cost of building = C0 = 370,000
Sale price in Year 1 = C1 = 420,000
Step 2: Estimate opportunity cost of capital
If equally risky investments in the capital market
offer a return of 5%, then
Cost of capital = r = 5%
Valuing an Office Building
Step 3: Discount future cash flows
PV 
C1
(1r )

420, 000
(1.05)
 400,000
Step 4: Go ahead if PV of payoff exceeds investment
NPV  400,000  370,000
 30,000
Net Present Value
NPV = PV - required investment
C1
NPV = C0 
1 r
Risk and Present Value


Higher risk projects require a higher rate of
return
Higher required rates of return cause lower PVs
PV of C1  $420,000 at 5%
420,000
PV 
 400,000
1  .05
Risk and Present Value
PV of C1  $420,000 at 12%
420,000
PV 
 375,000
1  .12
PV of C1  $420,000 at 5%
420,000
PV 
 400,000
1  .05
Risk and Net Present Value
NPV = PV - required investment
NPV = 375,000 - 370,000
 $5,000
Net Present Value Rule

Accept ALL investments that have positive net
present value
Example
Suppose we can invest $50 today and receive $60
in one year. Should we accept the project given a
10% expected return?
60
NPV = -50 +
 $4.55
1.10
Net Present Value Rule

Accept ALL investments that have positive net
present value
Example
Suppose we can invest $50 today and receive $60
in one year. Should we accept the project given a
25% expected return?
60
NPV = -50 +
 $2.00
1.25
Rate of Return Rule

Accept investments that offer rates of return in
excess of their opportunity cost of capital
Example
In the project listed below, the foregone investment
opportunity is 12%. Should we do the project?
profit
420,000  370,000
Return 

 .135 or 13.5%
investment
370,000
Additivity Principle
Good Company
Bad Company
Project
NPV
Project
A
$ 12 mil
A
$ 12 mil
B
$ 28 mil
B
$ 28 mil
C
$ 5 mil
C
- $ 5 mil
Total Value .….
$ 45 mil
Total Value ….
$ 35 mil
Project
NPV
A
$ 12 mil
B
$ 28 mil
C (discontinue)
0
Total Value ….
$ 40 mil
NPV
Stop negative
NPV Project
Short Cuts

Sometimes there are shortcuts that make it very
easy to calculate the present value of an asset that
pays off in different periods. These tools allow us
to cut through the calculations quickly.
Short Cuts
Perpetuity
C1
PV0 
r
Constant Growth Perpetuity
Annuity
C1
PV0 
rg
1
1 
PV0  C1  
t 
r
r
(
1

r
)


Short Cuts
Perpetuity - Financial concept in which a cash flow is
theoretically received forever.
cash flow
PV of Cash Flow 
discount rate
C1
PV0 
r
Present Values
Example
What is the present value of $1.2 billion every year, for all
eternity, if you estimate the perpetual discount rate to be
8%??
PV 
$1.2 bil
0.08
 $15 billion
Present Values
Example
Tiburon Autos offers you “easy payments” of $5,000 per year, at the end
of each year for 5 years. If interest rates are 7%, per year, what is the
cost of the car?
5,000
Present Value at
0
year 0
5,000 / 1.07  4,673
5,000 / 1.07   4,367
2
5,000 / 1.07   4,081
3
5,000 / 1.07   3,814
4
5,000 / 1.07   3,565
Total NPV  20,501
5
5,000
5,000
5,000
5,000
Year
1
2
3
4
5
Short Cuts
Annuity - An asset that pays a fixed sum each year
for a specified number of years.
1
1 
PV of annuity  C   
t
 r r 1  r  
Annuity Short Cut
Example
You agree to lease a car for 4 years at $300 per month.
You are not required to pay any money up front or at the
end of your agreement. If your opportunity cost of capital
is 0.5% per month, what is the cost of the lease?
Annuity Short Cut
Example - continued
You agree to lease a car for 4 years at $300 per
month. You are not required to pay any money up
front or at the end of your agreement. If your
opportunity cost of capital is 0.5% per month,
what is the cost of the lease?
 1

1
Lease Cost  300  

48 
 .005 .0051  .005 
Cost  $12,774.10
Annuity Short Cut
Example
The state lottery advertises a jackpot prize of $295.7
million, paid in 25 installments over 25 years of $11.828
million per year, at the end of each year. If interest rates
are 5.9% what is the true value of the lottery prize?
 1

1
Lottery Value  11.828  

25 
.
059
.0591  .059 

Value  $152,600,000
Constant Growth Perpetuity
C1
PV0 
rg
g = the annual growth rate of the
cash flow
Constant Growth Perpetuity
NOTE: This formula can be used to
value a perpetuity at any point in time.
C1
PV0 
rg
C t 1
PVt 
rg
Constant Growth Perpetuity
Example
What is the present value of $1 billion paid at the end of
every year in perpetuity, assuming a rate of return of 10%
and a constant growth rate of 4%?
1
PV0 
.10  .04
 $16.667 billion
Opportunity Cost of Capital
How much “return” do you
EXPECT to earn on your
money?
Opportunity Cost of Capital
Example
You may invest $100,000 today. Depending on the state of the
economy, you may get one of three possible cash payoffs:
Economy
Payoff
Slump
Normal
Boom
$80,000 110,000 140,000
80,000  110,000  140,000
Expected payoff  C1 
 $110,000
3
Opportunity Cost of Capital
Example - continued
The stock is trading for $95.65. Next year’s price, given a
normal economy, is forecast at $110
The stocks expected payoff leads to an expected return.
expected profit 110  95.65
Expected return 

 .15 or 15%
investment
95.65
Opportunity Cost of Capital
Example - continued
Discounting the expected payoff at the expected return leads to
the PV of the project
110,000
PV 
 $95,650
1.15
NPV requires the subtraction of the initial investment
NPV  95,650  100,000  $  4,350
Internal Rate of Return Rule
Example - continued
Accept the project only if the expected return exceeds the
opportunity cost of capital
Expected return 
expected profit 110,000  100,000

 .10 or 10%
investment
100,000
Internal Rate of Return
IRR is related to Opportunity Cost of Capital
Pay Attention to Math
Internal Rate of Return
Example
You can purchase a turbo powered machine tool
gadget for $4,000. The investment will generate
$2,000 and $4,000 in cash flows for two years,
respectively. What is the IRR on this investment?
Internal Rate of Return
Example
You can purchase a turbo powered machine tool gadget for $4,000. The
investment will generate $2,000 and $4,000 in cash flows for two years,
respectively. What is the IRR on this investment?
2,000
4,000
NPV  4,000 

0
1
2
(1  IRR ) (1  IRR )
IRR  28.08%
Internal Rate of Return
2500
2000
IRR=28%
1000
500
-1000
-1500
-2000
Discount rate (%)
0
10
90
80
70
60
50
40
30
-500
20
0
10
NPV (,000s)
1500
Internal Rate of Return
Pitfall 1 - Lending or Borrowing?
Pitfall 2 - Multiple Rates of Return
Pitfall 3 - Mutually Exclusive Projects
Pitfall 4 - Term Structure Assumption
Application of PV, NPV, DCF
•
•
•
•
•
Value bonds
Value stocks
Value projects (Capital Budgeting)
Value companies (M&A)
Value Capital Structure (debt vs. equity)
Valuing Common Stocks
Return Measurements
Div 1
Dividend Yield 
P0
Div1
Restated P0 
rg
Div1
r
g
P0
Return on Equity  ROE
EPS
ROE 
Book Equit y Per Share
Valuing Common Stocks
If we forecast no growth, and plan to hold out stock
indefinitely, we will then value the stock as a
PERPETUITY.
Div1
EPS1
Perpetuity  P0 
or
r
r
Assumes all earnings are
paid to shareholders.
Valuing Common Stocks
Capitalization Rate can be estimated using the
perpetuity formula, given minor algebraic
manipulation.
Div1
Capitalization Rate  P0 
rg
Div1
r
g
P0
Valuing Common Stocks
Dividend Discount Model - Computation of today’s stock
price which states that share value equals the present
value of all expected future dividends.
Div1
Div2
Div H  PH
P0 

...
1
2
H
(1  r ) (1  r )
(1  r )
H - Time horizon for your investment.
Valuing Common Stocks
Example
Current forecasts are for XYZ Company to pay
dividends of $3, $3.24, and $3.50 over the next three
years, respectively. At the end of three years you
anticipate selling your stock at a market price of
$94.48. What is the price of the stock given a 12%
expected return?
Valuing Common Stocks
Example
Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and
$3.50 over the next three years, respectively. At the end of three years you
anticipate selling your stock at a market price of $94.48. What is the price
of the stock given a 12% expected return?
3.00
3.24
350
.  94.48
PV 


1
2
3
(1.12) (1.12)
(1.12)
PV  $75.00
Valuing Common Stocks
Example
If a stock is selling for $100 in the stock market, what
might the market be assuming about the growth in
dividends?
$3.00
$100 
.12  g
g .09
Answer
The market is
assuming the dividend
will grow at 9% per
year, indefinitely.
Valuing Common Stocks

If a firm elects to pay a lower dividend, and reinvest
the funds, the stock price may increase because future
dividends may be higher.
Payout Ratio - Fraction of earnings paid out as
dividends
Plowback Ratio - Fraction of earnings retained by the
firm.
Valuing Common Stocks
Growth can be derived from applying the return on
equity to the percentage of earnings plowed back
into operations.
g = return on equity X plowback ratio
Valuing Common Stocks
Example
Our company forecasts to pay a $8.33
dividend next year, which represents 100% of
its earnings. This will provide investors with a
15% expected return. Instead, we decide to
plowback 40% of the earnings at the firm’s
current return on equity of 25%. What is the
value of the stock before and after the
plowback decision?
Valuing Common Stocks
Example
Our company forecasts to pay a $8.33 dividend next year, which represents
100% of its earnings. This will provide investors with a 15% expected
return. Instead, we decide to plowback 40% of the earnings at the firm’s
current return on equity of 25%. What is the value of the stock before and
after the plowback decision?
No Growth
8.33
P0 
 $55.56
.15
With Growth
g  .25  .40  .10
5.00
P0 
 $100.00
.15  .10
Valuing Common Stocks
Example - continued
If the company did not plowback some earnings, the stock price
would remain at $55.56. With the plowback, the price rose to
$100.00.
The difference between these two numbers is called the Present
Value of Growth Opportunities (PVGO).
PVGO  100.00  55.56  $44.44
Valuing Common Stocks
Present Value of Growth Opportunities (PVGO) - Net
present value of a firm’s future investments.
Sustainable Growth Rate - Steady rate at which a
firm can grow: plowback ratio X return on equity.
Constant Growth DDM - A version of the dividend
growth model in which dividends grow at a constant
rate (Gordon Growth Model).
* FCF and PV *




Free Cash Flows (FCF) should be the theoretical
basis for all PV calculations.
FCF is a more accurate measurement of PV than
either Div or EPS.
The market price does not always reflect the PV of
FCF.
When valuing a business for purchase, always use
FCF.
Valuing a Business
Valuing a Business or Project
The value of a business or Project is usually computed
as the discounted value of FCF out to a valuation
horizon (H).
The valuation horizon is sometimes called the terminal
value and is calculated like PVGO.
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
(1  r ) (1  r )
(1  r )
(1  r ) H
Valuing a Business
Valuing a Business or Project
FCF1
FCF2
FCFH
PVH
PV 

 ... 

1
2
H
(1  r ) (1  r )
(1  r )
(1  r ) H
PV (free cash flows)
PV (horizon value)
Valuing a Business
Example
Given the cash flows for Concatenator Manufacturing Division, calculate
the PV of near term cash flows, PV (horizon value), and the total value of
the firm. r=10% and g= 6%
Valuing a Business
Example - continued
Given the cash flows for Concatenator Manufacturing Division, calculate
the PV of near term cash flows, PV (horizon value), and the total value of
the firm. r=10% and g= 6%
 1.09 
Horizon Value  
  27.3
 .10  .06 
27.30
PV(Horizon Value) 
 15.4
6
1.10
0
0
0
0.42 0.46
.50





1.1 1.12 1.13 1.14 1.15 1.16
 0.90
PV(FCF) 
Valuing a Business
Example - continued
Given the cash flows for Concatenator Manufacturing Division, calculate the
PV of near term cash flows, PV (horizon value), and the total value of the
firm. r=10% and g= 6%
PV(business)  PV(FCF)  PV(horizon value)
 0.90  15.40
 $16.3 million
Valuing a Business
Example
Given the cash flows for Concatenator Manufacturing Division, calculate
the PV of near term cash flows, PV (horizon value), and the total value of
the firm. r=10% and g= 6%
Year
1
2
3
4
5
6
Asset Value
10.00 12.00 14.40 17.28 20.74 23.43
Earnings
1.20 1.44 1.73 2.07 2.49 2.81
Investment
2.00 2.40 2.88 3.46 2.69 3.04
Free Cash Flow
- .80 - .96 - 1.15 - 1.39 - .20 - .23
.EPS growth (%) 20
20
20
20
20
13
7
8
9
10
26.47 28.05 29.73 31.51
3.18 3.36 3.57 3.78
1.59 1.68 1.78 1.89
1.59 1.68 1.79 1.89
13
6
6
6
Valuing a Business
Example - continued
Given the cash flows for Concatenator Manufacturing Division, calculate
the PV of near term cash flows, PV (horizon value), and the total value of
the firm. r=10% and g= 6%
1  1.59 
PV(horizon value) 
  22.4
6 
1.1  .10  .06 
.80 .96
1.15 1.39
.20
.23
PV(FCF)  




2
3
4
5
6
1.1 1.1 1.1 1.1 1.1 1.1
 3.6
Valuing a Business
Example - continued
Given the cash flows for Concatenator Manufacturing Division, calculate
the PV of near term cash flows, PV (horizon value), and the total value of
the firm. r=10% and g= 6%
PV(busines s)  PV(FCF)  PV(horizon value)
 -3.6  22.4
 $18.8
Alternatives to NPV
•
•
•
•
•
Payback Method
Average Return on Book Value
Internal Rate of Return
Equivalent Annual Annuity
Profitability Index
CFO Decision Tools
Survey Data on CFO Use of Investment Evaluation Techniques
NPV, 75%
IRR, 76%
Payback, 57%
Book rate of
return, 20%
Profitability
Index, 12%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
SOURCE: Graham and Harvey, “The Theory and Practice of Finance: Evidence from the Field,” Journal of
Financial Economics 61 (2001), pp. 187-243.
Book Rate of Return
Book Rate of Return - Average income divided by average
book value over project life. Also called accounting rate of
return.
book income
Book rate of return 
book assets
Managers rarely use this measurement to make decisions.
The components reflect tax and accounting figures, not
market values or cash flows.
Payback



The payback period of a project is the number of years it
takes before the cumulative forecasted cash flow equals the
initial outlay.
The payback rule says only accept projects that “payback” in
the desired time frame.
This method is flawed, primarily because it ignores later year
cash flows and the the present value of future cash flows.
Payback
Example
Examine the three projects and note the mistake we
would make if we insisted on only taking projects with a
payback period of 2 years or less.
Project
C0
C1
C2
C3
A
- 2000
500
500
5000
B
- 2000
500
1800
0
C
- 2000 1800
500
0
Payback
Period
NPV@ 10%
Payback
Example
Examine the three projects and note the mistake we
would make if we insisted on only taking projects with a
payback period of 2 years or less.
C3
Payback
Project
C0
C1
C2
A
- 2000
500
500
B
- 2000
500
1800
0
2
- 58
C
- 2000 1800
500
0
2
 50
Period
5000
3
NPV@ 10%
 2,624
Problems with CB & NPV



1 – Determine relevant cash flows
2 - Cash flows not guaranteed
3 - Projects with different lives
 Timing
 Equivalent
annual annuity (cost)
 Profitability Index
 Linear Programming
Equivalent Annuities
Proj
0
1
2
3
4
A
-15
4.9
5.2
5.9
6.2
B
-20
8.1
8.7
10.4
assume 9% discount rate
NPV
Eq. Ann.
Equivalent Annuities
Proj
0
1
2
3
4
NPV
A
-15
4.9
5.2
5.9
6.2
2.82
B
-20
8.1
8.7
10.4
assume 9% discount rate
2.78
Eq. Ann.
Equivalent Annuities
Proj
0
1
2
3
4
NPV
A
-15
4.9
5.2
5.9
6.2
2.82
.87
B
-20
8.1
8.7
10.4
2.78
1.10
assume 9% discount rate
Eq. Ann.
Profitability Index



When resources are limited, the profitability index
(PI) provides a tool for selecting among various
project combinations and alternatives
A set of limited resources and projects can yield
various combinations.
The highest weighted average PI can indicate which
projects to select.
Profitability Index
Cash Flows ($ millions)
Project
A
C0
C1
 10  30
C2
5
NPV @ 10%
21
B
5
5
 20
16
C
5
5
 15
12
D
0
 40
60
13
Profitability Index
Cash Flows ($ millions)
Project
A
Investment ($)
10
NPV ($) Profitabil ity Index
21
2.1
B
5
16
3.2
C
5
12
2.4
D
0
13
0.4
Profitability Index
NPV
Profitabil ity Index 
Investment
Example
We only have $300,000 to invest. Which do we select?
Proj
A
B
C
D
NPV
230,000
141,250
194,250
162,000
Investment
200,000
125,000
175,000
150,000
PI
1.15
1.13
1.11
1.08
Profitability Index
Example - continued
Proj
NPV
A
230,000
B
141,250
C
194,250
D
162,000
Investment
200,000
125,000
175,000
150,000
PI
1.15
1.13
1.11
1.08
Select projects with highest Weighted Average P.I.
125
150
25
𝑊𝐴𝑃𝐼 𝐵𝐷 = 1.13 ×
+ 1.08 ×
+ 0.0 ×
300
300
300
=1.01
Profitability Index
Example - continued
Proj
NPV
A
230,000
B
141,250
C
194,250
D
162,000
Investment
200,000
125,000
175,000
150,000
PI
1.15
1.13
1.11
1.08
Select projects with highest Weighted Average P.I.
WAPI (BD) = 1.01
WAPI (A) = 0.77
WAPI (BC) = 1.12
Linear Programming


Maximize Cash flows or NPV
Minimize costs
Example
Max NPV = 21Xn + 16 Xb + 12 Xc + 13 Xd
subject to
10Xa + 5Xb + 5Xc + 0Xd <= 10
-30Xa - 5Xb - 5Xc + 40Xd <= 12
Capital Budgeting Rules
Valuing a project = capital budgeting
4 Rules of Capital Budgeting
1 - Consider all cash flows
2 - Discount all CF at opportunity cost of capital
3 - Select project that maximizes shareholder wealth
4 - Must consider projects independent of each other =
“Additivity Principle”
NPV is used to evaluate projects because its satisfies all rules
Capital Budgeting Rules
Only Cash Flow is Relevant
Capital Budgeting Rules
Points to “Watch Out For”






Do not confuse average with incremental payoff
Include all incidental effects
Do not forget working capital requirements
Forget sunk costs
Include opportunity costs
Beware of allocated overhead costs
Capital Budgeting Rules

INFLATION RULE
Be consistent in how you handle inflation!!
 Use nominal interest rates to discount nominal
cash flows.
 Use real interest rates to discount real cash
flows.
 You will get the same results, whether you use
nominal or real figures
