Lecture 1
Managerial Finance
FINA 6335
Ronald F. Singer
Finance
 The study of resource allocation under
conditions of uncertainty.
 Merges:
– Economics.
– Accounting.
– Statistics.
Areas
 Corporate Finance
From the viewpoint of the Financial Manager
– Capital Budgeting
– Dividend Policy
– Capital Structure
 Investments
From the viewpoint of individual and institutional
investors
– Risk
– Return
– Portfolio Decisions
Types of Financial Securities
 Equity Capital
– Common Stock
– Preferred Stock
 Debt Capital
– Bonds
 Hybrid Securities
– Why hold Securities?
The Rewards and Risks to
Security Holders
 The Rewards
– To Stockholders
– To Bondholders
 The Risks:
– To Stockholders
– To Bondholders
The Goal of Financial
Management
 What should be the goal?
 Possible measures
financial managers
of
performance
of
 How do managers achieve their objectives?
Make Decisions that
Investment
 The Problem
How can we determine if a project will make
stockholders’ better or worse off???
 What is an Investment?
Current Cash Expenditures which are
expected to generate cash inflows
sometime in the future
How to Make a Decision?
Inflow
Benefits
vs.
Costs
Complications
Uncertainty
Future Flows
Digression on
Conventions of Time
Cash Inflows
Cash Outflows
Example
•
For current Investment of $10,000, receive $5,000
within 1 year, $6,000 in years 3 through 5.
5000
6000
6000
6000.
0.
1
2
3
4
5
10000.
•
Observations:
1. t = 0
current time.
2. Everything happens at the end of a period unless
specified otherwise.
Using Market Prices
to Determine Cash Values
 Suppose a jewelry manufacturer has the
opportunity to trade 10 ounces of platinum
and receive 20 ounces of gold today. To
compare the costs and benefits, we first
need to convert them to a common unit.
Using Market Prices
to Determine Cash Values
(cont'd)
 Suppose gold can be bought and sold for a
current market price of $250 per ounce.
Then the 20 ounces of gold we receive has

a cash value of:
– (20 ounces of gold)

today
($250/ounce) = $5000
Using Market Prices
to Determine Cash Values
(cont'd)
 Similarly, if the current market price for
platinum is $550 per ounce, then the 10
ounces of platinum we give up has a cash

value of:
– (10 ounces of platinum)

$5500
($550/ounce) =
Using Market Prices
to Determine Cash Values
(cont'd)
 Therefore, the jeweler’s opportunity has a
benefit of $5000 today and a cost of $5500
today. In this case, the net value of the
project today is:
– $5000 – $5500 = –$500
 Because it is negative, the costs exceed the
benefits and the jeweler should reject the
trade.
Example 3.1
Example 3.1 (cont'd)
Example 3.2
Example 3.2 (cont'd)
Present Value
 The present value of receiving $1,000, one year
from today?
$1000
0
1
It is : What $1000 received one year from
today is worth today.
Present Value
 Present Value is:
– How much someone would lend me on that claim
– How much I could sell the claim for
– How much it would cost to engage in a "similar"
investment
 What is the Answer?
– In order to answer that question we have to know
what “interest rate” is assumed.
– Assume that the interest rate is 25%?
– Thus, you pay $200 interest to borrow $800 now
The Market Rate of Interest
(Future Amount - Initial Amount)
R=
Initial Amount
=
 In this case, the initial amount is
also the present value
Interest
Initial Amount
=
200
800
= 0.25
R=
Future Amount
-1
Present Value
 OR
Present Value =
=
Future Amount
1+ R
1000
= 800.
1.25
 1/1+R is called the Discount Factor
 Present Value = Future amount x Discount
Factor
 If R is 25 % Discount Factor is 1
1
=
= 0.80
1 + R 1.25
and PV (1,000; 25%; 1 yr)
=
1 [1000]
1.25
= 0.80 [1000]
= 800
3.2 Interest Rates
and the Time Value of Money
 Time Value of Money
– Consider an investment opportunity with the
following certain cash flows.
 Cost: $100,000 today
 Benefit: $105,000 in one year
– The difference in value between money today
and money in the future is due to the time value
of money.
The Interest Rate:
An Exchange Rate Across Time
– Suppose the current annual interest rate is 7%.
By investing or borrowing at this rate, we can
exchange $1.07 in one year for each $1 today.
– Is the above investment worthwhile?
 What is $105,000 worth today (i.e. its Present
Value)?
 It is Worth $105,000 divided by 1.07 = $98,130.84
– So is it worth giving up $100,000 to receive the
equivalent of $98,130.84 today?
Example 3.4
 Problem
– The cost of replacing a fleet of company trucks
with more energy efficient vehicles was $100
million
in 2007.
– The cost is estimated to rise by 8.5% in 2008.
– If the interest rate were 4%, what was the
cost of a delay in terms of dollars in 2007?
Example 3.4
 Solution
– If the project were delayed, it’s cost in 2008
would be:
 $100 million × (1.085) = $108.5 million
– Compare this amount to the cost of $100 million
in 2007 using the interest rate of 4%:
 $108.5 million ÷ 1.04 = $104.33 million in 2007
dollars.
– The cost of a delay of one year would be:
 $104.33 million – $100 million = $4.33 million in 2007
Future Value versus Present Value
 We compared the cost of replacing the fleet today with the
Present Value of replacing it in the future.
 Alternatively we could find the Future Value of replacing it
today, compared with the value of replacing it in the future.
 Thus, the Future Value of replacing it today is: $100 million
times (1.04) = $104 million
– Comparing that with the actual cost of replacing it one year in the
future gives a benefit of
 The benefit in future value terms is thus:
$108.5 million - $104 million or $4.5 million
Note that in present value terms the present value of $4.5 million is:
$4.5 million divided by 1.04 or $4.33 million!!!
Figure 3.1 Converting Between
Dollars Today and Gold, Euros, or
Dollars in the Future
3.3 Present Value
and the NPV Decision Rule
 The net present value (NPV) of a project or
investment is the difference between the
present value of its benefits and the present
value of
its costs.
– Net Present Value
NPV  PV (Benefits)  PV (Costs)
NPV  PV (All project cash flows)
The NPV Decision Rule (cont'd)
 Accepting or Rejecting a Project
– Accept those projects with positive NPV
because accepting them is equivalent to
receiving their NPV in cash today.
– Reject those projects with negative NPV
because accepting them would reduce the
wealth of investors.
Example 3.5
Example 3.5 (cont'd)
Choosing Among Projects
Choosing Among Projects
(cont'd)
 All three projects have positive NPV, and we
would accept all three if possible.
 If we must choose only one project, Project
B has the highest NPV and therefore is the
best choice.
NPV and Individual Preferences
 Although Project B has the highest NPV,
what if we do not want to spend the $20 for
the cash outlay? Would Project A be a better
choice? Should this affect our choice of
projects?
 NO! As long as we are able to borrow and
lend at the risk-free interest rate, Project B is
superior whatever our preferences regarding
the timing of the cash flows.
NPV and Individual Preferences
(cont'd)
NPV and Individual Preferences
(cont'd)
 Regardless of our preferences for cash
today versus cash in the future, we should
always maximize NPV first. We can then
borrow or lend to shift cash flows through
time and find our most preferred pattern of
cash flows.
Wealth
 Wealth is the present value of all Current and Future
income.
 Suppose that an individual has $1,000 in his/her
pocket and has a claim on $1,000 one year from
now. What is his wealth if the interest rate is
20%?
$1,000 in his/her pocket is worth $1,000.
$1,000 one year from now is worth
$833.33 = 1,000/(1 +R)
= 1000/(1.20)
Therefore, his/her Wealth is $1,833.33.
 You have to convert all future income to Present
Values before you can add them up
Market Opportunity Line
 The Market Opportunity Line
shows how an individual can
exchange current for future
consumption.

Endowment
1000
Now
1000
Next
Year
How?
500
“
1600
“
How?
Zero
“
2200
“
Wealth
1833
“
Zero
“
1500
“
?
“
2250
2200
1625
1000
375
500
1000
Possible Alternatives
1833
Wealth and the NPV of a Project
 Now suppose the investor has the
opportunity to invest in only one of the three
projects: Project A
2320
2292
2200
1625
1000
375
500
1000
1833 1910 1933
Wealth and the NPV of a Project
 Now suppose the investor has the
opportunity to invest in only one of the three
projects: Project B
2320
2292
2200
1625
1000
375
500
1000
1833 1910 1933
Market Opportunity Line
 Notice that this individual's wealth is indicated by the
horizontal intercept.
Wealth = $1,833
= $1,000 +
$1,000
1+ R
= $1,000 +
$1,000
1.20
Wealth = Current Income + Future IncomexDiscount Factor
 The Wealth is the maximum an individual can consume
today by borrowing against all of his/her future income
Market Opportunity Line
 The slope of the market opportunity line is:
- (1 + R)
 Slope = Rise/Run
= (Principal + Interest)
- Principal
= -( 1 + Interest )
Principal
= -(1 + R)
 If you give up $500 now, you can get:
500 X (1 + R) =
500(1.20) = $600 more next year.
 If you want to get $800 more now, you must give up:
800 X (1.20) or $960 next year
Bottom Line
1. Wealth is the PRESENT VALUE of income
stream
2. All individuals are unambiguously better off
when their wealth increases.
3. The net present value of an investment
project is the amount investors' wealth would
increase (decrease) if the project were
undertaken.
Lecture 2
Managerial Finance
FINA 6335
Ronald F. Singer
3.4 Arbitrage and the Law of One
Price
 Arbitrage
– The practice of buying and selling equivalent
goods in different markets to take advantage of
a price difference. An arbitrage opportunity
occurs when it is possible to make a profit
without taking any risk or making any
investment.
 Normal Market
– A competitive market in which there are no
arbitrage opportunities.
3.4 Arbitrage and the Law of
One Price (cont'd)
 Law of One Price
– If equivalent investment opportunities trade
simultaneously in different competitive markets,
then they must trade for the same price in both
markets.
3.5 No-Arbitrage and Security
Prices
 Valuing a Security
– Assume a security promises a risk-free payment
of $1000 in one year. If the risk-free interest rate
is 5%, what can we conclude about the price of
this bond in a normal market?
 Price(Bond) = $952.38
3.5 No-Arbitrage and
Security Prices (cont'd)
 Valuing a Security (cont’d)
– What if the price of the bond is not $952.38?
 Assume the price is $940.
– The opportunity for arbitrage will force the price
of the bond to rise until it is equal to $952.38.
3.5 No-Arbitrage and
Security Prices (cont'd)
 Valuing a Security (cont’d)
– What if the price of the bond is not $952.38?
 Assume the price is $960.
– The opportunity for arbitrage will force the price
of the bond to fall until it is equal to $952.38.
Determining the No-Arbitrage
Price
 Unless the price of the security equals the
present value of the security’s cash flows,
an arbitrage opportunity will appear.
 No Arbitrage Price of a Security
Price(Security)  PV (All cash flows paid by the security)
Example 3.6
Example 3.6 (cont'd)
Determining the Interest Rate
From Bond Prices
 If we know the price of a risk-free bond, we
can use
Price(Security)  PV (All cash flows paid by the security)
to determine what the risk-free interest rate
must be if there are no arbitrage
opportunities.
Determining the Interest Rate
From Bond Prices (cont'd)
 Suppose a risk-free bond that pays $1000 in
one year is currently trading with a
competitive market price of $929.80 today.
The bond’s price must equal the present
value of the $1000 cash flow it will pay.
Determining the Interest Rate
From Bond Prices (cont'd)
$929.80 today  ($1000 in one year)  (1  rf $ in one year / $ today)
1  rf 
$1000 in one year
 1.0755 $ in one year / $ today
$929.80 today
 The risk-free interest rate must be 7.55%.
The NPV of Trading Securities
 In a normal market, the NPV of buying or
selling a security is zero.
NPV (Buy security)  PV (All cash flows paid by the security)  Price(Security)
 0
NPV (Sell security)  Price(Security)  PV (All cash flows paid by the security)
 0
The NPV of Trading Securities
(cont’d)
 Separation Principle
– We can evaluate the NPV of an investment
decision separately from the decision the firm
makes regarding how to finance the investment
or any other security transactions the firm is
considering.
Example 3.7
Example 3.7 (cont'd)
Valuing a Portfolio
 The Law of One Price also has implications for
packages of securities.
– Consider two securities, A and B. Suppose a third
security, C, has the same cash flows as A and B
combined. In this case, security C is equivalent to a
portfolio, or combination, of the securities A and B.
Price(C)  Price(A  B)  Price(A)  Price(B)
 Value Additivity
Example 3.8
Example 3.8 (cont'd)
3.6 The Price of Risk
 Risky Versus Risk-free Cash Flows
– Assume there is an equal probability of either a
weak economy or strong economy.
3.6 The Price of Risk (cont'd)
 Risky Versus Risk-free Cash Flows (cont’d)
Price(Risk-free Bond)  PV(Cash Flows)
 ($1100 in one year)  (1.04 $ in one year / $ today)
 $1058 today
– Expected Cash Flow (Market Index)
 ½ ($800) + ½ ($1400) = $1100
 Although both investments have the same expected
value, the market index has a lower value since it
has a greater amount of risk.
Risk Aversion and the Risk
Premium
 Risk Aversion
– Investors prefer to have a safe income rather
than a risky one of the same average amount.
 Risk Premium
– The additional return that investors expect to
earn to compensate them for a security’s risk.
– When a cash flow is risky, to compute its
present value we must discount the cash flow
we expect on average at a rate that equals the
risk-free interest rate plus an appropriate risk
Risk Aversion
and the Risk Premium (cont’d)
Expected return of a risky investment 
Expected Gain at end of year
Initial Cost
– Market return if the economy is strong
 (1400 – 1100) / 1100 = 40%
– Market return if the economy is weak
 (800 – 1000) / 1000 = –20%
– Expected market return
 ½ (40%) + ½ (–20%) = 10%
The No-Arbitrage Price of a Risky
Security
– If we combine security A with a risk-free bond that pays
$800 in one year, the cash flows of the portfolio in one
year are identical to the cash flows of the market index.
– By the Law of One Price, the total market value of the
bond and security A must equal $1000, the value of the
market index.
The No-Arbitrage Price
of a Risky Security (cont'd)
 Given a risk-free interest rate of 4%, the market
price of the bond is:
– ($800 in one year) / (1.04 $ in one year/$ today) = $769
today
– Therefore, the initial market price of security A is
$1000 – $769 = $231.
Risk Premiums Depend on Risk
 If an investment has much more variable
returns, it must pay investors a higher risk
premium.
Risk Is Relative to the Overall
Market
 The risk of a security must be evaluated in
relation to the fluctuations of other
investments
in the economy.
 A security’s risk premium will be higher the
more its returns tend to vary with the overall
economy and the market index.
 If the security’s returns vary in the opposite
direction of the market index, it offers
insurance and will have a negative risk
Risk Is Relative
to the Overall Market (cont'd)
Example 3.9
Example 3.9 (cont'd)
Risk, Return, and Market Prices
 When cash flows are risky, we can use the
Law of One Price to compute present values
by constructing a portfolio that produces
cash flows with identical risk.
Figure 3.3 Converting Between
Dollars Today and Dollars in One
Year with Risk
 Computing prices in this way is equivalent to
converting between cash flows today and the
expected cash flows received in the future using a
discount rate rs that includes a risk premium
appropriate for the investment’s risk:
rs  rf  ( risk premium for investment s)
Figure 3.3 Converting Between
Dollars Today and Dollars in One
Year with Risk
Example 3.10
Example 3.10 (cont'd)
3.7 Arbitrage with Transactions
Costs
 What consequence do transaction costs
have for no-arbitrage prices and the Law of
One Price?
– When there are transactions costs, arbitrage
keeps prices of equivalent goods and securities
close to each other. Prices can deviate, but not
by more than the transactions cost of the
arbitrage.
Example 3.11
Example 3.11 (cont'd)
Problem of the Day
 Find the Wealth of an individual who will
earn $500,000 over the current year and who
has $2,000,000 equity in assets (such as a
home, a car, cash, etc.).
Assume the
interest rate is 8%
 Find the wealth of the same individual who
also can invest up to $200,000 in a machine
which will produce widgets. The rate of
return for this investment is 17%.
Questions?