Stephen Gray Fuqua School of Business Office 310 West Tel 6607786 Email sg12maildukeedu Web ltwwwdukeedusg12gt The Three Ideas in Finance The Time Value of Money Diversification and Risk ID: 783834
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Slide1
BA350: Financial Management
Stephen Gray
Fuqua School of Business
Office: 310 West
Tel: 660-7786
E-mail: sg12@mail.duke.edu
Web: <www.duke.edu/~sg12>
Slide2The Three Ideas in Finance
The Time Value of Money
Diversification and Risk
Arbitrage and Hedging
Slide3Topic 1: The Time Value of Money
A dollar in the future is worth less than a dollar now.
Should you take the $1000 cash back or the 4.9% APR financing on your new Ford?
Should you refinance your mortgage?
Should we convert our old warehouse into luxury apartments or a parking garage?
Slide4Topic 1: The Time Value of Money
Time Value of Money
Present values and future values
Valuation of stocks and bonds
Corporate investment decisions
Slide5Topic 2: Diversification and Risk
How should individuals invest their wealth?
Should you invest in stocks or bonds?
What
’
s a reasonable return for a particular investment?
What
’
s the relationship between risk and return?
Slide6Topic 2: Diversification and Risk
Diversification and Risk
Statistical review and utility theory
Portfolio theory
Relationship between risk and return: Capital Asset Pricing Model
Investment decisions under uncertainty
Slide7Topic 3: Arbitrage and Hedging
If two investments are guaranteed to produce the same set of cash flows, they must cost the same.
How can we hedge against common business risks?
How do option and futures contracts work?
When should a firm use derivatives?
Slide8Topic 3: Arbitrage and Hedging
Arbitrage and Hedging
Forwards
Futures
Options
Hedging in Practice
Foreign exchange rate risk
Interest rate risk
Stock market risk
Slide9Applications of the Three Ideas
Corporate Financial Policy
Investment decisions
Financing decisions
Dividend (payout) decisions
Mutual Fund Performance Evaluation
Real and Strategic Options
Slide10Goals of Course
Provide a solid foundation in the fundamental principles of finance.
Prepare students for subsequent courses in finance.
Introduce students to current issues and concerns regarding financial policy.
Slide11Course Material
Packet of course notes
Optional text:
R. Brealey and S. Myers,
Principles of Corporate Finance (5th Ed.)
Current financial publications:
Wall Street Journal
Fortune
Business Week
Slide12Course Requirements and Grading
Assignments (10%)
Midterm exam (30%)
Covers first five classes
Closed book
Final Exam (60%)
December 13 (9-noon)
Closed book
Passing grade requires 50% on exams.
Slide13Help!!!!!!!!!
Classmates
Help sessions
Posted on web site and bulletin board
Review sessions
Fridays 4-5 pm
Tutors
Posted on web site and bulletin board
Me
Slide14Class 1
Present Value Mechanics and Bond Valuation
Slide15Future Values
Suppose you have the opportunity to invest
$1,000 in a savings account that promises
to pay 7% interest per year. How much will
you have in your savings account at the end
of each of the next 2 years?
Slide16Future Value after One Year
0 1
$1,000
F
1
F
1
= P(1+i)
F
1
= $1,000(1.07)
F
1
= $1,070
Slide17Future Value after Two Years
0 1 2
$1,000
F
2
F
2
= F
1
(1+i)
F
2
= [P(1+i)](1+i) = P(1+i)
2
F
2
= $1,000(1.07)
2
F
2
= $1,144.90
Slide18Future Value after n Years
0 n
P
F
n
F
n
= P(1+i)
n
Slide19Manhattan Island
In 1626, Peter Minuit purchased Manhattan Island
for $24. Given today
’
s real estate values in New
York, this appears to be a great deal for Minuit.
But consider the current value of the $24 if it had
been invested at an interest rate of 8% for the last
370 years (1996-1626 = 370).
F
370
= $24(1.08)
370
F
370
= $55,847 Billion
Slide20Future Value of a Lump Sum
Example: A bank offers a rate of 10% per year, compounding quarterly. You invest $1000. How much is in your account after 1 year?
F
n
=P(1+i)
n
F
n
=1000(1.025)
4
=1103.81
Slide21Present Value of a Lump Sum
Example: You need $100,000 in 18 years to pay for your newborn
’
s college education. How much must you invest today if you can earn 10% p.a.?
P=F
n
/(1+i)
n
P=100,000/(1.1)
18
=17,985.87
Slide22Present Value of a Lump Sum
Example: If you invest $5,000 now, how long will it take you to triple your investment if you can earn 11% p.a.?
P=F
n
/(1+i)
n
5,000=15,000/(1.11)
n
ln
(5,000)=
ln
(15,000)-n
ln
(1.11)
n=10.53 years.
Slide23Future Value of an Annuity
Example: If you work for 30 years and invest $500 per month into your retirement account, how much will you have at retirement if you can earn 12% p.a. compounding monthly?
S
i
i
R
n
n
=
+
-
1
1
b
g
S
m
360
360
1
01
1
0
01
500
747
=
-
=
.
.
$1
.
b
g
Slide24Present Value of an Annuity
Example: You decide to fund a finance chair for the next 10 years. This requires $300,000 per year in salaries and add-ons. How much should you donate, if the school can earn 10% p.a?
Slide25Annuity Formulas
In all annuity formulas, it is assumed that the first payment in the stream occurs one period from now:
50
50
50
50
Slide26Mortgage Example
30-year $100,000 fixed rate mortgage at 12% p.a. with monthly repayments.
The present value of the repayment scheme is the amount you borrowed:
Slide27Mortgage Example
The payout figure is the present value of all remaining repayments. After 120 repayments, this is:
Slide28Mortgage Example
If you make an extra repayment, this reduces the outstanding principal balance. Consider a payment of $50,000 after 10 years:
Slide29Definition of a Bond
A
bond
is a security that obligates the issuer to make specified interest and principal payments to the holder on specified dates.
Coupon rate
Face value (or par)
Maturity (or term)
Bonds are sometimes called
fixed
income securities
.
Slide30Types of Bonds
Pure Discount or Zero-Coupon Bonds
Pay no coupons prior to maturity.
Pay the bond
’
s face value at maturity.
Coupon Bonds
Pay a stated coupon at periodic intervals prior to maturity.
Pay the bond
’
s face value at maturity.
Perpetual Bonds (Consuls)
No maturity date.
Pay a stated coupon at periodic intervals.
Slide31Types of Bonds
Self-Amortizing Bonds
Pay a regular fixed amount each payment period over the life of the bond.
Principal repaid over time rather than at maturity.
Slide32Bond Issuers
Federal Government and its Agencies
Local Municipalities
Corporations
Slide33U.S. Government Bonds
Treasury Bills
No coupons (zero coupon security)
Face value paid at maturity
Maturities up to one year
Treasury Notes
Coupons paid semiannually
Face value paid at maturity
Maturities from 2-10 years
Slide34U.S. Government Bonds
Treasury Bonds
Coupons paid semiannually
Face value paid at maturity
Maturities over 10 years
The 30-year bond is called the
long bond
.
Treasury Strips
Zero-coupon bond
Created by
“
stripping
”
the coupons and principal from Treasury bonds and notes.
Slide35Agencies Bonds
Mortgage-Backed Bonds
Bonds issued by U.S. Government agencies that are backed by a pool of home mortgages.
Self-amortizing bonds.
Maturities up to 20 years.
Slide36U.S. Government Bonds
No default risk. Considered to be
riskfree
.
Exempt from state and local taxes.
Sold regularly through a network of primary dealers.
Traded regularly in the over-the-counter market.
Slide37Municipal Bonds
Maturities from one month to 40 years.
Exempt from federal, state, and local taxes.
Generally two types:
Revenue bonds
General Obligation bonds
Riskier than U.S. Government bonds.
Slide38Corporate Bonds
Secured Bonds (Asset-Backed)
Secured by real property
Ownership of the property reverts to the bondholders upon default.
Debentures
General creditors
Have priority over stockholders, but are subordinate to secured debt.
Slide39Common Features of Corporate Bonds
Senior versus subordinated bonds
Convertible bonds
Callable bonds
Putable bonds
Sinking funds
Slide40Bond Ratings
Slide41Bond Valuation:
General Formula
0 1 2 3 4 ... n
C C C C C+F
Slide42Valuing Zero Coupon Bonds
What is the current market price of a U.S. Treasury strip that matures in exactly 5 years and has a face value of $1,000. The yield to maturity is r
d
=7.5%.
Slide43Finding the YTM on a Zero Coupon Bond
What is the yield to maturity on a U.S. Treasury strip that pays $1,000 in exactly 7 years and is currently selling for $591.11?
Slide44Valuing Coupon Bonds
What is the market price of a U.S. Treasury bond that has a coupon rate of 9%, a face value of $1,000 and matures exactly 10 years from today if the required yield to maturity is 10% compounded semiannually?
Slide45Valuing Coupon Bonds (cont.)
Semiannual coupon = $1,000(.09)/2 = $45
Semiannual yield = 10%/2 = 5%
Payment periods = 10 years x 2 = 20
Slide46Valuing Coupon Bonds (cont.)
Suppose you purchase the U.S. Treasury bond described earlier and immediately thereafter interest rates fall so that the new yield to maturity on the bond is 8% compounded semiannually. What is the bond
’
s new market price?
Slide47Valuing Coupon Bonds (cont.)
New Semiannual yield = 8%/2 = 4%
What is the price of the bond if the yield to maturity is 9% compounded semiannually?
Slide48Relationship Between Bond Prices and Yields
Bond prices are
inversely
related to interest rates (or yields).
A bond sells at
par
only if its coupon rate
equals
the required yield.
A bond sells at a
premium
if its coupon is
above
the required yield.
A bond sells a a
discount
if its coupon is
below
the required yield.
Slide49Duration: A Measure of Interest Rate Sensitivity
The
percentage
change in the bond
’
s price for a small change in interest rates is given by:
The term within square brackets is called the bond
’
s
duration
. It can be interpreted as the
weighted average maturity
.
Slide50Duration Example
What is the interest rate sensitivity of the
following two bonds. Assume coupons are
paid annually.
Bond A
Bond B
Coupon rate 10% 0%
Face value $1,000 $1,000
Maturity 5 years 10 years
YTM 10% 10%
Price $1,000 $385.54
Slide51Duration Example (cont.)
Slide52Duration Example (cont.)
Percentage change in bond price for a small increase in the interest rate:
Pct. Change = - [1/(1.10)][4.17] = - 3.79%
Bond A
Pct. Change = - [1/(1.10)][10.00] = - 9.09%
Bond B
Slide53Bond Prices and Yields
Bond Price
F
c Yield
Longer term bonds are more
sensitive to changes in interest
rates than shorter term bonds.
Slide54The Term Structure
of Interest Rates
The
term structure of interest rates
is the relationship between time to maturity and yield to maturity:
Yield
Maturity
1
2
3
5.00
5.75
6.00
Slide55Spot and Forward Rates
A
spot rate
is a rate agreed upon today, for a loan that is to be made today. (e.g. r
1
=5% indicates that the current rate for a one-year loan is 5%).
A
forward rate
is a rate agreed upon today, for a loan that is to be made in the future. (e.g.
2
f
1
=6.50% indicates that we could contract today to borrow money at 6.5% for one year, starting two years from today).
Slide56Forward Rates
r
1
=5.00%, r
2
=5.75%, r
3
=6.00%
If we invest $100 for three years we earn 100(1.06)
3
If we invest $100 for two years, and contract (today) at the one year rate, two years forward, we earn 100(1.0575)
2
(1+
2
f
1
)
Slide57Forward Rates
Since both of these positions are riskless, they must yield the same returns
(1.06)
3
=(1.0575)
2
(1+
2
f
1
)
2
f
1
=6.50%
More generally: (1+r
n+t
)
n+t
=(1+r
n
)
n
(1+
n
f
t
)