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>

The Three Ideas in Finance The Time Value of Money Diversification and Risk Arbitrage and Hedging

Topic 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?

Topic 1: The Time Value of Money

Time Value of Money Present values and future values Valuation of stocks and bonds Corporate investment decisions

Topic 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?

Topic 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

Topic 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?

Topic 3: Arbitrage and Hedging

Arbitrage and Hedging Forwards Futures Options Hedging in Practice

– Foreign exchange rate risk– Interest rate risk– Stock market risk

Applications of the Three Ideas

Corporate Financial Policy» Investment decisions» Financing decisions» Dividend (payout) decisions

Mutual Fund Performance Evaluation Real and Strategic Options

Goals 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.

Course 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

Course 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.

Help!!!!!!!!!

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

Class 1

Present Value Mechanics and Bond

Valuation

Future 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?

Future Value after One Year

0 1

$1,000

F1

F1 = P(1+i)

F1 = $1,000(1.07)

F1 = $1,070

Future Value after Two Years

0 1 2

$1,000

F2

F2 = F1(1+i)

F2 = [P(1+i)](1+i) = P(1+i)2

F2 = $1,000(1.07)2

F2 = $1,144.90

Future Value after n Years

0 n

P

Fn

Fn = P(1+i)n

Manhattan Island

In 1626, Peter Minuit purchased Manhattan Islandfor $24. Given today’s real estate values in NewYork, this appears to be a great deal for Minuit. But consider the current value of the $24 if it hadbeen invested at an interest rate of 8% for the last370 years (1996-1626 = 370).

F370 = $24(1.08)370

F370 = $55,847 Billion

Future 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?

Fn=P(1+i)n

Fn=1000(1.025)4=1103.81

Present 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=Fn/(1+i)n

P=100,000/(1.1)18=17,985.87

Present 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=Fn/(1+i)n

5,000=15,000/(1.11)n

ln(5,000)=ln(15,000)-nln(1.11) n=10.53 years.

Future 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?

Si

iRn

n

=+ -1 1b g

S m360

360101 1

0 01500 747=

-=

.

.$1.b g

Present 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?

Ai

iRn

n

1 1b g

A m10

101 110

010300 000 843

.

., $1.

b g

Annuity Formulas

In all annuity formulas, it is assumed that the first payment in the stream occurs one period from now:

50 50 50 50

Mortgage 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:

Ai

iRn

n

1 1b g

A R360

3601 101

0 01000

.

.$100,

b g

R $1, .028 61

Mortgage Example

The payout figure is the present value of all remaining repayments. After 120 repayments, this is:

Ai

iRn

n

1 1b g

A240

2401 101

0 011028 61 417 80

.

.. $93, .

b g

Mortgage Example

If you make an extra repayment, this reduces the outstanding principal balance. Consider a payment of $50,000 after 10 years:

A R240

2401 101

0 01417 80

.

.$43, .

b g

R $478.07

Definition 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.

Types 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.

Types 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.

Bond Issuers

Federal Government and its Agencies Local Municipalities Corporations

U.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

U.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.

Agencies 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.

U.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.

Municipal 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.

Corporate 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.

Common Features of Corporate Bonds

Senior versus subordinated bonds Convertible bonds Callable bonds Putable bonds Sinking funds

Bond RatingsMoody’s S&P Quality of Issue

Aaa AAA Highest quality. Very small risk of default.

Aa AA High quality. Small risk of default.

A A High-Medium quality. Strong attributes, but potentiallyvulnerable.

Baa BBB Medium quality. Currently adequate, but potentiallyunreliable.

Ba BB Some speculative element. Long-run prospectsquestionable.

B B Able to pay currently, but at risk of default in thefuture.

Caa CCC Poor quality. Clear danger of default .

Ca CC High specullative quality. May be in default.

C C Lowest rated. Poor prospects of repayment.

D - In default.

Bond Valuation:General Formula

0 1 2 3 4 ... n

C C C C C+F

Br

rC

F

rd

n

d d

n

1 1

1

b gb g

Valuing 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 rd=7.5%. 1000

1075565

.$696.b g

Finding 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?

591111000

17.

rdb grd 7 8%.

Valuing 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?

Valuing Coupon Bonds (cont.)

Semiannual coupon = $1,000(.09)/2 = $45 Semiannual yield = 10%/2 = 5% Payment periods = 10 years x 2 = 20

Br

rC

F

rd

n

d d

n

1 1

1

b gb g

B

1 105

0 0545

1000

10569

20

20

.

. .$937.

b gb g

Valuing 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?

Valuing 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?

Br

rC

F

rd

n

d d

n

1 1

1

b gb g

B

1 104

0 0445

1000

104067 95

20

20

.

. .$1, .

b gb g

Relationship 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.

Duration: 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.

B B

r r

t C r

B

n F r

Bd d

dt

t

n dn

/ / ( ) / ( )

LNMM

OQPP1

1

1 11

Duration 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

Duration Example (cont.)

Year (t) PV(A) PV(A) x t PV(B) PV(B)xt1 $90.91 $90.91 0 02 $82.64 $165.89 0 03 $75.13 $225.39 0 04 $68.30 $273.21 0 05 $683.01 $3,415.07 0 06 0 0 0 07 0 0 0 08 0 0 0 09 0 0 0 0

10 0 0 $385.54 $3,855.43Totals $1000.00 $4,170.47 $385.54 $3,855.43

Duration 4.17 10.00

Duration 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

Bond Prices and Yields

Bond Price

F

c Yield

Longer term bonds are moresensitive to changes in interestrates than shorter term bonds.

The Term Structure of Interest Rates

The term structure of interest rates is the relationship between time to maturity and yield to maturity:

Yield

Maturity1 2 3

5.00

5.75

6.00

Spot and Forward Rates

A spot rate is a rate agreed upon today, for a loan that is to be made today. (e.g. r1=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. 2f1=6.50% indicates that we could contract today to borrow money at 6.5% for one year, starting two years from today).

Forward Rates

r1=5.00%, r2=5.75%, r3=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+2f1)

Forward Rates

Since both of these positions are riskless, they must yield the same returns

(1.06)3=(1.0575)2(1+2f1)

2f1=6.50%

More generally: (1+rn+t)n+t=(1+rn)n(1+nft)