Finance 300Financial Markets

Lecture 10

Fall, 2001©

Professor J. Petry

http://www.cba.uiuc.edu/broker/fin300/fin300pp.htm

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Investment ChallengeTrading begins on Monday. Each student has management of hypothetical $1,000,000.00Each partnership can have up to 5 individuals, with each individual bringing

their 1,000,000.00 with them. You can dissolve partnerships, but don’t.The trading rules are specified on pages 25-29 of your book. UISES

(University of Illinois Securities Exchange Simulation) is down this semester. Use Yahoo Finance for quotes and information. Print off the yahoo page to record purchase of security. Turn these in along with client report.

Monthly client reports are due shortly after the end of October and November. See Calendar for details. Client Letter explaining your performance is due with the second and final client report. Details in the text.

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Debt Markets & Interest Rates• Bonds

• A bond is a loan. The borrower will issue a certificate which promises a specific interest rate (coupon), plus a guarantee of repayment of the principal amount at some future specified maturity date.

• Coupon—the rate of interest on the bond when issued at par. Bonds were issued as bearer bonds (who ever had it in their possession could cut off the coupon, and send it in for payment on the appropriate day). Now almost all bonds are registered bonds—whoever is the registered owner gets the payment automatically.

• Principal—The principal payment is the amount of the loan on which interest is calculated. Often referred to as the face value, it is generally repaid at the end of the loan on the maturity date.

• Maturity Date—The date at which the final payment is made on the loan and the bond contract expires.

• The coupon rate, principal value and maturity date are engraved on the bond and thus never change for the life of the bond. If this is true, how do interest rates adjust to economic conditions over time? Don’t interest rates change over time?

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Debt Markets & Interest Rates• Bonds

• Negotiable—A security which may be bought or sold in the secondary market. This is the defining characteristic of bonds vs. loans.

• Premium —When a bond sells for more than its face value, it sells at a premium. If you buy a bond at a premium, it will yield less than the coupon rate if you hold it to maturity.

– 10 year bond originally issued at $100 face value, with 8% coupon. Market interest rates go to 5%. Is this bond worth $100? What happens to its interest rate?

• Discount—When a bond sells for less than its face value it sells at a discount. If you buy a bond at a discount, it will yield more than its coupon rate if you hold to maturity.

– 10 year bond originally issued at $100 face value, with 8% coupon. Market interest rates go to 12%. Is this bond worth $100? What happens to its interest rate?

• Par—When a bond sells for precisely its face value, it sells for par. If you buy a bond at par it will yield exactly its coupon rate if you hold it to maturity.

– If you buy & hold to maturity the 10 year bond, what is your interest rate?

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Bond Pricing

BOND

Principal Value US$1,000,000.00Maturing August 15, 2004

$30,000 $30,000 $30,000 $30,00015-Aug-2001 15-Aug-2002 15-Aug-2003 15-Aug-2004

$30,000 $30,000 $30,000 $30,00015-Feb-2001 15-Feb-2002 15-Feb-2003 15-Feb-2004

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Bond Pricing• The price of a bond is given by:

nn

n

t

t

Yd

P

YdYdC

PRICE

PCPRICE nYdtYd

22

2

1

21

21

11*

2

2

21

21

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Bond Pricing• Where:

Ct = coupon rate x principal/2 = $30,000 = (.06 x $1,000,000)/2P = Principal; Yd = Market Yieldn = Maturity; Term to maturity in years

• Which is nothing more than the sum of the net present values of the amounts paid

• Price yield calculation assumes semi-annual compounding because in US almost all bonds pay twice a year.

• The first formula is most easily applied when using excel, while the second version can be completed with calculator.

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Bond Pricing

BOND

1,000,000/(1 + 0.06/2)8

789,409.23

30,000/(1+0.06/2)2 30,000/(1+0.06/2)4 30,000/(1+0.06/2)6 30,000/(1+0.06/2)8

28,277.88 26,654.61 25,124.53 23,682.28

30,000/(1+0.06/2)1 30,000/(1+0.06/2)3 30,000/(1+0.06/2)5 30,000/(1+0.06/2)7

29,126.21 27,454.25 25,878.26 24,392.75

So what is our bond worth to us at issuance if mkt yld = 6%?

Which equals?

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Bond PricingThings To Do: IV - 6So what is our bond worth to us at issuance if mkt yld = 7%?

Which equals?

BOND

1,000,000/(1 + 0.07/2)8

759,411.56

30,000/(1+0.07/2)2 30,000/(1+0.07/2)4 30,000/(1+0.07/2)6 30,000/(1+0.07/2)8

28,005.32 26,143.27 24,405.02 22,782.35

30,000/(1+0.07/2)1 30,000/(1+0.07/2)3 30,000/(1+0.07/2)5 30,000/(1+0.07/2)7

28,985.51 27,058.28 25,259.20 23,579.73

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Bond PricingSo what is our bond worth to us at issuance if mkt yld = 5%?

Which equals?

BOND

1,000,000/(1 + 0.05/2)8

820,746.57

30,000/(1+0.05/2)2 30,000/(1+0.05/2)4 30,000/(1+0.05/2)6 30,000/(1+0.05/2)8

28,554.43 27,178.52 25,868.91 24,622.40

30,000/(1+0.05/2)1 30,000/(1+0.05/2)3 30,000/(1+0.05/2)5 30,000/(1+0.05/2)7

29,268.29 27,857.98 26,515.63 25,237.96

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Bond PricingWhich allows us to build the Price Yield Curve for this bond

Price Yield4,762,407$ 1%2,509,852$ 2%1,757,335$ 3%1,379,854$ 4%1,152,409$ 5%1,000,000$ 6%

890,483$ 7%807,785$ 8%742,977$ 9%690,703$ 10%647,551$ 11%611,250$ 12%580,223$ 13%553,348$ 14%529,800$ 15%

Price Yield Curve

$-

$1,000,000

$2,000,000

$3,000,000

0% 5% 10% 15% 20%

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Bond PricingThings To Do: IV-7

You have 6% $1,000,000 bond issued June 1, 1987 and maturing June 1, 1999.

A. John Q. Investor purchases this bond at issue when yields were 6%. Calculate the price of the bond at that time.

Price = B. Yields increased to 8% by June 1989 when John sold his bond to

Warren Buffet. At what price should the bond have changed hands?Price =

C. Yields fell to 4% by June 1993 when Warren sold the bond to you. What price did you pay for the bond?

Price =