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BondsBonds

Bills – short term contracts usually one year or less

Notes – from 1 to 10 years

Bonds – 10 years or longer but "bonds" used loosely

Time to mature, coupon rate, par (face) value

More complicated bonds can be convertible or callable

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Types of BondsTypes of Bonds

U.S. government securities,

Municipal bonds,

Corporate bonds,

Mortgage and asset—backed securities,

Federal agency securities and

Foreign government bonds

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ExampleExample

A bond with a face amount of $20,000 maturing in 20 years might be purchased for about $5,050. At the end of the 20 years, the investor will receive $20,000. The difference between $20,000 and $5,050 represents the interest, based on an interest rate of 7%, which compounds automatically until the bond matures. If the bond is taxable, the interest is taxed as it accrues, even though it is not paid to the investor before maturity or redemption.

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Maturity Maturity

Short-term notes: up to 5 years;

Intermediate notes/bonds: 5 to 12 years;

Long-term bonds: 12 or more years.

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Market Fluctuations: The Link BetweenPrice and Yield From the time a bond is originally issued until the day it matures, its price in the marketplace will fluctuate according to changes in market conditions or credit quality. The constant fluctuation in price is true of individual bonds—and true of the entire bond market—with every change in the level of interest rates typically having an immediate, and predictable, effect on the prices of bonds.

When prevailing interest rates rise, prices of outstanding bonds fall to bring the yield of older bonds into line with higher—interest new issues.When prevailing interest rates fall, prices of outstanding bonds rise, until the yield of older bonds is low enough to match the lower interest rate on new issues.The value of a bond can be higher or lower than its original face value if you sell it before it matures

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Bond ParametersBond Parameters

Face or par value ($: 100 1K 5K 10K)

Redemption or Disposal Price

Bond rate (nominal interest per period)

Number of pay periods before redemption

Bond yield rate per period (ieff)

Value (price) of bond number of interest periods before redemption. PW(i%)

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ClassificationClassification of Bonds of BondsClassification Issued by Characteristics Examples

Treasury securities

Federal government

Backed by US government

Bills(<= 1 year)Notes (2-10 years)Bonds(10-30 years)

Municipal Local governments Federal tax-exemptIssued against taxes received

General obligation Revenue Zero coupon

Mortgage Corporation Backed by specific assets or mortgage low rate/low risk on mortgage; Foreclosure

First or Second mortgages

Equipment trust

Debenture Corporation Not backed by collateral, but by reputation; high interest rate

Convertible

Subordinated

Junk or high yield

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Bond RatingBond Rating

Moody's S&P/Fitch Grade Risk

Aaa AAA Investment Highest Quality

Aa AA Investment High Quality

A A Investment Strong

Baa BBB Investment Medium Grade

Ba, B BB, B Junk Speculative

Caa/Ca/C CCC/CC/C Junk Highly speculative

C D Junk In Default

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Example 1Example 1

P&G issued $5,00,000 worth of $5,000 10-year debenture bonds paying quarterly a 6% coupon rate. a) Determine what the buyer receives each 3 months and after

10 years.Suppose bond is bought when discounted by 2% to $4900. What are the quarterly interest amounts and the final payment at maturity?

a) i = 5000*0.06/4 = $75 where the quarterly rate is 1.5%. After 10 years the buyer is paid the face value of $5,000.b) Original specs apply and the new buyer receives $75 each quarter and $5,000 at maturity.

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Example 2Example 2

Find the current price of a 10-year, face value $1000 bond paying 6% per year (payable semiannually) that is redeemable at par value if bought by purchaser to yield 10% per year.

SolutionIf the desired effective yield is 10% per year, the APR is 9.76% => i = 4.88% semiannual yield

PW(4.88%) = 0.03 * 1000(P/A, 4.88%, 20) + 1000(P/F, 4.88%, 20) = $763.31.

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Example 3Example 3

For $1000 you buy a 10-year $1000 face value bond with a coupon rate of 10% per year and sell it after 2 years for $990. Compute your effective rate of return.

1000 = 100(P/A, i%, 2) + 990(P/F, i% 2)

Let x = 1 + i and resolve at year 2

1000x2 – 100x – 1090 = 0

(quadratic 100 -10 -109) (1.095227 -0.995227) => 9.52%.

X = 1 + i = 1.0952 => i = 9.52%

100

100 + 990

1000

1 2

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Example 4Example 4

Joe buy a 10-year bond for $1000 with a coupon rate of 9% paid semiannually. After 2 years Joe sell the bond to Jane for $900.

a) What was the yield on Joe's investment?

b) What is Jane's yield if she keeps the bond to maturity?

c) What was the current yield when Jane bought the bond? 45 45+900

a) 1000 = 45(P/A, i% 4) + 900(P/F, i%, 4) 1K 1 2 3 4

(quartic 1000 -45 -45 -45 -945) 1.020765 => is = 2.08% => APR = 4.16% => ia = 4.20%.

b) (UIRR 900 45 16 1000) is = 5.45% => APR = 10.9% => ia = 11.2%

c) 45/900 = 5% = is => APR = 10% => ia = 10.25%.

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Example 5Example 5

A $5,000 face value, 20-year bond pays 8% coupon rate per year. a) How much should be paid for the bond to receive a 10% per year yield? b) If purchased now for $4,586.27, find the annual yield.

Solution

a) Paid = 400(P/A, 10%, 20) + 5K(P/F, 10%, 20) = $4,148.64.

b) 4,586.27 = 400(P/A, i%, 20) + 5K(P/F, i%, 20).

Guess and test to get 8.9% or use the Genie command

(UIRR 4586.27 400 20 5000) 8.9%.

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Zero Coupon CDsZero Coupon CDs

Zero coupon CDs are sold at a discount to their face amount and pay the entire face amount at maturity.

Example: You pay $900 for a $1,000 CD and receive the full $1,000 at maturity for $100 in interest.

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Your firm needs capital to finance growth. Should you issue debt or equity or obtain a bank loan? If you choose debt, should the bonds be convertible? Callable? If you choose equity, should you use common or preferred stock? How will the stock market react to your decision?

In 1998, IBM announced that it would repurchase $2.5 billion in stock. How should it structure the stock repurchase? IBM’s price jumped 7% after the announcement. Why? How would the market have reacted if IBM increased dividends instead? Suppose Intel made the same announcement. Would we expect the same price response?

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A 10-year bond with a face value of $5,000 pays a dividend of $250 every six months. Calculate the bond interest rate. If the bond is purchased for $4,000 at the end of year one, what is the effective interest rate? What is the nominal and effective annual interest rate?

Solution:Face value = $5,000; Dividend = $250 every six monthsn = ½ Year. 250 = 5,000(i) (1/2) Pin (bond pays simple interest)

i = 0.1 = 10%.

Purchase price at the end of year 1 = $4,0004,000 = 250(P/A, i%, 18) + 5,000 (P/F, i%, 18)(UIRR 4000 250 18 5000) 6.986284 effective semi-annual or

14% APR or 14.5% effective annual rate.

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Bond ValueBond Value

You buy a 10-year $1000 corporate bond at market price of $996.25, with coupon rate 9.625% paid semiannually. Find the yield to maturity and the current yield. Find value of bond 1 year later. Repeat if rate drops to 9%.

Yield to maturity: 996.25 = 48.13(P/A, i%, 20) + 1K(P/F, i%, 20)

(UIRR 996.25 48.13 20 1000) 4.8427% => 9.6854% = APR

Ia = 9.92% effective annual yield

Current yield: 2 * 48.13/996.25 = 9.66% APR

Ia = 9.90%, 0.02% less than yield to maturity.

48.13(P/A, 4.84%, 18) + 1000(P/F, 4.84%, 18) = $996.80

48.13(P/A, 4.5%, 18) + 1000(P/F, 4.5%, 18) = $1,038.06

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Short Bond GlossaryShort Bond Glossary

Coupon -- The rate of interest payable annually.

Current Yield -- The ratio of interest to the actual market price of the bond, stated as a percentage. For example, a bond with a current market price of $1,000 that pays $60 per year in interest would have a current yield of 6%.

Face or Par value -- The par value of a security, as distinct from its market value.

Premium or Discount price -- When the dollar price of a bond is above its face value, it is said to be selling at a premium. When the dollar price is below face value, it is said to be selling at a discount.

Yield -- The annual percentage rate of return earned on a security. Yield is a function of a security’s purchase price and coupon interest rate