Bond Prices and Yields

Objectives:

1. Analyze the relationship between bond prices and bond yields.

2. Calculate how bond prices will change over time for a given interest-rate projection.

3. Identify the determinants of bond safety and rating.

4. Analyze how callable, convertible, and sinking fund provisions will affect a bond's equilibrium yield to maturity.

5. Define the yield curve and study its properties

Long-term debt contract Fixed interest payment is paid throughout the life of

bond Entire principal payment is paid at maturity date Coupon rate: determines the fixed interest payment Yield to maturity: the average return per year that the

investors (or the market) require on the bond if they buy and hold the bond until maturity

Coupon rate is fixed, determined by the issuing firm YTM can fluctuate, depending on the investors in the

market Zero-coupon bond

◦ zero coupon payment◦ par at maturity date

T Note maturities range up to 10 years T bond maturities range from 10 – 30 years Bid and ask price

◦ Quoted in points and as a percent of par Accrued interest

◦ Quoted price does not include interest accrued Example: if the coupon payments are made on

May 1 and Nov 1, you buy a bond on June 11. Assume the price on June 11 is 990, how much you have to pay in order to buy the bond. (assume there are 40 days from May 1-June 11

Most bonds are traded over the counter Registered Bearer bonds Secured and unsecured

◦ Secured: Collateral Mortgage

◦ Unsecured Debentures Notes

Call provisions: allows issuer to buy back bond before maturity date at a specific call price◦ Why the company wants to call the bond?◦ Call provision is in favor of the issuer. So if everything else is

the same, callable bond would have to give higher yield, higher coupon to investors than regular bonds

Convertible bond: a bond with option allowing the bondholder to exchange the bond for a specific number of shares of common stock in the firm◦ When bondholder want to convert bond into stocks?

Puttable bond: gives the option to bondholder to either exchange the bond for par value at some date or to extend for a given number of year◦ When bondholders want to exchange for par value before

maturity◦ When bondholders want to extend the bond for a given

number of year after maturity Floating rate bond

◦ coupon rate is tied to current market rates Preferred stocks

Federal Home Loan Bank Board Farm Credit Agencies Ginnie Mae Fannie Mae Freddie Mac

Reverse floaters◦ Reverse of floating rate bond

Asset-backed bonds◦ backed by assets of the firm

Pay-in-kind bonds◦ issuers may choose to pay interest either in cash or in

additional bon Catastrophe bonds

◦ issued by insurance company, give high yield◦ In the event of catastrophe, the obligation to pay interest and

principal can be delayed or forgiven Indexed bonds

◦ payments are tied to a general price index or price of a particular commodity

◦ TIPS (Treasury Inflation Protected Securities)

TIPS: adjust for inflationExample: n = 3 years, annual coupon, par 1000, coupon 4%

T

T

B r

par

rr

CP)1(

)1(1

1

Price of bond = present value of all future coupon payments + present value of the par value

PB = Price of the bondCt = interest or coupon paymentsT = number of periods to maturityr = semi-annual discount rate or the semi-annual yield

to maturity

P Cr

Par Valuer

B tT

t

T

TT

( ) ( )1 11

1) 8% coupon, pay annually, 10 years to maturity, par = 1000, YTM = 6%

•Using formula

•Using calculator

•PMT = 80, FV = 1000, n = 10, I/Y = 6

2) The same information, but the bond is paying interest semi-annually. What is the price of the bond?

Yield to maturity is a measure of the average rate of return that will be earned if the bond is held to maturity.

YTM is the discount rate that makes the present value of a bond’s payments equal to its price

YTM is the solution of :

T

T

tt

t

YTM

par

YTM

coupon

)1()1( Price Bond

1

8% coupon, 30-year bond selling at $1,276.76, what is the yield to maturity?

Prices and Yields (required rates of return) have an inverse relationship

If YTM increase, then the price decreases and vice versa MarketMaturity Coupon Interest Bond Value Rate Rate Price

$ 1,000 8% 8% $1,000.00

$ 1,000 8% 10% $ 810.71

$ 1,000 8% 6% $1,276.75

rd 1-year Change 10-year Change

5% $1,048 $1,386

10% 1,000 4.8% 1,000 38.6%

15% 956 4.4% 749 25.1%

Interest rate risk: change in rd causes bond’s price to change.

Bond Prices and Yields

Longer time to maturity, higher change in price when interest rate changes (or higher interest rate risk)

0

500

1,000

1,500

0% 5% 10% 15%

1-year

10-year

rd

Value

Bond Prices and Yields

Yield to Call◦ Call price replaces par◦ Call date replaces maturity◦ Example: 8% coupon, semi-annual, 30 years to

maturity, current price = 1150, callable in 10 years, call price = 1100. What is the yield to call and yield to maturity

yieldgain capital yieldcurrent

P

)P-(P

P

Coupon

P

)P-(PCoupon

price beginnning

(loss)gain capital incomeinterest HPR

t

t1t

t

t

t

t1tt

WherePt = Bond Price at time tPt+1= Bond Price at time t+1

Current yield =

Capital gains yield =

= YTM = +

Annual coupon pmtCurrent price

Change in priceBeginning price

Expected totalreturn

Expected Curr yld

Expected capgains yld

Current yield =

= 0.1015 = 10.15%.

$90 $887

YTM = Current yield + Capital gains yield.

Cap gains yield = YTM - Current yield = 10.91% - 10.15% = 0.76%.

Could also find values in Years 1 and 2,get difference, and divide by value inYear 1. Same answer.

BOND PRICES OVER TIME

Premium Bond◦ price > par◦ Coupon rate exceeds yield to maturity◦ Bond price will decline to par over its maturity

Discount Bond◦ price < par◦ Yield to maturity exceeds coupon rate◦ Bond price will increase to par over its maturity

Bond selling at par◦ price = par◦ Yield to maturity = coupon rate◦ bond price is constant throughout the life of bond

BOND PRICES OVER TIME

M

Bond Value ($)

Years remaining to Maturity

1,372

1,211

1,000

837

775

30 25 20 15 10 5 0

rd = 7%.

rd = 13%.

rd = 10%.

At maturity, the value of any bond must equal its par value.

The value of a premium bond would decrease to $1,000.

The value of a discount bond would increase to $1,000.

A par bond stays at $1,000 if rd (YTM) remains constant.

BOND PRICES OVER TIME

DEFAULT RISK AND BOND PRICING

Rating companies◦ Moody’s Investor Service◦ Standard & Poor’s◦ Fitch

Rating Categories◦ Investment grade◦ Speculative grade

Investment Grade Junk Bonds

Moody’s Aaa Aa A Baa Ba B Caa C

S&P AAA AA A BBB BB B CCC D

Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt

Sinking funds◦ A bond that calls for the issuer to periodically

repurchase some proportion of the outstanding bonds prior to maturity

Subordination of future debt◦ Restrictions on additional borrowing that stipulates that

senior bondholders will be paid first in the event of bankruptcy

Dividend restrictions◦ Limit dividend payout to protect bondholders

Collateral◦ Uses assets to back up bonds: mortgage bond,

collateral trust bond, equipment obligation bond. ◦ Collaterals are secured bonds◦ Unsecured bond: debentures

Risk structure of interest rates Default premiums

◦Yields compared to ratings◦Yield spreads over business cycles

•Inverse relationship between bond prices and bond yields

•Premium and discount bonds•Corporate bonds and default risk•Next Class: Managing Bond Portfolios