7-1

CHAPTER 7Bonds and Their Valuation

Key features of bonds Bond valuation Measuring yield Assessing risk

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What is a bond? A long-term debt instrument in

which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.

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What is a bond?Long Term debt(Bond certificate sample)

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Firm A Other BondholdersBondholders

“IOU” (bond)

Capital (RM)

OTC market

(RM)Coupon interest (periodically)

Par Value (at maturity date)(RM)

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Key Features of a Bond Par value – face amount of the bond, which

is paid at maturity (assume $1,000). Coupon interest rate – stated interest rate

(generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest.

Maturity date – years until the bond must be repaid.

Issue date – when the bond was issued. Yield to maturity - rate of return earned on

a bond held until maturity (also called the “promised yield”).

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The value of financial assets

nn

22

11

r)(1CF ... r)(1

CF r)(1CF Value

0 1 2 nr%

CF1 CFnCF2Value

...

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What is the value of a 10-year, 10% annual coupon bond, if rd = 10%?

$1,000 V$385.54 $38.55 ... $90.91 V

(1.10)$1,000 (1.10)

$100 ... (1.10)$100 V

BB

10101B

0 1 2 nr

100 100 + 1,000100VB = ?

...

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Using a financial calculator to value a bond

This bond has a $1,000 lump sum (the par value) due at maturity (t = 10), and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows.

INPUTS

OUTPUTN I/YR PMTPV FV

10 10 100 1000

-1000

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The same company also has 10-year bonds outstanding with the same risk but a 13% annual coupon rate

This bond has an annual coupon payment of $130. Since the risk is the same the bond has the same yield to maturity as the previous bond (10%). In this case the bond sells at a premium because the coupon rate exceeds the market rate (rd).

INPUTS

OUTPUTN I/YR PMTPV FV

10 10 130 1000

-1184.34

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The same company also has 10-year bonds outstanding with the same risk but a 7% annual coupon rate

This bond has an annual coupon payment of $70. Since the risk is the same the bond has the same yield to maturity as the previous bonds (10%). In this case, the bond sells at a discount because the coupon rate is less than the market rate (rd).

INPUTS

OUTPUTN I/YR PMTPV FV

10 10 70 1000

-815.66

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What is the rd ( ie. Yield to maturity-YTM) on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887? (selling at Discount) Must find the rd that solves this model.

10d

10d

1d

Nd

Nd

1d

B

)r(11,000 )r(1

90 ... )r(190 $887

)r(1M )r(1

INT ... )r(1INT V

N =10, PV = -887, Pmt = 90, FV = 1,000, I/yr = ?? 10.91YTM > Coupon

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Find YTM, if the bond price is $1,134.20 Solving for I/YR, the YTM of this bond

is 7.08%. This bond sells at a premium, because YTM < coupon rate.

INPUTS

OUTPUTN I/YR PMTPV FV

10

7.08

90 1000-1134.2

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What is interest rate (or price) risk? Does a 1-year or 10-year bond have more interest rate risk?

Assume coupon payments is 10% and par value $1,000

Interest rate risk is the concern that rising rd will cause the value of a bond to fall.

rd 1-year Change 10-year Change5% $1,048 $1,38610% 1,000 1,00015% 956 749

The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.

+ 4.8%

– 4.4%

+38.6%

–25.1%

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1- year Bond (10% coupon)

I/ yr= 5%, FV= 1,000, Pmt= 100, PV= 1,047

I/ yr= 15%, FV= 1,000, Pmt= 100, PV=956

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10- year Bond (10% coupon)

I/ yr= 5%, FV= 1,000, Pmt= 100, PV= 1,386

I/ yr= 15%, FV= 1,000, Pmt= 100, PV= 749

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So, the 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk. The relationship between price of bond and interest rates is inverse

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Illustrating interest rate risk

0200400600800

1,0001,2001,4001,600

0 5 10 15 20Interest rates (% )

Valu

e ($

)

n = 1

n = 10

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Reinvestment Risk

100

CF

100 + 1,000100 100 100

CFCF CFCF

“reinvest cash inflow at going market rates”

Thus, if market rates , may experience income reduction

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What is reinvestment rate risk? Reinvestment rate risk is the

concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.

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What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%?

1. Multiply years by 2 : N = 2 * 10 = 20.2. Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5.3. Divide annual coupon by 2 : PMT = 100 / 2 =

50.

INPUTS

OUTPUTN I/YR PMTPV FV

20 6.5 50 1000

- 834.72

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Bonds call back

Corp A

Bank loan at 6%

Bondholdersie: coupon= 10%

new financing

BondCall back

Pay principle + penalty

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Callable Bond Valuation

i.e: Northern Timber issued a $1,000 25 years bond. The bond has a call provision that allowed it to be retired any time after 5 years, with additional coupon put as penalty. The coupon rate is 18%, interest rate is 8%

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0 5 10 15

n= 5

Principle = 1,000 + 180 (penalty)Pmt = 180I/ yr = 8%, PV = (?)

20 25

valuation

Callable Bond Valuation

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Callable bond Valuation

INPUTS

OUTPUTN I/YR PMTPV FV

5

8

180 11801,521

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Callable bond & yield to call (i.e.1) A 10-year, 10% annual coupon

bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)?

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Callable bond & yield to call (i.e.1)

1 6 7 8 9 102 3 4 50

Call Back Bond

- Principle + Penalty = RM 1,050

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Because annual Coupon,1. n = 4 2. Coupon pmt

= 10% x 1,000= 100

3. Principle (FV) - RM 1,050

4. Original price (PV) - RM 1,135

5. YTC ?

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Callable bond & yield to call (i.e.1) A 10-year, 10% annual coupon

bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)?

INPUTS

OUTPUTN I/YR PMTPV FV

4

7.12

100 1050- 1135.90

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Callable bond & yield to call (i.e.2)

A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)?

Solving for the YTC is identical to solving for rd, except the time to call is used for N and the call premium is FV.

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Callable bond & yield to call (i.e.2)

1 6 7 8 9 102 3 4 50

Call Back Bond

- Principle + Penalty = RM 1,050

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Because Semiannual Coupon,

1. n x 2 = 4 x 2

= 8

2. Coupon pmt x 1,000 2= 10% / 2 x 1,000= 50

3. Principle (FV) - RM 1,050

4. Original price (PV) - RM 1,135

5. YTC ?

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Callable bond & yield to call (i.e.2) A 10-year, 10% semiannual

coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)?

INPUTS

OUTPUTN I/YR PMTPV FV

8

3.568

50 1050- 1135.90

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Default risk If an issuer defaults, investors

receive less than the promised return.

The default risk is influenced by the issuer’s financial strength and the terms of the bond contract.

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Evaluating default risk:Bond ratings

Bond ratings are designed to reflect the probability of a bond issue going into default.

Investment Grade Junk BondsMoody’s

Aaa Aa A Baa Ba B Caa C

S & P AAA AA A BBB BB B CCC D

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Factors affecting default risk and bond ratings Debt ratio, TIE ratio, Current

ratio Bond contract provisions

Secured vs. Unsecured debt Guarantee and sinking fund

provisions Earnings stability

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Other types (features) of bonds Convertible bond – may be exchanged

for common stock of the firm, at the holder’s option.

Putable bond – allows holder to sell the bond back to the company prior to maturity.

Income bond – pays interest only when income is earned by the firm.

Indexed bond – interest rate paid is based upon the rate of inflation.