fm10e ch07

Chapter 7 - Chapter 7 - Valuation and Valuation and Characteristics of BondsCharacteristics of Bonds

2005, Pearson Prentice Hall

Characteristics of Bonds

Bonds pay fixed coupon (interest) payments at fixed intervals (usually every six months) and pay the par value at maturity.

Characteristics of Bonds

Bonds pay fixed coupon (interest) payments at fixed intervals (usually every six months) and pay the par value at maturity.

00 1 1 2 . . .2 . . . nn

$I $I $I $I $I $I+$M$I $I $I $I $I $I+$M

Example: Example: AT&T 6 ½ 32AT&T 6 ½ 32

Par valuePar value = = $1,000$1,000 CouponCoupon = = 6.5%6.5% or par value per year, or par value per year,

or or $65$65 per year ( per year ($32.50$32.50 every six months). every six months). MaturityMaturity = 28 years (matures in 2032). = 28 years (matures in 2032). Issued by AT&T.Issued by AT&T.

Example: Example: AT&T 6 ½ 32AT&T 6 ½ 32

Par valuePar value = = $1,000$1,000 CouponCoupon = = 6.5%6.5% or par value per year, or par value per year,

or or $65$65 per year ( per year ($32.50$32.50 every six months). every six months). MaturityMaturity = 28 years (matures in 2032). = 28 years (matures in 2032). Issued by AT&T.Issued by AT&T.

0 1 2 … 28

$32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000

Types of BondsTypes of Bonds

DebenturesDebentures - unsecured bonds.- unsecured bonds. Subordinated debenturesSubordinated debentures - unsecured - unsecured

“junior” debt.“junior” debt. Mortgage bondsMortgage bonds - secured bonds.- secured bonds. ZerosZeros - bonds that pay only par value at - bonds that pay only par value at

maturity; no coupons.maturity; no coupons. Junk bondsJunk bonds - speculative or below-- speculative or below-

investment grade bonds; rated BB and investment grade bonds; rated BB and below. High-yield bonds.below. High-yield bonds.

EurobondsEurobonds - bonds denominated in - bonds denominated in one currency and sold in another one currency and sold in another country. (Borrowing overseas.)country. (Borrowing overseas.)

exampleexample - - suppose Disney decides to sell suppose Disney decides to sell $1,000 bonds in France. These are U.S. $1,000 bonds in France. These are U.S. denominated bonds trading in a foreign denominated bonds trading in a foreign country. Why do this?country. Why do this?

EurobondsEurobonds - bonds denominated in - bonds denominated in one currency and sold in another one currency and sold in another country. (Borrowing overseas.)country. (Borrowing overseas.)

If borrowing rates are lower in France.If borrowing rates are lower in France.

EurobondsEurobonds - bonds denominated in - bonds denominated in one currency and sold in another one currency and sold in another country. (Borrowing overseas).country. (Borrowing overseas).

If borrowing rates are lower in France.If borrowing rates are lower in France. To avoid SEC regulations.To avoid SEC regulations.

The Bond IndentureThe Bond Indenture

The The bond contractbond contract between the firm between the firm and the trustee representing the and the trustee representing the bondholders.bondholders.

Lists all of the bond’s features:Lists all of the bond’s features:

coupon, par value, maturity, coupon, par value, maturity, etc.etc. ListsLists restrictive provisionsrestrictive provisions which are which are

designed to protect bondholders.designed to protect bondholders. Describes repayment provisions.Describes repayment provisions.

ValueValue

Book value:Book value: value of an asset as shown on value of an asset as shown on a firm’s balance sheet; historical cost.a firm’s balance sheet; historical cost.

Liquidation value:Liquidation value: amount that could be amount that could be received if an asset were sold individually.received if an asset were sold individually.

Market value:Market value: observed value of an asset observed value of an asset in the marketplace; determined by supply in the marketplace; determined by supply and demand.and demand.

Intrinsic value:Intrinsic value: economic or fair value of economic or fair value of an asset; the present value of the asset’s an asset; the present value of the asset’s expected future cash flows.expected future cash flows.

Security ValuationSecurity Valuation

In general, the In general, the intrinsic valueintrinsic value of an of an asset = the asset = the present valuepresent value of the stream of the stream of expected cash flows discounted at of expected cash flows discounted at an appropriate an appropriate required rate of required rate of returnreturn..

Can the Can the intrinsic valueintrinsic value of an asset of an asset differ from its differ from its market valuemarket value??

ValuationValuation

CCtt = cash flow to be received at time = cash flow to be received at time tt..

kk = the investor’s required rate of return.= the investor’s required rate of return. VV = the intrinsic value of the asset.= the intrinsic value of the asset.

V = V = t = 1t = 1

(1 + k)t

Bond ValuationBond Valuation

Discount the bond’s cash flows at Discount the bond’s cash flows at the investor’s required rate of the investor’s required rate of return.return.

Discount the bond’s cash flows at Discount the bond’s cash flows at the investor’s required rate of the investor’s required rate of return.return. The The coupon payment streamcoupon payment stream (an (an

annuity).annuity).

Discount the bond’s cash flows at Discount the bond’s cash flows at the investor’s required rate of the investor’s required rate of return.return. The The coupon payment streamcoupon payment stream (an (an

annuity).annuity). The The par value paymentpar value payment (a single (a single

sum).sum).

Vb = $It (PVIFA kb, n) + $M (PVIF kb, n)

$It $M

(1 + kb)t (1 + kb)nVVbb = + = +

t = 1t = 1

Bond ExampleBond Example

Suppose our firm decides to issue Suppose our firm decides to issue 20-year20-year bonds with a par value of bonds with a par value of $1,000$1,000 and and annual coupon payments. The return on annual coupon payments. The return on other corporate bonds of similar risk is other corporate bonds of similar risk is currently 12%, so we decide to offer a currently 12%, so we decide to offer a 12% 12% couponcoupon interest rate. interest rate.

What would be a fair price for these What would be a fair price for these

bonds?bonds?

0 1 2 3 . . . 20

1000 120 120 120 . . . 120

P/YR = 1 N = 20 I%YR = 12

FV = 1,000 PMT = 120

Solve PV = -$1,000

NoteNote:: If the If the coupon ratecoupon rate = = discount discount raterate, the bond will sell for , the bond will sell for par valuepar value..

Mathematical Solution:Mathematical Solution:

PV = PMT (PVIFA PV = PMT (PVIFA k, nk, n ) + FV (PVIF ) + FV (PVIF k, nk, n ) )

PV = 120 (PVIFA PV = 120 (PVIFA .12, 20.12, 20 ) + 1000 (PVIF ) + 1000 (PVIF .12, 20.12, 20 ))

PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn

PV = 120 1 - (1.12 )PV = 120 1 - (1.12 )2020 + + 1000/ (1.12) 1000/ (1.12) 2020 = = $1000$1000

.12.12

Suppose Suppose interest rates fallinterest rates fall immediately after we issue the immediately after we issue the bonds. The required return on bonds. The required return on bonds of similar risk drops to bonds of similar risk drops to 10%10%..

What would happen to the bond’s What would happen to the bond’s intrinsic value?intrinsic value?

P/YR = P/YR = 11

Mode = Mode = endend

N = N = 2020

I%YR = I%YR = 1010

PMT = PMT = 120120

FV = FV = 10001000

Solve PV = Solve PV = --$1,170.27$1,170.27

P/YR = P/YR = 11

N = N = 2020

I%YR = I%YR = 1010

PMT = PMT = 120120

FV = FV = 10001000

Solve PV = Solve PV = --$1,170.27$1,170.27

Note: If the coupon rate > discount rate, the bond will sell for a premium.

PV = 120 1 - (1.10 )PV = 120 1 - (1.10 )2020 + 1000/ (1.10) + 1000/ (1.10) 2020 = = $1,170.27$1,170.27

.10.10

Suppose Suppose interest rates riseinterest rates rise immediately after we issue the immediately after we issue the bonds. The required return on bonds. The required return on bonds of similar risk rises to bonds of similar risk rises to 14%14%..

What would happen to the bond’s What would happen to the bond’s intrinsic value?intrinsic value?

P/YR = P/YR = 11

N = N = 2020

I%YR = I%YR = 1414

PMT = PMT = 120120

FV = FV = 10001000

Solve PV = Solve PV = -$867.54-$867.54

P/YR = P/YR = 11

N = N = 2020

I%YR = I%YR = 1414

PMT = PMT = 120120

FV = FV = 10001000

Solve PV = -Solve PV = -$867.54$867.54

Note: If the coupon rate < discount rate, the bond will sell for a discount.

PV = 120 1 - (1.14 )PV = 120 1 - (1.14 )2020 + 1000/ (1.14) + 1000/ (1.14) 2020 = = $867.54$867.54

.14.14

Suppose coupons are semi-annualSuppose coupons are semi-annual

P/YR = P/YR = 22

N = N = 4040

I%YR = I%YR = 1414

PMT = PMT = 6060

FV = FV = 10001000

Solve PV = -Solve PV = -$866.68$866.68

PV = 60 1 - (1.07 )PV = 60 1 - (1.07 )4040 + 1000 / (1.07) + 1000 / (1.07) 4040 = = $866.68$866.68

.07.07

Yield To MaturityYield To Maturity

The The expected rate of returnexpected rate of return on a on a bond.bond.

The rate of return investors earn on The rate of return investors earn on a bond if they hold it to maturity.a bond if they hold it to maturity.

Yield To MaturityYield To Maturity

The The expected rate of returnexpected rate of return on a on a bond.bond.

The rate of return investors earn on The rate of return investors earn on a bond if they hold it to maturity.a bond if they hold it to maturity.

$It $M

(1 + kb)t (1 + kb)nPP00 = + = +

t = 1t = 1

YTM ExampleYTM Example

Suppose we paid Suppose we paid $898.90$898.90 for a for a $1,000$1,000 par par 10%10% coupon bond coupon bond with 8 years to maturity and with 8 years to maturity and semi-annual coupon payments.semi-annual coupon payments.

What is our What is our yield to maturityyield to maturity??

P/YR = 2P/YR = 2

Mode = endMode = end

N = 16N = 16

PV = -898.90PV = -898.90

PMT = 50PMT = 50

FV = 1000FV = 1000

Solve I%YR = Solve I%YR = 12%12%

YTM Example

898.90 = 50 (PVIFA 898.90 = 50 (PVIFA k, 16k, 16 ) + 1000 (PVIF ) + 1000 (PVIF k, 16k, 16 ))

898.90 = 50 1 - (1 + 898.90 = 50 1 - (1 + ii ) )1616 + + 1000 / (1 + 1000 / (1 + ii) ) 1616

ii solve using trial and errorsolve using trial and error

Zero Coupon BondsZero Coupon Bonds

No coupon interest payments.No coupon interest payments. The bond holder’s return is The bond holder’s return is

determined entirely by the determined entirely by the price discountprice discount..

Zero ExampleZero Example

Suppose you pay Suppose you pay $508$508 for a zero for a zero coupon bond that has coupon bond that has 10 years10 years left to maturity. left to maturity.

What is your What is your yield to maturityyield to maturity??

Suppose you pay Suppose you pay $508$508 for a zero for a zero coupon bond that has coupon bond that has 10 years10 years left to maturity. left to maturity.

What is your What is your yield to maturityyield to maturity??

0 100 10

-$508 $1000-$508 $1000

P/YR = 1P/YR = 1

Mode = EndMode = End

N = 10N = 10

PV = -508PV = -508

FV = 1000FV = 1000

Solve: I%YR = Solve: I%YR = 7%7%

PV = FV (PVIF PV = FV (PVIF i, ni, n ))

508 = 1000 (PVIF508 = 1000 (PVIF i, 10 i, 10 ) )

.508 = (PVIF.508 = (PVIF i, 10 i, 10 ) ) [use PVIF table][use PVIF table]

PV = FV /(1 + i) PV = FV /(1 + i) 1010

508 = 1000 /(1 + i)508 = 1000 /(1 + i)10 10

1.9685 = 1.9685 = (1 + i)(1 + i)10 10

i = i = 7%7%

PV = -508 FV = 1000

The Financial Pages: The Financial Pages: Corporate BondsCorporate Bonds

CurCur Net Net

Yld Vol Close ChgYld Vol Close Chg

Polaroid 11 Polaroid 11 11//22 06 19.3 395 59 06 19.3 395 59 33//44 ... ...

What is the yield to maturity for this bond?What is the yield to maturity for this bond?

P/YR = P/YR = 22, N = , N = 1010, FV = , FV = 10001000, ,

PV = PV = $-597.50$-597.50, ,

PMT = 57.50PMT = 57.50

Solve: I/YR = 26.48%Solve: I/YR = 26.48%

The Financial Pages: The Financial Pages: Corporate BondsCorporate Bonds

CurCur Net Net

Yld Vol Close ChgYld Vol Close Chg

HewlPkd zr 17 ... 20 51 HewlPkd zr 17 ... 20 51 11//22 +1 +1

What is the yield to maturity for this bond?What is the yield to maturity for this bond?

P/YR = P/YR = 11, N = 16, FV = , N = 16, FV = 10001000, ,

PV = PV = $-515$-515, ,

PMT = PMT = 00

The Financial Pages: The Financial Pages: Treasury BondsTreasury Bonds

Maturity Maturity AskAsk

Rate Mo/Yr Rate Mo/Yr Bid Asked Bid Asked Chg Chg YldYld

99 Nov 18 Nov 18 139:14 139:20 -34139:14 139:20 -34 5.46 5.46

What is the yield to maturity for this What is the yield to maturity for this

Treasury bond? (assume 35 half years)Treasury bond? (assume 35 half years)

P/YR = P/YR = 22, N = 35, FV = , N = 35, FV = 10001000, ,

PMT = PMT = 4545,,

PV = PV = - 1,396.25- 1,396.25 (139.625% of par) (139.625% of par)

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