9-1 2014_5_8

CHAPTER 9 Bonds and Their Valuation

Bond valuation

Measuring yield

Assessing risk

9-2 2014_5_8

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.

Treasury bond, Corporate bond, Municipal bond, International bond (Eurobond, Foreign bond), etc.

9-3 2014_5_8

The value of financial assets

n

n

2

2

1

1

k)(1

CF ...

k)(1

CF

k)(1

CF Value

0 1 2 n k

CF1 CFn CF2 Value

...

ㅇ The value of any financial asset is simply the present

value of the cash flows the asset is expected to produce.

9-4 2014_5_8

Bond Valuation ㅇ 채권(bond)의 수익구조: 이자 + 액면가

- 일정만기 내에 규칙적으로 발행금리(coupon rate)에 해당하는 이

자를 지급하고 만기 시 액면가(face value)를 지급

현금흐름예상되는시점에

만기수익률할인율만기

액면가액표면이자율채권가격

:

)(,:),(:

)(:,:,:

)1()1()1()1(1

0

1t20

tC

YTMkmaturityn

valuefaceFiB

k

CF

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Fi

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ddd

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1

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)k(1

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)k(1

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)k(1

I valuesBond'

FNTNTNT

9-5 2014_5_8

ㅇ Bonds with Semiannual Coupons

ㅇ Bonds paying interests m times/year

n

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ddd k

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지급별기분예회수이자지급년간

Bond Valuation (cont’d)

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What is the opportunity cost of debt capital?

The discount rate (kd ) is the opportunity cost of debt capital, and is the rate that could be earned on alternative investments of equal risk.

kd = k* + IP + MRP + DRP + LP

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What is the value of a 10-year, FV of $1,000, 10% annual coupon bond, if kd = 10%?

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

(1.10)

$1,000

(1.10)

$100 ...

(1.10)

$100 V

B

B

10101B

0 1 2 10 kd

100 100 + 1,000 100 VB = ?

...

9-8 2014_5_8

INPUTS

OUTPUT

N I/YR PMT PV FV

10 10 100 1000

-1000

Using a Financial Calculator to Value a Bond

i=10% kd=10%

INPUTS

OUTPUT

N I/YR PMT PV FV

10 10 130 1000

-1184.34

i=13% kd=10%

INPUTS

OUTPUT

N I/YR PMT PV FV

10 10 100 1000

-815.66

i=7% kd=10%

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Bond Yields YTM (Yield to Maturity): The average rate of

return earned on a bond if it is held to maturity

10d

10d

1d

Nd

Nd

1d

B

)k(1

1,000

)k(1

90 ...

)k(1

90 $887

)k(1

M

)k(1

INT ...

)k(1

INT V

a 10-year, 9% annual coupon bond, sells for $887, a face value of $1,000 (YTM=10.91%)

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INPUTS

OUTPUT

N I/YR PMT PV FV

10

10.91

90 1000 - 887

Using a Financial Calculator to Solve for the YTM

9-11 2014_5_8

N

d

N

d

1

d

B)k(1

Price Call

)k(1

INT ...

)k(1

INT V

YTC (Yield to Call): The rate of return on a

bond if it is called before its maturity

Bond Yields (cont’d)

551 )Y(1

1,100

)Y(1

90 ...

)Y(1

90 $887

TCTCTC

(YTC example) a 10-year, 9% annual coupon bond, sells for $887, a face value of $1,000, callable in 5 years at a call price of $1,100 (YTC=13.79%)

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Effect of a call provision

Allows issuer to redeem the bond issue prior to the maturity date (a refunding operation* when interest rates fall => helps the issuer, but hurts the investor). *sell a new issue of low-yielding securities, use the proceeds of the new issue to retire the high-rate seasoned issue, and thus reduce its interest expense

Borrowers are willing to pay more, and lenders require more, for callable bonds.

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Find the current yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000.

Current yield = $90 / $887 = 0.1015 = 10.15%

CY (Current Yield): The annual interest

payment on a bond divided by the bond’s

current price

Bond Yields (cont’d)

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The price path of a bond What would happen to the value of this bond if

its coupon rate are different at 10%, at 13%, or at 7%? (FV:$1,000;Kd=10%;N=15)

Years

to Maturity

1,228

1,000

772

15 12 9 6 3 0

i = 13%.

i = 7%.

i = 10%.

VB

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Bond values over time

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

If kd remains constant:

The value of a premium bond would decrease over time, until it reached $1,000.

The value of a discount bond would increase over time, until it reached $1,000.

A value of a par bond stays at $1,000.

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Assessing the Bond Risk

Interest Rate Risk

Reinvestment Rate Risk

Default Risk

Callable Risk

Liquidity (Marketability) Risk

Purchasing Power (Inflation) Risk

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What is interest rate (price) risk?

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

% change 1 yr kd 10yr % change +4.8% $1,048 5% $1,386 +38.6% $1,000 10% $1,000 -4.4% $956 15% $749 -25.1%

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

* coupon interest: 10%, FV: $1,000

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Illustrating Interest Rate Risk

0

200

400

600

800

1,000

1,200

1,400

1,600

0 5 10 15 20

Valu

e (

$)

YTM (%)

10-Year Bond

1-Year Bond

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What is reinvestment rate risk?

Reinvestment rate risk is the concern that kd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.

Example: $500,000 Investments in either a 10-year bond or a 1-year bond. Both bonds currently yield 10%. 1-year bond strategy: After Year 1, you receive

$50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000.

10-year bond strategy: You can lock in a 10% interest rate, and $50,000 annual income.

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Default risk

If an issuer defaults, investors receive less than the promised return.

Influenced by the issuer’s financial strength and the terms of the bond contract.

Debt ratio, TIE ratio, Current ratio, etc.

Secured vs. Unsecured debt; Senior vs. subordinated debt; Guarantee and sinking fund provisions;

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Evaluating default risk: Bond ratings

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

한신평, 한기평, NICE신용평가

Investment Grade Junk Bonds

Moody’s Aaa Aa A Baa Ba B Caa C

S & P AAA AA A BBB BB B CCC D