채권과 주식의
가치평가
8장
Bond Definitions
Bond
 Par value (face value)
 Coupon rate
 Coupon payment
 Maturity date
 Yield or Yield to maturity

이표채의 가치평가
Bond Value = PV of coupons + PV of par
 Bond Value = 연금의 현가+원금의 현가

1

1- ( 1  R) t
Bond Value  C 
R




F

t
(
1

R)


F
 C  PVIFA( R, t ) 
(1  R) t
이표채 가치평가(예제)

이표율 8%, 액면가 1억, 3년 만기 회사채




1년 후 시장금리가 10%로 상승했다면
채권가치는?


연금의 현가=800만원*PVIFA(8,3)=2,061.7만원
원금의 현가=10,000만원/1.08^3=7,938.3만원
채권가치=10,000만원(why?)
채권가치=800*PVIFA(10,2)+10,000/1.1^2=
9,652.9만원(할인채)
1년 후 시장금리가 6%로 하락한다면?

할증 채
채권의 가치평가

분기마다 이표를 지급하는 회사채



순수할인채(pure discount bond or zero
coupon bond)



연간 이표율이 8%, 액면가 1억 원, 만기가 3년,
만기수익률이 10%라 하자
채권가치=200만원*PVIFA(2.5%, 12)
+1억/(1.025)^12 = 9,487.1만원
만기 5년, 액면가 5천만 원, 만기수익률 10%
채권가치=5천만/(1.1)^5=3,104.6만원
영구 채(consol)

채권가치=의표금액/만기수익률
Interest Rate Risk

Price Risk



Change in price due to changes in interest
rates
Long-term bonds have more price risk than
short-term bonds
Reinvestment Rate Risk


Uncertainty concerning rates at which cash
flows can be reinvested
Short-term bonds have more reinvestment
rate risk than long-term bonds
Graphical Relationship Between Price and
Yield-to-maturity
1500
1400
1300
1200
1100
1000
900
800
700
600
0%
2%
4%
6%
8%
10%
12%
14%
채권가격의 잔존만기 또는
이표율과의 관계
잔존만기가
길수록 채권가격은
크게 변한다
금리가 상승할 때보다 금리가
하락할 때 채권가격이 크게
변한다
이표율이 낮을수록 채권가격은
크게 변한다
잔존만기와 금리위험(10% 이표율)
Bond Characteristics and Required
Returns
The coupon rate depends on the risk
characteristics of the bond when issued
 Which bonds will have the higher coupon,
all else equal?





Secured debt versus a debenture
Subordinated debenture versus senior debt
A bond with a sinking fund versus one without
A callable bond versus a non-callable bond
만기수익률

만기수익률(yield to maturity; YTM)




해당 채권의 현재 시장금리
해당 채권에 대한 시장(채권자)의 요구수익률
채권의 시장가격과 현재가치를 일치시키는 할인율
계산예제(만기 3년, 이표율 10%, 액면가
1,000만원, 현재 시장 가 950만원)-예제8-3



방정식에 의한 방법
간이 법
재무계산기의 이용
금리의 기간구조

Term structure of interest rates




단기금리와 장기금리 사이에 존재하는 관계
만기수익률과 잔존만기 간의 관계
default-free, zeros를 대상으로 함
Yield curve – graphical representation of
the term structure


Normal – upward-sloping, long-term yields are
higher than short-term yields
Inverted – downward-sloping, long-term yields
are lower than short-term yields
Upward-Sloping Yield Curve
Downward-Sloping Yield Curve
Treasury Yield Curve May 11, 2001
Factors Affecting Required Return
Default risk premium – remember bond
ratings
 Taxability premium – remember municipal
versus taxable
 Liquidity premium – bonds that have more
frequent trading will generally have lower
required returns
 Anything else that affects the risk of the
cash flows to the bondholders, will affect
the required returns

spot interest rate vs yield-to-maturity


현물이자율의 도출(순수
할인국채를 이용)
이표채의 가격 산출
(이표율=5%, 만기=2년,
액면가=100만원)

Forward rate의 도출
(f=10%)

이표채의 만기수익률은
r=7.94%
(6%와 8%의 가중 평균)
100
94.34 
 r1  6%,
(1  r1 )
100
85.73 
 r2  8%
2
(1  r2 )
5
105

 94.74만원
2
1.06 (1.08)
5
105

 94.74만원
1.06 (1.06)(1  f )
5
105
94.74 

1  r (1  r ) 2
주식의 현금흐름

일기간 예(one period example)



1년 후 주가 7만원, 1년 후 배당 주당 만원, 주식에
대한 요구수익률 25%
주식가치=(7만원+1만원)/1.25=64,000원
2기간 예(two period example)



만약 주식을 2년간 보유한다면 어떻게 될까?
2년 후 주가 8만원, 2년 후 배당 주당 12,000원,
같은 요구수익률
주식가치=1만원/1.25+(12,000+80,000)/1.25^
2=8,000+58,880=66,880원
Developing The Model
You could continue to push back when
you would sell the stock
 You would find that the price of the stock
is really just the present value of all
expected future dividends
 So, estimating all future dividend
payments only matter

D1
D2
D
P0 


2

(1  R) (1  R)
(1  R)
Estimating Dividends: Special Cases

Constant dividend (Zero growth)


Constant dividend growth


The firm will pay a constant dividend
forever
The firm will increase the dividend by a
constant percent every period
Supernormal growth

Dividend growth is not consistent initially,
but settles down to constant growth
eventually
Zero Growth (Constant Dividend)
If dividends are expected at regular
intervals forever, then this is like preferred
stock and is valued as a perpetuity
 P0 = ?
 Suppose stock is expected to pay a $10
dividend every year forever and the
required return is 10%. What is the price
of this stock?

Dividend Growth Model
(Gordon Model)

Dividends are expected to grow at a
constant percent per period.
D0 (1  g)
D1
P0 

R -g
R -g

Suppose Big D Inc. just paid a dividend of
$.50. It is expected to increase its
dividend by 2% per year. If the market
requires a return of 15% on this stock,
how much should the stock be selling for?
Stock Price Sensitivity to Dividend
Growth, g
D1 = $2; R = 20%
250
Stock Price
200
150
100
50
0
0
0.05
0.1
Growth Rate
0.15
0.2
Stock Price Sensitivity to Required
Return, R
D1 = $2; g = 5%
250
Stock Price
200
150
100
50
0
0
0.05
0.1
0.15
Required Return
0.2
0.25
0.3
Nonconstant Growth Problem
Suppose a firm is expected to increase
dividends by 20% in one year and by 15%
in two years. After that dividends will
increase at a rate of 5% per year
indefinitely. If the last dividend was $1
and the required return is 20%, what is
the price of the stock?
 Remember that we have to find the PV of
all expected future dividends.

Nonconstant Growth – Solution

Compute the dividends until growth levels
off




Find the expected future price


D1 =
D2 =
D3 =
P2 =
Find the present value of the expected
future cash flows

P0 =