manajemen keuangan keown fmch07
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Ch. 7:
Valuation
and
Characteristicsof
2002, Prentice Hall, Inc.
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Characteristics of Bonds
Bonds pay fixed coupon(interest)payments at fixed intervals (usually
every 6 months) and pay the parvalueat maturity.
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Characteristics of Bonds
Bonds pay fixed coupon(interest)payments at fixed intervals (usually
every 6 months) and pay the parvalueat maturity.
0 1 2 . . . n
$I $I $I $I $I $I+$M
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example: ATT 6 1/229
par value = $1000
coupon= 6.5% of par value per year.
= $65per year ($32.50every 6 months).
maturity= 28 years (matures in 2029).
issued by AT&T.
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example: ATT 6 1/229
par value = $1000
coupon= 6.5% of par value per year.
= $65per year ($32.50every 6 months).
maturity= 28 years (matures in 2029).
issued by AT&T.
0 1 2 28
$32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000
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Types of Bonds
Eurobonds- bonds denominated inone currency and sold in another
country. (Borrowing overseas).
example- suppose Disney decides to sell$1,000 bonds in France. These are U.S.
denominated bonds trading in a foreign
country. Why do this?
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Types of Bonds
Eurobonds- bonds denominated inone currency and sold in another
country. (Borrowing overseas).
example- suppose Disney decides to sell$1,000 bonds in France. These are U.S.
denominated bonds trading in a foreign
country. Why do this?
If borrowing rates are lower in France,
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Types of Bonds
Eurobonds- bonds denominated inone currency and sold in another
country. (Borrowing overseas).
example- suppose Disney decides to sell$1,000 bonds in France. These are U.S.
denominated bonds trading in a foreign
country. Why do this?
If borrowing rates are lower in France,
To avoid SEC regulations.
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The Bond I ndenture
The bond contractbetween the firm
and the trustee representing the
bondholders. Lists all of the bonds features:
coupon, par value, maturity, etc.
Listsrestrictive provisionswhich are
designed to protect bondholders.
Describes repayment provisions.
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Value
Book Value: value of an asset as shown on
a firms balance sheet; historical cost.
Liquidation value: amount that could be
received if an asset were sold individually.
Market value: observed value of an asset
in the marketplace; determined by supply
and demand.
Intrinsic value: economic or fair value of
an asset; the present value of the assets
expected future cash flows.
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Secur ity Valuation
In general, the intrinsic valueof an
asset = the present valueof the stream
of expected cash flows discounted at
an appropriate required rate of
return.
Can the intrinsic valueof an asset
differ from its market value?
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Valuation
Ct= cash flow to be received at time t.
k= the investors required rate of return.
V= the intrinsic value of the asset.
V = t = 1
n$Ct
(1 + k)t
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Bond Valuation
Discount the bonds cash flows at
the investors required rate of
return.
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Bond Valuation
Discount the bonds cash flows at
the investors required rate of
return. the coupon payment stream(an
annuity).
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Bond Valuation
Discount the bonds cash flows at
the investors required rate of
return. the coupon payment stream(an
annuity).
the par value payment(a singlesum).
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Bond Valuation
Vb= $It(PVIFA kb, n) + $M (PVIF kb, n)
$It $M
(1 + kb)
t
(1 + kb)
n
Vb= +
n
t = 1
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Bond Example
Suppose our firm decides to issue 20-year
bonds with a par value of $1,000and
annual coupon payments. The return onother corporate bonds of similar risk is
currently 12%, so we decide to offer a 12%
couponinterest rate.
What would be a fair price for these
bonds?
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0 1 2 3 . . . 20
1000
120 120 120 . . . 120
P/YR = 1
N = 20
I%YR = 12FV = 1,000
PMT = 120
Solve PV = -$1,000
Note: If the coupon rate= discount
rate, the bond will sell for par value.
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 120 (PVIFA .12, 20) + 1000 (PVIF .12, 20)
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Suppose interest rates fall
immediately after we issue thebonds. The required return on
bonds of similar risk drops to 10%.
What would happen to the bonds
intrinsic value?
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P/YR = 1
Mode = end
N = 20
I%YR = 10
PMT = 120
FV = 1000
Solve PV = -$1,170.27
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P/YR = 1
Mode = end
N = 20
I%YR = 10
PMT = 120
FV = 1000
Solve PV = -$1,170.27
Note: If the coupon rate> discount rate,
the bond will sell for a premium.
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 120 (PVIFA .10, 20) + 1000 (PVIF .10, 20)
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 120 (PVIFA .10, 20) + 1000 (PVIF .10, 20)
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 120 (PVIFA .10, 20) + 1000 (PVIF .10, 20)
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 120 1 - (1.10 )20 + 1000/ (1.10) 20= $1,170.27
.10
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Suppose interest rates rise
immediately after we issue the
bonds. The required return on
bonds of similar risk rises to 14%.
What would happen to the bonds
intrinsic value?
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P/YR = 1
Mode = end
N = 20
I%YR = 14
PMT = 120FV = 1000
Solve PV = -$867.54
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 120 (PVIFA .14, 20) + 1000 (PVIF .14, 20)
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 120 (PVIFA .14, 20) + 1000 (PVIF .14, 20)
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 120 (PVIFA .14, 20) + 1000 (PVIF .14, 20)
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 120 1 - (1.14 )20 + 1000/ (1.14) 20= $867.54
.14
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Suppose coupons are semi-annual
P/YR = 2
Mode = end
N = 40
I%YR = 14
PMT = 60FV = 1000
Solve PV = -$866.68
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 60 (PVIFA .14, 20) + 1000 (PVIF .14, 20)
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 60 (PVIFA .14, 20) + 1000 (PVIF .14, 20)
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
PV = 60 (PVIFA .14, 20) + 1000 (PVIF .14, 20)
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
PV = 60 1 - (1.07 )40 + 1000 / (1.07) 40= $866.68
.07
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Yield To Matur ity
The expected rate of returnon a
bond.
The rate of return investors earn ona bond if they hold it to maturity.
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Yield To Matur ity
The expected rate of returnon a
bond.
The rate of return investors earn ona bond if they hold it to maturity.
$It $M
(1 + kb)t (1 + kb)
nP0= +
n
t = 1
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YTM Example
Suppose we paid $898.90for a
$1,000par 10%coupon bond
with 8 years to maturity andsemi-annual coupon payments.
What is our yield to maturity?
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P/YR = 2
Mode = end
N = 16
PV = -898.90
PMT = 50FV = 1000
Solve I%YR = 12%
YTM Example
B d E l
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
898.90 = 50 (PVIFA k, 16) + 1000 (PVIF k, 16)
B d E l
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
898.90 = 50 (PVIFA k, 16) + 1000 (PVIF k, 16)
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
B d E l
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
898.90 = 50 (PVIFA k, 16) + 1000 (PVIF k, 16)
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
898.90 = 50 1 - (1 + i)16 + 1000 / (1 + i) 16
i
B d E l
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Bond Example
Mathematical Solution:
PV = PMT (PVIFA k, n) + FV (PVIF k, n)
898.90 = 50 (PVIFA k, 16) + 1000 (PVIF k, 16)
1
PV = PMT 1 - (1 + i)n + FV / (1 + i)n
i
1
898.90 = 50 1 - (1 + i)16 + 1000 / (1 + i) 16
i solve using tr ial and error
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Zero Coupon Bonds
No coupon interest payments.
The bond holders return is
determined entirely by the
price discount.
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Zero Example
Suppose you pay $508for a zero
coupon bond that has 10 years
left to maturity. What is your yield to maturity?
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Zero Example
Suppose you pay $508for a zero
coupon bond that has 10 years
left to maturity. What is your yield to maturity?
0 10
-$508 $1000
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Zero Example
P/YR = 1
Mode = End
N = 10
PV = -508
FV = 1000
Solve: I%YR = 7%
Zero Example
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Mathematical Solution:
PV = FV (PVIF i, n)
508 = 1000 (PVIFi, 10).508 = (PVIFi, 10) [use PVIF table]
PV = FV /(1 + i) 10
508 = 1000 /(1 + i)10
1.9685 = (1 + i)10
i = 7%
Zero Example
0 10
PV = -508 FV = 1000
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The F inancial Pages: Corporate Bonds
Cur NetYld Vol Close Chg
Polaroid 11 1/2 06 19.3 395 59 3/4 ...
What is the yield to maturity for this bond?
P/YR = 2, N = 10, FV = 1000,
PV = $-597.50,PMT = 57.50
Solve: I/YR = 26.48%
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The F inancial Pages: Corporate Bonds
Cur NetYld Vol Close Chg
HewlPkd zr 17 ... 20 51 1/2 +1
What is the yield to maturity for this bond?
P/YR = 1, N = 16, FV = 1000,
PV = $-515,PMT = 0
Solve: I/YR = 4.24%
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The F inancial Pages: Treasury Bonds
Maturity Ask
Rate Mo/Yr Bid Asked Chg Yld
9 Nov 18 139:14 139:20 -34 5.46
What is the yield to maturity for this
Treasury bond? (assume 35 half years)
P/YR = 2, N = 35, FV = 1000,
PMT = 45,
PV = - 1,396.25 (139.625% of par)