Download - Ch. 7: Valuation and Characteristics of
![Page 1: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/1.jpg)
Ch. 7:Valuation
and Characteristics
of
MF 2000
![Page 2: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/2.jpg)
Characteristics of BondsCharacteristics of Bonds
Bonds pay fixed Bonds pay fixed couponcoupon (interest) (interest) payments at fixed intervals (usually payments at fixed intervals (usually every 6 months) and pay the every 6 months) and pay the par par valuevalue at at maturitymaturity..
![Page 3: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/3.jpg)
Characteristics of BondsCharacteristics of Bonds
Bonds pay fixed Bonds pay fixed couponcoupon (interest) (interest) payments at fixed intervals (usually payments at fixed intervals (usually every 6 months) and pay the every 6 months) and pay the par par valuevalue at at maturitymaturity..
00 1 1 2 . . .2 . . . nn
$I $I $I $I $I $I+$M$I $I $I $I $I $I+$M
![Page 4: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/4.jpg)
example: AT&T 8 24
par valuepar value = = $1000$1000 couponcoupon = 8% of par value per year.= 8% of par value per year.
= = $80$80 per year ( per year ($40$40 every 6 months). every 6 months). maturitymaturity = 24 years (matures in = 24 years (matures in 20242024).). issued by AT&T.issued by AT&T.
![Page 5: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/5.jpg)
example: AT&T 8 24
par valuepar value = = $1000$1000 couponcoupon = 8% of par value per year.= 8% of par value per year.
= = $80$80 per year ( per year ($40$40 every 6 months). every 6 months). maturitymaturity = 24 years (matures in = 24 years (matures in 20242024).). issued by AT&T.issued by AT&T.
00 1 1 22 …… 48 48
$40 $40 $40 $40 $40 $40+$1000$40 $40 $40 $40 $40 $40+$1000
![Page 6: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/6.jpg)
Types 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.
![Page 7: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/7.jpg)
Types of 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?
![Page 8: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/8.jpg)
Types of 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?
If borrowing rates are lower in France,If borrowing rates are lower in France,
![Page 9: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/9.jpg)
Types of 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?
If borrowing rates are lower in France,If borrowing rates are lower in France, To avoid SEC regulations.To avoid SEC regulations.
![Page 10: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/10.jpg)
The 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.
![Page 11: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/11.jpg)
Value
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.
![Page 12: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/12.jpg)
Security 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??
![Page 13: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/13.jpg)
Valuation
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
nn
$Ct
(1 + k)t
![Page 14: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/14.jpg)
Bond 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.
![Page 15: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/15.jpg)
Bond 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. the the coupon payment streamcoupon payment stream (an (an
annuity).annuity).
![Page 16: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/16.jpg)
Bond 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. the the coupon payment streamcoupon payment stream (an (an
annuity).annuity). the the par value paymentpar value payment (a single (a single
sum).sum).
![Page 17: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/17.jpg)
Bond Valuation
Vb = $It (PVIFA kb, n) + $M (PVIF kb, n)
$It $M
(1 + kb)t (1 + kb)nVVbb = + = +
nn
t = 1t = 1
![Page 18: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/18.jpg)
Bond 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?
![Page 19: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/19.jpg)
00 1 1 2 2 3 3 . . . . . . 2020
10001000 120120 120 120 120 . . . 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..
![Page 20: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/20.jpg)
Bond Example
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 ))
![Page 21: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/21.jpg)
Bond Example
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 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
![Page 22: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/22.jpg)
Bond Example
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 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
11
PV = 120 1 - (1.12 )PV = 120 1 - (1.12 )2020 + + 1000/ (1.12) 1000/ (1.12) 2020 = = $1000$1000
.12.12
![Page 23: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/23.jpg)
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?
![Page 24: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/24.jpg)
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
![Page 25: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/25.jpg)
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
NoteNote:: If the If the coupon ratecoupon rate > > discount ratediscount rate,, the bond will sell for the bond will sell for a a premiumpremium..
![Page 26: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/26.jpg)
Bond Example
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 .10, 20.10, 20 ) + 1000 (PVIF ) + 1000 (PVIF .10, 20.10, 20 ))
![Page 27: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/27.jpg)
Bond Example
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 .10, 20.10, 20 ) + 1000 (PVIF ) + 1000 (PVIF .10, 20.10, 20 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
![Page 28: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/28.jpg)
Bond Example
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 .10, 20.10, 20 ) + 1000 (PVIF ) + 1000 (PVIF .10, 20.10, 20 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
11
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
![Page 29: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/29.jpg)
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?
![Page 30: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/30.jpg)
P/YR = P/YR = 11
Mode = Mode = endend
N = N = 2020
I%YR = I%YR = 1414
PMT = PMT = 120120
FV = FV = 10001000
Solve PV = Solve PV = -$867.54-$867.54
![Page 31: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/31.jpg)
P/YR = P/YR = 11
Mode = Mode = endend
N = N = 2020
I%YR = I%YR = 1414
PMT = PMT = 120120
FV = FV = 10001000
Solve PV = -Solve PV = -$867.54$867.54
NoteNote:: If the If the coupon ratecoupon rate < < discount ratediscount rate, , the bond will sell for a the bond will sell for a discountdiscount..
![Page 32: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/32.jpg)
Bond ExampleBond Example
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 .14, 20.14, 20 ) + 1000 (PVIF ) + 1000 (PVIF .14, 20.14, 20 ))
![Page 33: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/33.jpg)
Bond ExampleBond Example
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 .14, 20.14, 20 ) + 1000 (PVIF ) + 1000 (PVIF .14, 20.14, 20 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
![Page 34: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/34.jpg)
Bond ExampleBond Example
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 .14, 20.14, 20 ) + 1000 (PVIF ) + 1000 (PVIF .14, 20.14, 20 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
11
PV = 120 1 - (1.14 )PV = 120 1 - (1.14 )2020 + 1000/ (1.14) + 1000/ (1.14) 2020 = = $867.54$867.54
.14.14
![Page 35: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/35.jpg)
Suppose coupons are semi-annual
P/YR = P/YR = 22
Mode = Mode = endend
N = N = 4040
I%YR = I%YR = 1414
PMT = PMT = 6060
FV = FV = 10001000
Solve PV = -Solve PV = -$866.68$866.68
![Page 36: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/36.jpg)
Bond Example
Mathematical Solution:Mathematical Solution:
PV = PMT (PVIFA PV = PMT (PVIFA k, nk, n ) + FV (PVIF ) + FV (PVIF k, nk, n ) )
PV = 60 (PVIFA PV = 60 (PVIFA .14, 20.14, 20 ) + 1000 (PVIF ) + 1000 (PVIF .14, 20.14, 20 ))
![Page 37: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/37.jpg)
Bond Example
Mathematical Solution:Mathematical Solution:
PV = PMT (PVIFA PV = PMT (PVIFA k, nk, n ) + FV (PVIF ) + FV (PVIF k, nk, n ) )
PV = 60 (PVIFA PV = 60 (PVIFA .14, 20.14, 20 ) + 1000 (PVIF ) + 1000 (PVIF .14, 20.14, 20 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
![Page 38: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/38.jpg)
Bond Example
Mathematical Solution:Mathematical Solution:
PV = PMT (PVIFA PV = PMT (PVIFA k, nk, n ) + FV (PVIF ) + FV (PVIF k, nk, n ) )
PV = 60 (PVIFA PV = 60 (PVIFA .14, 20.14, 20 ) + 1000 (PVIF ) + 1000 (PVIF .14, 20.14, 20 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
11
PV = 60 1 - (1.07 )PV = 60 1 - (1.07 )4040 + 1000 / (1.07) + 1000 / (1.07) 4040 = = $866.68$866.68
.07.07
![Page 39: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/39.jpg)
Yield 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.
![Page 40: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/40.jpg)
Yield 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 = + = +
nn
t = 1t = 1
![Page 41: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/41.jpg)
YTM 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??
![Page 42: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/42.jpg)
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
![Page 43: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/43.jpg)
Bond Example
Mathematical Solution:Mathematical Solution:
PV = PMT (PVIFA PV = PMT (PVIFA k, nk, n ) + FV (PVIF ) + FV (PVIF k, nk, n ) )
898.90 = 50 (PVIFA 898.90 = 50 (PVIFA k, 16k, 16 ) + 1000 (PVIF ) + 1000 (PVIF k, 16k, 16 ))
![Page 44: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/44.jpg)
Bond Example
Mathematical Solution:Mathematical Solution:
PV = PMT (PVIFA PV = PMT (PVIFA k, nk, n ) + FV (PVIF ) + FV (PVIF k, nk, n ) )
898.90 = 50 (PVIFA 898.90 = 50 (PVIFA k, 16k, 16 ) + 1000 (PVIF ) + 1000 (PVIF k, 16k, 16 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
![Page 45: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/45.jpg)
Bond Example
Mathematical Solution:Mathematical Solution:
PV = PMT (PVIFA PV = PMT (PVIFA k, nk, n ) + FV (PVIF ) + FV (PVIF k, nk, n ) )
898.90 = 50 (PVIFA 898.90 = 50 (PVIFA k, 16k, 16 ) + 1000 (PVIF ) + 1000 (PVIF k, 16k, 16 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
11
898.90 = 50 1 - (1 + 898.90 = 50 1 - (1 + ii ) )1616 + + 1000 / (1 + 1000 / (1 + ii) ) 1616
ii
![Page 46: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/46.jpg)
Bond Example
Mathematical Solution:Mathematical Solution:
PV = PMT (PVIFA PV = PMT (PVIFA k, nk, n ) + FV (PVIF ) + FV (PVIF k, nk, n ) )
898.90 = 50 (PVIFA 898.90 = 50 (PVIFA k, 16k, 16 ) + 1000 (PVIF ) + 1000 (PVIF k, 16k, 16 ))
11
PV = PMT 1 - (1 + i)PV = PMT 1 - (1 + i)nn + FV / (1 + i) + FV / (1 + i)nn
ii
11
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
![Page 47: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/47.jpg)
Zero 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..
![Page 48: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/48.jpg)
Zero 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??
![Page 49: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/49.jpg)
Zero 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??
0 100 10
-$508 $1000-$508 $1000
![Page 50: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/50.jpg)
Zero Example
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%
![Page 51: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/51.jpg)
Mathematical Solution:Mathematical Solution:
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%
Zero Example
00 10 10
PV = -508PV = -508 FV = 1000 FV = 1000
![Page 52: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/52.jpg)
The Financial Pages: Corporate Bonds
CurCur Net Net
Yld Vol Close ChgYld Vol Close Chg
Polaroid 11 Polaroid 11 11//22 06 11.2 52 10306 11.2 52 103 ... ...
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 = 1212, FV = , FV = 10001000, ,
PV = PV = $-1,030$-1,030, ,
PMT = 57.50PMT = 57.50
Solve: I/YR = 10.81%Solve: I/YR = 10.81%
![Page 53: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/53.jpg)
The Financial Pages: Corporate Bonds
CurCur Net Net
Yld Vol Close ChgYld Vol Close Chg
Honywll zr 09 ... 10 46 Honywll zr 09 ... 10 46 55//88 -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 = 9, FV = , N = 9, FV = 10001000, ,
PV = PV = $-466.25$-466.25, ,
PMT = PMT = 00 Solve: I/YR = 8.85%Solve: I/YR = 8.85%
![Page 54: Ch. 7: Valuation and Characteristics of](https://reader030.vdocuments.us/reader030/viewer/2022020320/56813fed550346895daaeed5/html5/thumbnails/54.jpg)
The Financial Pages: Treasury Bonds
Maturity Maturity AskAsk
Rate Mo/Yr Rate Mo/Yr Bid Asked Bid Asked Chg Chg YldYld
99 Nov 18 Nov 18 127:16 127:22 +11127:16 127:22 +11 6.39 6.39
What is the yield to maturity for this What is the yield to maturity for this
Treasury bond?Treasury bond?
P/YR = P/YR = 22, N = 36, FV = , N = 36, FV = 10001000, ,
PMT = PMT = 4545,,
PV = PV = - 1,276.875- 1,276.875 (127.6875% of par) (127.6875% of par) Solve: I/YR = 6.39%Solve: I/YR = 6.39%