Unformatted text preview: Chapter 7
Valuation and Characteristics of Bonds Characteristics of Bonds
• Bonds pay fixed coupon (interest)
payments at fixed intervals (usually
every six months) and pay the par
value at maturity.
$I
0 $I
1 $I $I $I $I+$M 2 ... n Example: AT&T 6 ½ 32
Example: ►
► ►
► Par value = $1,000
Coupon = 6.5% or par value per year,
or $65 per year ($32.50 every six months).
Maturity = 28 years (matures in 2032).
Issued by AT&T. $32.50 0 $32.50 $32.50 $32.50 $32.50 1 2 … $32.50+$1000 28 Types of Bonds
Types of Bonds
►
►
►
►
► Debentures unsecured bonds.
Subordinated debentures unsecured “junior” debt.
Mortgage bonds secured bonds.
Zeros bonds that pay only par value at maturity; no coupons.
Junk bonds speculative or belowinvestment grade bonds; rated BB and below. Highyield bonds. Types of Bonds
Types of Bonds
► ► Eurobonds bonds denominated in one currency and sold in another country. (Borrowing overseas).
example suppose Chang Beer decides to sell B1,000 bonds in England. These are Baht denominated bonds trading in a foreign country. Why do this? If borrowing rates are lower in England. To avoid SEC regulations in his/her country. The Bond Indenture
The Bond Indenture
The bond contract between the firm and the trustee representing the bondholders.
► Lists all of the bond’s features: coupon, par value, maturity, etc.
► Lists restrictive provisions which are designed to protect bondholders.
► Describes repayment provisions.
► Value
Value
►
►
►
► Book value: value of an asset as shown on a firm’s 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 asset’s expected future cash flows. Security Valuation
Security Valuation
► In general, the intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return. ► Can the intrinsic value of an asset differ from its market value? Bond Valuation
Bond Valuation
n Vb = Σ t=1 $ It
(1 + kb)t + $M
(1 + kb)n Vb = $It (PVIFA kb, n) + $M (PVIF kb, n)
►
►
► Ct = cash flow to be received at time t.
k = the investor’s required rate of return.
V = the intrinsic value of the asset. Bond Valuation
Bond Valuation
► Discount the bond’s cash flows at the investor’s required rate of return. The coupon payment stream (an annuity). The par value payment (a single sum). Bond Example
Bond Example
► Suppose our firm decides to issue 20year bonds with a par value of $1,000 and annual coupon payments. The return on other corporate bonds of similar risk is currently 12%, so we decide to offer a 12% coupon interest rate. ► What would be a fair price for these bonds? 120
0 120 120 ... 1000
120 1 2 3 ... 20 P/YR = 1
N = 20
I%YR = 12
FV = 1,000
PMT = 120
Solve PV = $1,000
Note: If the coupon rate = discount rate, the bond Note
will sell for par value. Bond Example
Bond Example
Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA .12, 20 ) + 1000 (PVIF .12, 20 ) 1 PV = PMT 1 (1 + i)n + FV / (1 + i)n i 1
PV = 120 1 (1.12 )20 + 1000/ (1.12) 20 = $1000 .10 ► Suppose interest rates fall immediately after we issue the bonds. The required return on bonds of similar risk drops to 10%. ► What would happen to the bond’s intrinsic value? Bond Example
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 = $1170.27 .10 ► 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 bond’s intrinsic value? Bond Example
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 Suppose coupons are semi
Suppose coupons are semi
annual
P/YR = 2
Mode = end
N = 40
I%YR = 14
PMT = 60
FV = 1000
Solve PV = $866.68 Bond Example
Bond Example
Mathematical Solution: PV = PMT (PVIFA k, n ) + FV (PVIF k, n ) PV = 120 (PVIFA .07, 40 ) + 1000 (PVIF .07, 40 ) 1 PV = PMT 1 (1 + i)n + FV / (1 + i)n i 1
PV = 120 1 (1.07 )40 + 1000/ (1.07) 40 = $866.68 .07 Yield To Maturity
Yield To Maturity
► The expected rate of return on a bond. ► The rate of return investors earn on a bond if they hold it to maturity. n P0 = Σ t=1 $ It
(1 + kb)t + $M
(1 + kb)n YTM Example
YTM Example
► Suppose we paid $898.90 for a $1,000 par 10% coupon bond with 8 years to maturity and semiannual coupon payments. ► What is our yield to maturity? YTM Example
P/YR = 2
P/YR = 2
Mode = end
N = 16
PV = 898.90
PMT = 50
FV = 1000
Solve I%YR = 12% Bond Example
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 trial and error Zero Coupon Bonds
Zero Coupon Bonds
►
►
► No coupon interest payments.
The bond holder’s return is determined entirely by the price discount.
Always, sell at a discount. (Price<PAR) Zero Example
Zero Example
► Suppose you pay $508 for a zero coupon bond that has 10 years left to maturity. ► What is your yield to maturity? $508
0 $1000
10 Zero Example
Zero Example
P/YR = 1
Mode = End
N = 10
PV = 508
FV = 1000
Solve: I%YR = 7% PV = 508
0 Zero Example
FV = 1000 Mathematical Solution:
Mathematical Solution:
PV = FV (PVIF i, n ) 508 = 1000 (PVIF i, 10 ) .508 = (PVIF i, 10 ) [use PVIF table] PV = FV /(1 + i) 10 508 = 1000 /(1 + i)10 1.9685 = (1 + i)10 i = 7% 10 ...
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 Spring '11
 tengihla
 Corporate Finance, Interest, Valuation, Payment, Bond Example

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