ch07 - Chapter 7 Valuation and Characteristics of Bonds...

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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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This note was uploaded on 07/11/2011 for the course FINANCE fin 3701 taught by Professor Tengihla during the Spring '11 term at Assumption College.

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