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. 0 1 2 . . . n $I $I $I $I $I $I+$M

Example: AT&T 6 ½ 36 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 2036) Issued by AT&T. 0 1 2 … 28 $32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000

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 below-investment grade bonds; rated BB and below. High-yield bonds.

Types of Bonds Eurobonds - bonds denominated in one 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.

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.

Bond Ratings Moody’s Standard & Poor’s Fitch Investor Services Involve judgment about the future risk potential of the bond AAA, AA, …, BB, …, CC,…, D

Current Yield The ratio of the annual interest payment to the bond’s market price Bond with 8 percent coupon interest rate, a par value of 1,000, and a market price of 700, what is its current yield? Current Yield = (0.08 * 1,000) / 700 = 11.4%

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 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.

S V = Valuation $Ct (1 + k)t n t = 1 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 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).

S Vb = + Bond Valuation $It $M (1 + kb)t (1 + kb)n Vb = $It (PVIFA kb, n) + $M (PVIF kb, n)

Bond Example Suppose our firm decides to issue 20-year 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?

0 1 2 3 . . . 20 1000 120 120 120 . . . 120 N = 20 I%YR = 12 FV = 1,000 PMT = 120 Solve PV = -$1,000 Note: If the coupon rate = discount rate, the bond will sell for par value.

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 PV = 120 1 - (1.12 )20 + 1000/ (1.12) 20 = $1000 .12

Suppose interest rates fall immediately after we issue the bonds 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?

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.

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 PV = 120 1 - (1.10 )20 + 1000/ (1.10) 20 = $1,170.27 .10

Suppose interest rates rise immediately after we issue the bonds 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?

Mode = end N = 20 I%YR = 14 PMT = 120 FV = 1000 Solve PV = -$867.54 Note: If the coupon rate < discount rate, the bond will sell for a discount.

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 PV = 120 1 - (1.14 )20 + 1000/ (1.14) 20 = $867.54 .14

Suppose coupons are semi-annual Mode = end N = 40 I%YR = 14/2=7 PMT = 60 FV = 1000 Solve PV = -$866.68

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 PV = 60 1 - (1.07 )40 + 1000 / (1.07) 40 = $866.68 .07

S P0 = + Yield To Maturity $It $M (1 + kb)t (1 + kb)n The expected rate of return on a bond. The rate of return investors earn on a bond if they hold it to maturity. $It $M (1 + kb)t (1 + kb)n P0 = + n t = 1 S

YTM Example Suppose we paid $898.90 for a $1,000 par 10% coupon bond with 8 years to maturity and semi-annual coupon payments. What is our yield to maturity?

YTM Example Mode = end N = 16 PV = -898.90 PMT = 50 FV = 1000 Solve I%YR = 6% 6%*2 = 12%

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 898.90 = 50 1 - (1 + i )16 + 1000 / (1 + i) 16 i solve using trial and error

Bond Example Mathematical Solution: 10%  5 %  1000 14%  7%  811.06 10%  5 %  1000 14%  7%  811.06 We know i is between 10% and 14%, because 898.9 is between 811.06 and 1000. Then we try 11% and 13%.... Finally we try 12% to get the correct answer.

Zero Coupon Bonds No coupon interest payments. The bond holder’s return is determined entirely by the price discount.

Zero Example Suppose you pay $508 for a zero coupon bond that has 10 years left to maturity. What is your yield to maturity? 0 10 -$508 $1000

Zero Example Mode = End N = 10 PMT = 0 PV = -508 FV = 1000 Solve: I%YR = 7%

Mathematical Solution: Zero Example 0 10 PV = -508 FV = 1000 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%

The Financial Pages: Corporate Bonds Cur Net Yld Vol Close Chg Polaroid 11 1/2 13 19.3 395 59 3/4 ... What is the yield to maturity for this bond? N = 10, FV = 1000, PV = $-597.50, PMT = 57.50 Solve: I/YR = 13.24% *2 = 26.48%

The Financial Pages: Corporate Bonds Cur Net Yld Vol Close Chg HewlPkd zr 24 ... 20 51 1/2 +1 What is the yield to maturity for this bond? N = 16, FV = 1000, PV = $-515, PMT = 0 Solve: I/YR = 4.24%

The Financial Pages: Treasury Bonds Maturity Ask Rate Mo/Yr Bid Asked Close Yld 9 Nov 25 139:14 139:20 139 5/8 5.46 What is the yield to maturity for this Treasury bond? (assume 35 half years) N = 35, FV = 1000, PMT = 45, PV = - 1,396.25 (139.625% of par) Solve: I/YR = 2.728%*2 = 5.457%

Five Relationships Value of bond is inversely related to changes in the investor’s present required rate of return Interest rate increases, bond value decreases

Five Relationships Market value of bond will be less than the par value if investor’s required rate is above the coupon interest rate

Five Relationships As maturity date approaches, the market value of bond approaches its par value

Five Relationships Long-term bonds have greater interest rate risk than do short-term bonds

Five Relationships The sensitivity of bond’s value to changing interest rate depends not only on length of time to maturity, but also on the pattern of cash flows provided by the bond

Five Relationships Duration: weighted average of time to maturity in which the weight attached to each year is the present value of the cash flow for that year

Five Relationships A, B mature in 3 years, present value $1000, par value $1000, market interest is 10% A: coupon $100 per year B: pay whole interest $331 at the end of year 3 The duration of the two bonds?

Five Relationships Duration for A: [(1) * 100 /(1.1) + (2) * 100 /(1.1)^2 + (3) * 1,100 / (1.1)^3] / 1000 = 2.74 Duration for B: [(1) * 0 /(1.1) + (2) * 0/(1.1)^2 + (3) * 1,331 / (1.1)^3] / 1000 = 3

Five Relationships If interest rate falls to 6% from 10% Value of A = $1,106 Value of B = $1,117 B’s cash flows are received in more distant future, and change in interest rate has a greater impact on the present value of later cash flow

Five Relationships Conclusion: -- the longer the duration, the greater the relative percentage change in bond price in response to a given percentage change in the interest rate -- duration is more proper than term to maturity in measuring bond’s sensitivity to interest rate change