Valuation and Characteristics of Bonds Chapter 7 Valuation and Characteristics of Bonds

Chapter 7 Topic Overview Bond Characteristics Annual and Semi-Annual Bond Valuation Finding Returns on Bonds Reading Bond Quotes Bond Risk and Other Important Bond Valuation Relationships 2

Bond Characteristics Par Value = stated face value that is the amount the issuer must repay. Coupon Interest Rate Coupon = Coupon Rate x Par Value Maturity Date = when the par value is repaid. This makes a bond’s cash flows look like this: 3

Characteristics of Bonds Bonds pay fixed coupon (interest) payments at fixed intervals (usually every 6 months) and pay the par value at maturity. 0 1 2 . . . n $I $I $I $I $I $I+$M

Types of Bonds Debentures: unsecured debt = bonds. Subordinated Debentures Mortgage Bonds Zero Coupon Bonds: no coupon payments, just par value. Convertible Bonds: can be converted into shares of stock. 4

Types of Bonds(cont.) Indexed Bonds: coupon payments and/or par value indexed to inflation. TIPs: Indexed US Treasury coupon bond, fixed coupon rate, par value indexed. I-Bonds: Indexed US Treasury zero coupon bond. Junk bonds: speculative or below-investment grade bonds; rated BB and below. High-yield bonds. 4

Types of Bonds(cont.) 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.

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. Can the intrinsic value of an asset differ from its market value?

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

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

Bond Valuation Example #1 Duff’s Beer has $1,000 par value bonds outstanding that make annual coupon payments. These bonds have an 8% annual coupon rate and 12 years left to maturity. Bonds with similar risk have a required return of 10%, and Moe Szyslak thinks this required return is reasonable. What’s the most that Moe is willing to pay for a Duff’s Beer bond? 6

P/Y = 1 12 = N 10 = I/Y 1,000 = FV 80 = PMT CPT PV = -$863.73 0 1 2 3 . . . 12 1000 80 80 80 . . . 80 P/Y = 1 12 = N 10 = I/Y 1,000 = FV 80 = PMT CPT PV = -$863.73 Note: If the coupon rate < discount rate, the bond will sell for less than the par value: a discount.

Let’s Play with Example #1 Homer Simpson is interested in buying a Duff Beer bond but demands an 8 percent required return. What is the most Homer would pay for this bond? 7

P/Y = 1 12 = N 8 = I/Y 1,000 = FV 80 = PMT CPT PV = -$1,000 0 1 2 3 . . . 12 1000 80 80 80 . . . 80 P/Y = 1 12 = N 8 = I/Y 1,000 = FV 80 = PMT CPT PV = -$1,000 Note: If the coupon rate = discount rate, the bond will sell for its par value.

Let’s Play with Example #1 some more. Barney (belch!) Barstool is interested in buying a Duff Beer bond and demands on a 6 percent required return. What is the most Barney (belch!) would pay for this bond? 7

P/Y = 1 12 = N 6 = I/Y 1,000 = FV 80 = PMT CPT PV = -$1,167.68 0 1 2 3 . . . 12 1000 80 80 80 . . . 80 P/Y = 1 12 = N 6 = I/Y 1,000 = FV 80 = PMT CPT PV = -$1,167.68 Note: If the coupon rate > discount rate, the bond will sell for more than the par value: a premium.

Bonds with Semiannual Coupons Double the number of years, and divide required return and annual coupon by 2. VB = I/2(PVIFAkb/2,2N) + M(PVIFkb/2,2N) 15

Semiannual Example A $1000 par value bond with an annual coupon rate of 9% pays coupons semiannually with 15 years left to maturity. What is the most you would be willing to pay for this bond if your required return is 8% APR? Semiannual coupon = 9%/2($1000) = $45 15x2 = 30 remaining coupons 16

P/Y = 1 15x2 =30 = N 8/2 = 4 = I/Y 1,000 = FV 90/2 = 45 = PMT 0 1 2 3 . . . 30 1000 45 45 45 . . . 45 P/Y = 1 15x2 =30 = N 8/2 = 4 = I/Y 1,000 = FV 90/2 = 45 = PMT CPT PV = -$1,086.46

Finding a bond’s rate of return? Expected Return In the marketplace, we know a bond’s current price(PV), but not its return. Yield to Maturity (YTM) = the rate of return the bond would earn if purchased at today’s price and held until maturity. Annual Actual Return Current Yield + Capital Gains Yield I/P0 + (P1 – P0)/P0 = (P1 – P0 + I)/P0 12

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

Yield to Maturity Example $1000 face value bond with a 10% coupon rate paid annually with 20 years left to maturity sells for $1091.29. What is this bond’s yield to maturity? 13

P/Y = 1 -1091.29 = PV 20 = N 1,000 = FV 100 = PMT CPT I/Y = 9% = YTM 0 1 2 3 . . . 20 1000 -1091.29 100 100 100 . . . 100 P/Y = 1 -1091.29 = PV 20 = N 1,000 = FV 100 = PMT CPT I/Y = 9% = YTM

Let’s try this together. Imagine a year later, the YTM for the bond on the previous slide fell to 8%. What is the bond’s expected price? What is the holding period return, if we sell the bond at this time assuming we bought the bond a year earlier? PMT =100, FV = 1000

Reading Corporate Bond Quotes Cur Net Bonds Yld Vol. Close Chg. IBM 6 ½ 28 6.6 14 98 1/4 -2 1/8 Most info is expressed as % of par value. Par value = 100. For IBM, 6.5% annual coupon rate, matures in year 2028, Price is 98.25% of par value. 21

YTM Estimate for IBM Bond Assuming $1000 Par (or Face) Value and semi-annual coupons Price = 98.25% (1000) = 982.50, INT/2=1000(6.5%)/2= 32.50, FV = 1000 Assuming N = 26 (2028-2002): YTM? 982.50 =32.50(PVIFAYTM/2,2N)+1000(PVIFYTM/2,2N) Calculator Solution: -982.50 = PV,1000 = FV, 32.50 = PMT, 2N = 2(26) = 52 = N, CPT I/Y I/Y=YTM/2=3.32% YTM(APR) = 2(3.32%)= 6.64% 22

The Financial Pages: Treasury Bonds Maturity Ask Rate Mo/Yr Bid Asked Chg Yld 6 Feb 26 104:25 104:26 -15 5.63 What is the yield to maturity for this Treasury bond? (assume (2026-2002) 24x2 = 48 half years) P/Y = 1, N = 48, FV = 1000, PMT = 1000(6%/2) = 30, PV = - 1,048.125 (104.8125% of par) Solve: I/Y = ytm/2 = 2.816%, YTM = 5.63%

Bond Valuation: What have we learned? 5 Important Relationships Our Example 1: Duff’s Beer bonds 12-year bond kb=6%, V = $1,167.68 kb=8%, V = $1,000 kb=10%, V = $863.73 These values illustrate the First & Second Important Relationships

First Relationship: Bond Prices and Interest Rates have an inverse relationship!

Second Important Relationship From example 1: The coupon rate was 8% kb=6%, V = $1,167.68 kb=8%, V = $1,000 kb=10%, V = $863.73 When required rate = coupon rate Bond Value = Par Value (M) When required rate > coupon rate Bond Value < Par Value (M) When required rate < coupon rate Bond Value > Par Value (M) 8

Bond Value Changes Over Time Returning to the original example #1, where k = 10%, N = 12, INT(PMT) = $80, M(FV) = $1000, & V = $863.73. What is bond value one year later when N = 11 and k is still = 10%? VB = $80(PVIFA10%,11) + $1000(PVIF10%,11) = $870.10 9

What is the bond’s return over this year. (Proof of YTM = Expected Ret Total Rate of Return = Current Yield + Capital Gains Yield (C.G.Y) Beg. V = 863.73, End V = 870.10 Current Yield = Annual Coupon (INT) divided by Beginning Bond Value Current Yld = $80/863.73 = 9.26% C.G.Y.=(870.10-863.73)/863.73= 0.74% Total Return = 9.26% + 0.74% = 10% 10

Third Relationship: Market Value approaches par value as maturity date approaches. 11

Fourth Relationship: Interest Rate Risk Measures Bond Price Sensitivity to changes in interest rates. Long-term bonds have more interest rate risk than short-term bonds.

Interest Rate Risk Example Recall from our earlier example (#1), the 12-year, 8% annual coupon bond has the following values at kd = 6%, 8%, & 10%. Let’s compare with a 2-yr, 8% annual coupon bond. 12-year bond 2-year bond kb=6%, V = $1,167.68 V = $1,036.67 kb=8%, V = $1,000 V = $1,000 kb=10%, V = $863.73 V = $965.29

Bond Price Sensitivity Graph

Other Bond Risks Reinvestment Rate Risk = opposite of interest rate risk, greater for short-term bonds, risk that income from bonds will fall. Default Risk = measured by bond ratings = ability of issuer to fulfill debt obligations Aaa, AAA, best rating, lowest default risk 20

Fifth Relationship In addition to length of time to maturity, the pattern ( and size) of cash flows affects a bond’s price sensitivity to changes in interest rates. Duration measures and illustrates this relationship.

Duration Weighted average time to maturity. Higher (longer) duration means greater bond price sensitivity to changes in interest rates.

Duration Formula t = year the cash flow is to be received, n = the number of years to maturity, Ct = the cash flow to be received at year t, kb = the bondholder’s required return, P0 = the bond’s present value (or today’s price).

Duration Example Krusty Burger and Burns Power bonds both have 3 years to maturity, $1,000 par value, and a required return of 8 percent. However, Krusty Burger makes annual coupon payments of 8%, while Burns Power is a zero coupon bond. What is the duration of each bond?

Suggested Duration Calculation Steps First, calculate today’s value of the bond. Second, find the PV today of each time weighted bond CF (CF x time period the CF occurs). Third, add up all the time weighted PVs Note: The CF and NPV calculator functions can be used to do steps 2 and 3. Fourth, divide sum of time weighted PVs by today’s bond value = duration.

Krusty Burger Duration Since Krusty’s required return and coupon rate are equal, today’s value = $1,000. 80 = PMT, 1000 = FV, 8 = I/Y, 3 = N, CPT PV = $1000 t C t x C PV(tC) 80 80 C01 74 80 160 C02 137 1080 3240 C03 2572 NPV: I = 8, CPT NPV = 2783 Krusty Burger Duration = 2783/1000 = 2.783

Burns Power Duration Today’s Burns Power Bond Value: 0 = PMT, 1000 = FV, 8 = I/Y, 3 = N, CPT PV = $793.83 t C t x C PV(tC) 0 0 C01 0 0 0 C02 0 1000 3000 C03 2381.50 NPV: I = 8, CPT NPV = 2381.50 Burns Power Duration = 2381.50/793.83 = 3.00 NOTE: Duration for zero coupon bond = time to maturity.

Duration Example Conclusion Krusty Burger Duration = 2.783 Burns Power Duration = 3.000 Burns Power bonds are more sensitive to changes in interest rates. This is good if interest rates go down, but bad if interest rates go up! From this example, you can see for bonds with the same time to maturity, lower coupon rate bonds have more interest rate risk.