CHAPTER 7 Bonds and Their Valuation Key features of bonds Bond valuation Measuring yield Assessing risk

What is a bond? A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.

What is a bond? Long Term debt(Bond certificate sample)

Firm A Bondholders Other Bondholders (RM) Coupon interest (periodically) “IOU” (bond) OTC market Firm A Bondholders Other Bondholders Capital (RM) Par Value (at maturity date) (RM)

Key Features of a Bond Par value – face amount of the bond, which is paid at maturity (assume $1,000). Coupon interest rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par value to get dollar payment of interest. Maturity date – years until the bond must be repaid. Issue date – when the bond was issued. Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”).

The value of financial assets 1 2 n r% CF1 CFn CF2 Value ...

What is the value of a 10-year, 10% annual coupon bond, if rd = 10%? 1 2 n r 100 100 + 1,000 VB = ? ...

Using a financial calculator to value a bond This bond has a $1,000 lump sum (the par value) due at maturity (t = 10), and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows. 10 10 100 1000 INPUTS N I/YR PV PMT FV OUTPUT -1000

The same company also has 10-year bonds outstanding with the same risk but a 13% annual coupon rate This bond has an annual coupon payment of $130. Since the risk is the same the bond has the same yield to maturity as the previous bond (10%). In this case the bond sells at a premium because the coupon rate exceeds the market rate (rd). 10 10 130 1000 INPUTS N I/YR PV PMT FV OUTPUT -1184.34

The same company also has 10-year bonds outstanding with the same risk but a 7% annual coupon rate This bond has an annual coupon payment of $70. Since the risk is the same the bond has the same yield to maturity as the previous bonds (10%). In this case, the bond sells at a discount because the coupon rate is less than the market rate (rd). 10 10 70 1000 INPUTS N I/YR PV PMT FV OUTPUT -815.66

Must find the rd that solves this model. What is the rd ( ie. Yield to maturity-YTM) on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887? (selling at Discount) Must find the rd that solves this model. N =10, PV = -887, Pmt = 90, FV = 1,000, I/yr = ?? 10.91 YTM > Coupon

Find YTM, if the bond price is $1,134.20 Solving for I/YR, the YTM of this bond is 7.08%. This bond sells at a premium, because YTM < coupon rate. 10 -1134.2 90 1000 INPUTS N I/YR PV PMT FV OUTPUT 7.08

What is interest rate (or price) risk What is interest rate (or price) risk? Does a 1-year or 10-year bond have more interest rate risk? Assume coupon payments is 10% and par value $1,000 Interest rate risk is the concern that rising rd will cause the value of a bond to fall. rd 1-year Change 10-year Change 5% $1,048 $1,386 10% 1,000 1,000 15% 956 749 The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk. + 4.8% – 4.4% +38.6% –25.1%

1- year Bond (10% coupon) I/ yr= 5%, FV= 1,000, Pmt= 100, PV= 1,047 I/ yr= 15%, FV= 1,000, Pmt= 100, PV=956

10- year Bond (10% coupon) I/ yr= 5%, FV= 1,000, Pmt= 100, PV= 1,386 I/ yr= 15%, FV= 1,000, Pmt= 100, PV= 749

So, the 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk. The relationship between price of bond and interest rates is inverse

Illustrating interest rate risk

Reinvestment Risk “reinvest cash inflow at going market rates” CF CF CF CF CF 100 100 100 100 100 + 1,000 “reinvest cash inflow at going market rates” Thus, if market rates , may experience income reduction

What is reinvestment rate risk? Reinvestment rate risk is the concern that rd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.

What is the value of a 10-year, 10% semiannual coupon bond, if rd = 13%? Multiply years by 2 : N = 2 * 10 = 20. Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5. Divide annual coupon by 2 : PMT = 100 / 2 = 50. 20 6.5 50 1000 INPUTS N I/YR PV PMT FV OUTPUT - 834.72

Bonds call back Bondholders ie: coupon= 10% Corp A Bank loan at 6% Pay principle + penalty new financing Bank loan at 6%

Callable Bond Valuation i.e: Northern Timber issued a $1,000 25 years bond. The bond has a call provision that allowed it to be retired any time after 5 years, with additional coupon put as penalty. The coupon rate is 18%, interest rate is 8%

Callable Bond Valuation 5 10 15 20 25 valuation n= 5 Principle = 1,000 + 180 (penalty) Pmt = 180 I/ yr = 8%, PV = (?)

Callable bond Valuation 5 1,521 180 1180 INPUTS N I/YR PV PMT FV OUTPUT 8

Callable bond & yield to call (i.e.1) A 10-year, 10% annual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)?

Callable bond & yield to call (i.e.1) 1 2 3 4 5 6 7 8 9 10 Call Back Bond - Principle + Penalty = RM 1,050

Because annual Coupon, 1. n = 4 Coupon pmt = 10% x 1,000 = 100 3. Principle (FV) - RM 1,050 4. Original price (PV) - RM 1,135 5. YTC ?

Callable bond & yield to call (i.e.1) A 10-year, 10% annual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)? 4 - 1135.90 100 1050 INPUTS N I/YR PV PMT FV OUTPUT 7.12

Callable bond & yield to call (i.e.2) A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)? Solving for the YTC is identical to solving for rd, except the time to call is used for N and the call premium is FV.

Callable bond & yield to call (i.e.2) 1 2 3 4 5 6 7 8 9 10 Call Back Bond - Principle + Penalty = RM 1,050

Because Semiannual Coupon, 1. n x 2 = 4 x 2 = 8 2. Coupon pmt x 1,000 2 = 10% / 2 x 1,000 = 50 3. Principle (FV) - RM 1,050 4. Original price (PV) - RM 1,135 5. YTC ?

Callable bond & yield to call (i.e.2) A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)? 8 - 1135.90 50 1050 INPUTS N I/YR PV PMT FV OUTPUT 3.568

Default risk If an issuer defaults, investors receive less than the promised return. The default risk is influenced by the issuer’s financial strength and the terms of the bond contract.

Evaluating default risk: Bond ratings Investment Grade Junk Bonds Moody’s Aaa Aa A Baa Ba B Caa C S & P AAA AA A BBB BB B CCC D Bond ratings are designed to reflect the probability of a bond issue going into default.

Factors affecting default risk and bond ratings Debt ratio, TIE ratio, Current ratio Bond contract provisions Secured vs. Unsecured debt Guarantee and sinking fund provisions Earnings stability

Other types (features) of bonds Convertible bond – may be exchanged for common stock of the firm, at the holder’s option. Putable bond – allows holder to sell the bond back to the company prior to maturity. Income bond – pays interest only when income is earned by the firm. Indexed bond – interest rate paid is based upon the rate of inflation.