 # FIN303 Vicentiu Covrig 1 Bonds and their valuation (chapter 7)

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FIN303 Vicentiu Covrig 1 Bonds and their valuation (chapter 7)

FIN303 Vicentiu Covrig 2 Bond markets 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 Primarily traded in the over-the-counter (OTC) market. Most bonds are owned by and traded among large financial institutions. Full information on bond trades in the OTC market is not published, but a representative group of bonds is listed and traded on the bond division of the NYSE.

FIN303 Vicentiu Covrig 3 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 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”) Some bonds are callable Call provision: Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor)

FIN303 Vicentiu Covrig 4 What is the value of a 10-year, 10% annual coupon bond, if r d (discount rate)= 10%? 012n kdkd 100 100 + 1,000 100V B = ?...

FIN303 Vicentiu Covrig 5 What is the opportunity cost of debt capital? The discount rate (r d ) is the opportunity cost of capital, and is the rate that could be earned on alternative investments of equal risk. r d = r* + IP + MRP + DRP + LP

FIN303 Vicentiu Covrig 6 We have a bond with a coupon rate of 10%, paid annually, that matures in 10 years, with a face/par value of \$1,000, and r d is 13%. Calculate the bond’s value. When r d is above the coupon rate, the bond’s value falls below par, and sells at a discount. INPUTS OUTPUT NI/YRPMTPVFV 10131001000 -837.21 Using a financial calculator to value a bond

FIN303 Vicentiu Covrig 7 What is the value of a 10-year, 10% semiannual coupon bond, if r d = 13%? 1. Multiply years by 2 : N = 2 * 10 = 20. 2. Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5. 3. Divide annual coupon by 2 : PMT = 100 / 2 = 50. INPUTS OUTPUT NI/YRPMTPVFV 206.5501000 - 834.72

FIN303 Vicentiu Covrig 8 Exam type question You intend to purchase a 10-year, \$1,000 face value bond that pays interest of \$60 every 6 months. If your nominal annual required rate of return is 10 percent with semiannual compounding, how much should you be willing to pay for this bond? a.\$ 826.31 b.\$1,086.15 c.\$ 957.50 d.\$1,124.62 * Financial calculator solution: Inputs: N = 20; I = 5; PMT = 60; FV = 1000. Output: PV = -\$1,124.62; VB = \$1,124.62.

FIN303 Vicentiu Covrig 9 What is the YTM on a 10-year, 9% annual coupon, \$1,000 par value bond, selling for \$887? Must find the r d that solves this model.

FIN303 Vicentiu Covrig 10 Using a financial calculator to find YTM Solving for I/YR, the YTM of this bond is 10.91%. This bond sells at a discount, because YTM > coupon rate. INPUTS OUTPUT NI/YRPMTPVFV 10 10.91 901000- 887

FIN303 Vicentiu Covrig 11 Definitions

FIN303 Vicentiu Covrig 12 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)? The bond’s yield to maturity can be determined to be 8%. Solving for the YTC is identical to solving for YTM, except the time to call is used for N and the call premium is FV. INPUTS OUTPUT NI/YRPMTPVFV 8 3.568 501050 - 1135.90

FIN303 Vicentiu Covrig 13 Exam type question Consider a \$1,000 par value bond with a 7 percent annual coupon. The bond pays interest annually. There are 9 years remaining until maturity. What is the current yield on the bond assuming that the required return on the bond is 10 percent? a.10.00% b. 8.46% * c. 7.00% d. 8.52% Current yield = Annual coupon payment/Current price. Step 1:Find the price of the bond: N = 9; I/YR = 10; PMT = 70; FV = 1000; and then solve for PV = -\$827.23. VB = \$827.23. Step 2:Calculate the current yield: CY = \$70/\$827.23 = 8.46%.

FIN303 Vicentiu Covrig 14 When is a call more likely to occur? In general, if a bond sells at a premium, then (1) coupon > r d, so (2) a call is more likely. So, expect to earn: - YTC on premium bonds. - YTM on par & discount bonds.

FIN303 Vicentiu Covrig 15 Bond values over time At maturity, the value of any bond must equal its par value. If k d remains constant: - The value of a premium bond would decrease over time, until it reached \$1,000. - The value of a discount bond would increase over time, until it reached \$1,000. - A value of a par bond stays at \$1,000.

FIN303 Vicentiu Covrig 16 What is interest rate (or price) risk? Interest rate risk is the concern that rising k d will cause the value of a bond to fall. % change 1 yr r d 10yr % change +4.8%\$1,048 5% \$1,386 +38.6% \$1,00010% \$1,000 -4.4% \$95615% \$749 -25.1% The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.

FIN303 Vicentiu Covrig 17 What is reinvestment rate risk? Reinvestment rate risk is the concern that k d will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won \$1,000,000 playing the lottery. You intend to invest the money and live off the interest. If you choose to invest in series of 1-year bonds, that pay a 8% coupon you receive \$80,000 in income and have \$1,000,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to \$30,000. If you choose a 30-year bond that pay a 10 % coupon you receive \$100,000 in income ; you can lock in a 10% interest rate, and \$100,000 annual income for 30 years

FIN303 Vicentiu Covrig 18 Conclusions about interest rate and reinvestment rate risk CONCLUSION: Nothing is riskless! Short-term AND/OR High coupon bonds Long-term AND/OR Low coupon bonds Interest rate risk LowHigh Reinvestment rate risk HighLow

FIN303 Vicentiu Covrig 19 Evaluating default risk: Bond ratings Bond ratings are designed to reflect the probability of a bond issue going into default Mortgage bonds: a bond backed by fixed assets Debentures: unsecured bond Investment-grade bonds Junk bonds Investment GradeJunk Bonds Moody’s Aaa Aa A BaaBa B Caa C S & P AAA AA A BBBBB B CCC D

FIN303 Vicentiu Covrig 20 Factors affecting default risk and bond ratings Financial performance - Debt ratio - TIE ratio - Current ratio Bond contract provisions - Secured vs. Unsecured debt - Senior vs. subordinated debt - Debt maturity

FIN303 Vicentiu Covrig 21 Other factors affecting default risk Earnings stability Regulatory environment Potential antitrust or product liabilities Pension liabilities Potential labor problems Accounting policies

FIN303 Vicentiu Covrig 22 Exam type question Which of the following Treasury bonds will have the largest amount of interest rate risk (price risk)? a.A 7 percent coupon bond that matures in 12 years. * b.A 9 percent coupon bond that matures in 10 years. c.A 12 percent coupon bond that matures in 7 years. d.A 7 percent coupon bond that matures in 9 years. Statement a is correct. The longer the maturity and the lower the coupon of a bond, the more sensitive it is to interest rate (price) risk. The bond in answer a has a maturity greater than or equal to and a coupon less than or equal to all the other bonds.

FIN303 Vicentiu Covrig 23 Exam type question Which of the following statements is most correct? a.Junk bonds typically have a lower yield to maturity relative to investment grade bonds. b.A debenture is a secured bond that is backed by some or all of the firm’s fixed assets. c.Subordinated debt has less default risk than senior debt. d. None of the statements above is correct. * Statement d is correct; the others are false. Junk bonds have a higher yield to maturity relative to investment grade bonds. A debenture is an unsecured bond, while subordinated debt has greater default risk than senior debt.

FIN303 Vicentiu Covrig 24 Learning objectives What is a bond? Discuss the key features of a bond Why are US treasury bonds not riskless? What is the call provision? Why is a call provision advantageous to a bond issuer? Know how to calculate YTM, YTC, value of a bond Discuss the interest rate and reinvestment risks Define mortgage bonds, debentures, investment grade bonds, junk bonds Know how to discuss the factors that affect default risk and bond ratings (see the previous two slides and pages 229-234 in the text) Make sure you know the answers to end-of-chapter ST-1, ST-2 (a-e) Recommended end-of-chapter problems: 7.1 to 7.5;7-7 to 7-10; 7-16,7-18

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