# Topics in Chapter. Key features of bonds Bond valuation Measuring yield Assessing risk

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1 Bond Valuation 1

2 Topics in Chapter Key features of bonds Bond valuation Measuring yield Assessing risk 2

3 Determinants of Intrinsic Value: The Cost of Debt Net operating profit after taxes Free cash flow (FCF) = Required investments in operating capital Value = FCF + FCF FCF (1 + WACC) 1 (1 + WACC) 2 (1 + WACC) Weighted average cost of capital (WACC) Market interest rates Market risk aversion Cost of debt Cost of equity Firm s debt/equity mix Firm s business risk 3

4 Key Features of a Bond Bond is a long-term contract where the seller agrees to pay a fixed interest payments and a maturity payment at defined times. Par value: Face amount; paid at maturity. Assume \$1,000. Coupon interest rate: Stated interest rate. Multiply by par value to get dollars of interest. Generally fixed. Can have zero coupon bonds Yield to Maturity (YTM): the rate of return earned on a bond held to maturity. Also called promised yield. It assumes the bond will not default. Maturity: Years until bond must be repaid. Issue date: Date when bond was issued. Default risk: Risk that issuer will not make interest or principal payments. 4

5 Bonds 4 types of bond issuers: Treasury: Issued by federal government Assumed default free Corporate : Issued by corporations Not free from default and default varies by company Municipal: Issued by state and local governments Interest earned is exempt from state and federal taxes Foreign: Issued by foreign governments or companies Not free from default but also can suffer from other risks 5

6 Value of a 10-year, 10% coupon bond if r d = 10% %... V =? ,000 V B = \$100 \$100 \$1, (1 + r d ) 1 (1 + r d ) N (1 + r d ) N = \$ \$ \$ = \$1,000 6

7 Valuing Bonds Example What is the price of a 10-year bond, paying a 10% coupon payment annually if the yield to maturity is 10%? Answer: \$1000 7

8 Call Provision Call provisions allow the company the right to call the bond for redemption Issuer can refund if rates decline. That helps the issuer but hurts the investor. Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds. Most bonds have a deferred call and a declining call premium. 8

9 What s a sinking fund? Sinking Fund facilitates the orderly retirement of the bond issue Provision to pay off a loan over its life rather than all at maturity. Similar to amortization on a term loan. Reduces risk to investor, shortens average maturity. But not good for investors if rates decline after issuance. 9

10 Sinking funds are generally handled in 2 ways Call x% at par per year for sinking fund purposes. Call if r d is below the coupon rate and bond sells at a premium. Buy bonds on open market. Use open market purchase if r d is above coupon rate and bond sells at a discount. 10

11 Other Provisions Convertible bonds: Option to convert bond to a fixed number of shares of common stocks Warrants: Permit the owner to buy stock at a fixed price Income bonds: The company only pays interest if earnings are high enough to cover interest expense Indexed bonds: Interest payments and maturity payment rises when inflation rises 11

12 What would happen if expected inflation rose by 3%, causing r = 13%? INPUTS OUTPUT N I/YR PV PMT FV When r d rises, above the coupon rate, the bond s value falls below par, so it sells at a discount. 12

13 What would happen if inflation fell, and r d declined to 7%? INPUTS OUTPUT N I/YR PV PMT FV -1, If coupon rate > r d, price rises above par, and bond sells at a premium. 13

14 Bond Value over Time Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%? 14

15 Bond Value (\$) vs Years remaining to Maturity 1,372 1,211 r d = 7%. 1,000 r d = 10%. M r d = 13%

16 Maturity At maturity, the value of any bond must equal its par value. The value of a premium bond would decrease to \$1,000. The value of a discount bond would increase to \$1,000. A par bond stays at \$1,000 if r d remains constant. 16

17 YTM on a 10-year, 9% annual coupon, \$1,000 par value bond selling for \$ r d =? ,000 PV 1... PV 10 PV M 887 Find r d that works! 17

18 Find r d INT V B = + (1 + rd ) 1... INT + + (1 + r d ) N M (1 + r d ) N ,000 = (1 + r d ) 1 (1 + r (1 + r d ) N d ) N INPUTS OUTPUT N I/YR PV PMT FV

19 Discount/Premium If coupon rate < r d, bond sells at a discount. If coupon rate = r d, bond sells at its par value. If coupon rate > r d, bond sells at a premium. If r d rises, price falls. Price = par at maturity. 19

20 Example A 10-year bond is currently selling for \$ The coupon rate is 9%. What is the yield to maturity? Is the bond selling at a premium or discount? Answer: 7.082% The bond is selling at a premium because price > 1000 and coupon > YTM 20

21 Definitions Current yield = Annual coupon pmt Current price Capital gains yield = Change in price Beginning price Exp total return Exp = YTM = + Curr yld Exp cap gains yld 21

22 Example A 10 year bond is currently selling for \$887. The coupon rate is 9% and the YTM is 10.91%. What is the current yield and capital gains yield? Current yield = 10.15% Capital Gains Yield = 0.76% 22

23 Semiannual Bonds 1. Multiply years by 2 to get periods = 2N. 2. Divide nominal rate by 2 to get periodic rate = r d /2. 3. Divide annual INT by 2 to get PMT = INT/2. INPUTS OUTPUT 2N r d /2 OK INT/2 OK N I/YR PV PMT FV 23

24 Example A 10 year bond has a YTM of 13% The bond pays a 10% coupon semiannually. What is the bond selling for? Answer: \$

25 Callable Bonds and Yield to Call A 10-year, 10% semiannual coupon, \$1,000 par value bond with an 8% yield to maturity. It can be called after 5 years at \$1,050. What is the nominal yield to call if the bond is called? (Hint: There are 2 steps required for this problem) Answer: Price in Market = \$ , YTC=3.7650*2=7.5301% 25

26 If you bought bonds, would you be more likely to earn YTM or YTC? Coupon rate = 10% vs. YTC = r d = 7.53%. Could raise money by selling new bonds which pay 7.53%. Could thus replace bonds which pay \$100/year with bonds that pay only \$75.30/year. Investors should expect a call, hence YTC = 7.5%, not YTM = 8%. In general, if a bond sells at a premium, then coupon > r d, so a call is likely. So, expect to earn: YTC on premium bonds. YTM on par & discount bonds. 26

27 Quoted Market Interest Rate r d = r* + IP + DRP + LP + MRP Here: r d = Required rate of return on a debt security. r* = Real risk-free rate. IP DRP LP MRP = Inflation premium. = Default risk premium. = Liquidity premium. = Maturity risk premium. 27

28 Risk-free Rate Example What is the real risk-free rate given the required return on a 10-year bond is 6.8%, the inflation premium is 2.0%, and the default risk is 1.3%? Answer: 3.5% 28

29 Estimating IP Treasury Inflation-Protected Securities (TIPS) are indexed to inflation. Difference between TIPS and treasury security of the same maturity is can be good estimate of inflation premium The IP for a particular length maturity can be approximated as the difference between the yield on a nonindexed Treasury security of that maturity minus the yield on a TIPS of that maturity. The inflation premium is the average rate of inflation expected over the securities life, not the historical rate II N = I 1 + I I N N 29

30 What is the nominal risk-free rate? r RF = (1+r*)(1+IP)-1 = r*+ IP + (r*xip) r*+ IP. (Because r*xip is small) r RF = Rate on Treasury securities. 30

31 Default Risk Premium DRP is a premium on corporate bonds that covers the risk that the company might default on payments The greater the risk of default, the higher the YTM Bond rating provide measure of default risk Higher rating implies there is less of a change of bond default Investment grade and junk or speculative ratings Bond rating agencies: Moody s, Standard & Poor s, and Fitch 31

32 What factors affect bond ratings? Financial Ratios: debt ratio, coverage ratios, profitability ratios, and current ratios Bond Contract Terms: Secured versus unsecured debt, senior versus subordinated debt, guarantee provisions, sinking fund provisions, and debt maturity Qualitative Factors: Earnings stability, regulatory environment, potential product liability, and accounting policies 32

33 Bond Ratings Median Ratios (S&P) Interest coverage Return on capital Debt to capital AAA % 12.4% AA % 28.3% A % 37.5% BBB % 42.5% BB % 53.7% B % 75.9% CCC % 113.5% 33

34 Bond Spreads, the DRP, and the LP Liquidity Premium (LP): is the risk that the security could not be quickly converted to cash If not liquid investment may be hard to sell Bond s of large, strong companies often have very small LPs. Bond s of small companies often have LPs as high as 2%. A bond spread is often calculated as the difference between a corporate bond s yield and a Treasury security s yield of the same maturity. Therefore: Spread = DRP + LP 34

35 Bond Ratings and Bond Spreads (YahooFinance, February 2011) Long-term Bonds Yield (%) Spread (%) 10-Year T-bond 3.32 AAA AA A BBB BB B CCC

36 Maturity Risk Premium (MRP) MRP: depending on the maturities of the bonds they can carry additional risks Interest Rate Risk: the risk of a decline in bond values due to rising interest rates If rates increase, then the bond price falls Reinvestment Rate Risk: The risk that CFs will have to be reinvested in the future at lower rates, reducing income. Risk that if rate fall then bonds might be called and you are forced to invest in lower yielding bonds High on callable bonds and short-term maturities 36

37 Maturity Risk Premium Long-term bonds: High interest rate risk, low reinvestment rate risk. Short-term bonds: Low interest rate risk, high reinvestment rate risk. Nothing is riskless! Yields on longer term bonds usually are greater than on shorter term bonds, so the MRP is more affected by interest rate risk than by reinvestment rate risk. 37

38 Interest rate (or price) risk for 1-year and 10- year 10% bonds Interest rate risk: Rising r d causes bond s price to fall. r d 1-year Change 10-year Change 5% \$1,048 \$1, % 38.6% 10% 1,000 1, % 25.1% 15%

39 Value 1, year 1,000 1-year r d 0% 5% 10% 15% 39

40 Term Structure Yield Curve Term structure of interest rates: the relationship between interest rates (or yields) and maturities. A graph of the term structure is called the yield curve. Historically, long-term rates are higher than short-term rates so the yield curves slopes upward Short-term rates have been known to be higher than long-term rates forming an inverted yield curve 40

41 Hypothetical Treasury Yield Curve Interest Rate 14% 12% 10% 8% 6% 4% 2% 0% MRP IP r* Years to Maturity 41

42 Bankruptcy When a firm becomes insolvent and interest and principal obligations can not be met, a decision must be made about the firm. Two main chapters of Federal Bankruptcy Act: Chapter 11, Reorganization Chapter 7, Liquidation Typically, company wants Chapter 11, creditors may prefer Chapter 7. 42

43 Chapter 11 If company can t meet its obligations, it files under Chapter 11. That stops creditors from foreclosing, taking assets, and shutting down the business. Company has 120 days to file a reorganization plan. Court appoints a trustee to supervise reorganization. Management usually stays in control. Company must demonstrate in its reorganization plan that it is worth more alive than dead. Otherwise, judge will order liquidation under Chapter 7. 43

44 If the company is liquidated, here s the payment priority: Past due property taxes Secured creditors from sales of secured assets. Trustee s costs Expenses incurred after bankruptcy filing Wages and unpaid benefit contributions, subject to limits Unsecured customer deposits, subject to limits Taxes Unfunded pension liabilities Unsecured creditors Preferred stock Common stock 44

45 Chapter 7 In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back. Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, company emerges from bankruptcy with lower debts, reduced interest charges, and a chance for success. 45

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