Chapter 7 Bonds and Their Valuation Key Features of Bonds Bond Valuation Measuring Yield Assessing Risk  companies raise capital in two main forms: debt and equity. In this chapter, we examine the characteristics of bonds and discuss the various factors that influence bond prices © Cengage Learning Modified by Dr. Bader Alhashel

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. Issued by governments and corporations looking for long-term debt capital © Cengage Learning Modified by Dr. Bader Alhashel

What is a bond? In 1993 Disney issued $300 million 100-year bonds to yield 7.55% In 1993 Disney iised $300 milliom 100-year bonds to yield 7.55% © Cengage Learning Modified by Dr. Bader Alhashel

What is a bond? Bonds until the 1970s were beautifully engraved pieces of paper and their key terms were spelled out on the bonds © Cengage Learning Modified by Dr. Bader Alhashel

Classifying bonds based on the issuer Treasury bonds: Bonds issued by the US federal government, sometimes referred to as government bonds. Corporate bonds: Bonds issued by corporations. Foreign bonds: Bonds issued by foreign governments or by foreign corporations. Treasury bonds are issued by the government. Have no or low default risk © Cengage Learning Modified by Dr. Bader Alhashel

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. Fixed-rate bonds: A bond whose interest rate is fixed for its entire life. Floating-rate bonds: A bond whose interest rate fluctuates with shifts in the general level of interest rates. Coupon payment: The specified number of dollars of interest paid each year. 𝐶𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡=𝐶𝑜𝑢𝑝𝑜𝑛 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒×𝑃𝑎𝑟 𝑣𝑎𝑙𝑢𝑒. Zero-coupon bonds: A bond that pays no interest but is sold at discount to par value. Fixed-rate bonds Floating-rate bonds (interest rate I adjusted every 6 months) Zero-coupon bonds: pay no interest-sold at discount © Cengage Learning Modified by Dr. Bader Alhashel

Why are they called coupons? © Cengage Learning Modified by Dr. Bader Alhashel

Key Features of a Bond Maturity date: A specified date on which the par value of a bond must be repaid. Call provision: A provision that gives the bond issuer the right to redeem the bonds before maturity date.

Effect of a Call Provision Why would an issuer call a bond? If interest rates decline the bond issuer might find it cheaper to call a bond and issue a new bond with the lower interest rate. (helps the issuer, but hurts the investor). Borrowers are willing to pay more for this provision, and lenders require more, for callable bonds. What is a deferred call? What is a call premium? Call premium is the dollar amount over the par value of a callable fixed-income debt security that is given to holders when the security is called by the issuer © Cengage Learning Modified by Dr. Bader Alhashel

What is a sinking fund? Provision that requires the bond issuer to pay off the loan over its life rather than all at maturity. Bonds that have a sinking fund are regarded as being safer than those without such a provision. Why safer? © Cengage Learning Modified by Dr. Bader Alhashel

How are sinking funds executed? The issuer can choose between two options: Call x% of the issue at par, for sinking fund purposes. Likely to be used if rd is below the coupon rate and the bond sells at a premium. Buy bonds in the open market. Likely to be used if rd is above the coupon rate and the bond sells at a discount. © Cengage Learning Modified by Dr. Bader Alhashel

Other Types (Features) of Bonds Convertible bond: may be exchanged for common stock of the firm, at the holder’s option. Warrant: long-term option to buy a stated number of shares of common stock at a specified price. Putable bond: allows holder to sell the bond back to the company prior to maturity. Income bond: pays interest only when the firm has earned enough income to pay interest. Indexed bond: interest rate paid is based upon the rate of inflation. © Cengage Learning Modified by Dr. Bader Alhashel

The Value of Financial Assets 1 2 N r% CF1 CFN CF2 Value ... What is the value of any asset? What are the CFs? R% is a function of risk? INT The value of any financial asset is the present value of its expected future cash flows. © Cengage Learning Modified by Dr. Bader Alhashel

What is the value of a 10-year, 10% annual coupon bond, if rd = 10%? 1 2 N rd=10% 100 100 + 1,000 VB = ? ... rd is market rate of interest. This is the discount rate used to calculate the present value of the cash flows. Note that rd is not the coupon interest rate. Coupon payment=coupon rate x par value =0.1*1000=$100 $1000= par value or maturity value or face value. © Cengage Learning Modified by Dr. Bader Alhashel 𝑉 𝐵 = $100 1.05 1 +…+ $100 1.05 10 + $1,000 1.05 10 𝑉 𝐵 =$95.24+… $61.39+$613.91 𝑉 𝐵 =$1386.09

What is the value of a 10-year, 10% annual coupon bond, if rd = 10%? 1 2 N rd=10% 100 100 + 1,000 VB = ? ... © Cengage Learning Modified by Dr. Bader Alhashel 𝑉 𝐵 = $100 1.05 1 +…+ $100 1.05 10 + $1,000 1.05 10 𝑉 𝐵 =$95.24+… $61.39+$613.91 𝑉 𝐵 =$1386.09

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. When Price (PV) = Par value we say the bond is selling at par. This happens when I% or r% = Coupon I% When a bond is issued its coupon interest rate is set equal to the market rate which makes its price equal to par INPUTS 10 10 100 1000 N I/YR PV PMT FV OUTPUT -1000 © Cengage Learning Modified by Dr. Bader Alhashel

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 This is a premium bond since its price is larger than its par value. When does a bond sell at a premium? INPUTS 10 10 130 1000 N I/YR PV PMT FV OUTPUT -1184.34 When coupon rate> market interest rate © Cengage Learning Modified by Dr. Bader Alhashel

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. This is a discount bond since its price is lower than its par value. When does a bond sell at a discount? INPUTS OUTPUT N I/YR PMT PV FV 10 70 1000 -815.66 Coupon rate< interest rate © Cengage Learning Modified by Dr. Bader Alhashel

To summarize… coupon rate = rd: fixed-rate bond sells at par; hence, it is a par bond coupon rate < rd: fixed-rate bond sells below par; hence, it is a discount bond coupon rate > rd: fixed-rate bond sells above par; hence, it is a premium bond

Problem 7-1 © Cengage Learning Modified by Dr. Bader Alhashel

Bond Yields Unlike the coupon interest rate, which is fixed, the bond’ s yield varies from day to day depending on current market conditions.

Yield to Maturity (YTM) The rate of return earned on a bond if it is held to maturity. It is the discount rate that will set the bond price equal to the present value of the bond’s future cash flows.

What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887? Must find the rd that solves this model. Again what is YTM? YTM is equal to coupon rate at issuance © Cengage Learning Modified by Dr. Bader Alhashel

Using a Financial Calculator to Solve for the YTM Solving for I/YR, the YTM of this bond is 10.91%. This bond sells at a discount, because YTM > coupon rate. INPUTS 10 - 887 90 1000 N I/YR PV PMT FV OUTPUT 10.91 © Cengage Learning Modified by Dr. Bader Alhashel

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. INPUTS 10 -1134.2 90 1000 N I/YR PV PMT FV OUTPUT 7.08 © Cengage Learning Modified by Dr. Bader Alhashel

Yield to Maturity (YTM) YTM changes as the interest rates change If you buy a bond on its issuance date and hold it till maturity you will receive the YTM calculated on the purchase date If you buy a bond later on, the YTM will depend on your purchase price © Cengage Learning Modified by Dr. Bader Alhashel

Changes in Bond Value over Time What would happen to the value of these three bonds if the required rate of return remained at 10%? Years to Maturity 1,184 1,000 816 10 13% coupon rate 7% coupon rate 10% coupon rate VB 5 Why is the value of the bond affected by the r%? Why does it sell at a premium or a discount based on its coupon rate? © Cengage Learning Modified by Dr. Bader Alhashel

Bond Values over Time At maturity, the value of any bond must equal its par value. If rd 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. © Cengage Learning Modified by Dr. Bader Alhashel

Definitions Why is it expected? Because a company could default on its payments? © Cengage Learning Modified by Dr. Bader Alhashel

An Example: Current and Capital Gains Yield Find the current yield and the capital gains yield for a 10- year, 9% annual coupon bond that sells for $887, and has a face value of $1,000. © Cengage Learning Modified by Dr. Bader Alhashel

Calculating Capital Gains Yield YTM = Current yield + Capital gains yield Could also find the expected price one year from now and divide the change in price by the beginning price, which gives the same answer. © Cengage Learning Modified by Dr. Bader Alhashel

Problem 7-10 © Cengage Learning Modified by Dr. Bader Alhashel

Semiannual Bonds Multiply years by 2: Number of periods = 2N Divide nominal rate by 2: Periodic rate (I/YR) = rd/2 Divide annual coupon by 2: PMT = Annual coupon/2 If we have bonds that make semi-annual payments, what should we do to the number of periods and the interest rate? INPUTS 2N rd/2 OK cpn/2 OK N I/YR PV PMT FV OUTPUT © Cengage Learning Modified by Dr. Bader Alhashel

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

Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10% semiannual coupon bond, all else equal? The semiannual bond’s effective rate is: 10.25% > 10% (the annual bond’s effective rate), so you would prefer the semiannual bond. © Cengage Learning Modified by Dr. Bader Alhashel

If the proper price for this semiannual bond is $1,000, what would be the proper price for the annual coupon bond? The semiannual coupon bond has an effective rate of 10.25%, and the annual coupon bond should earn the same EAR. At these prices, the annual and semiannual coupon bonds are in equilibrium, as they earn the same effective return. INPUTS 10 10.25 100 1000 N I/YR PV PMT FV OUTPUT - 984.80 © Cengage Learning Modified by Dr. Bader Alhashel

Problem 7-16 © Cengage Learning Modified by Dr. Bader Alhashel

Yield to Call (YTC) If a company calls its bonds, investors will not earn YTM. Instead, they will earn Yield to Call (YTC). This will happen if interest rates are below the coupon rate. rd is YTC © Cengage Learning Modified by Dr. Bader Alhashel

A 10-year, 10% semiannual coupon bond selling for $1,135 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 8 - 1135.90 50 1050 N I/YR PV PMT FV OUTPUT 3.568 © Cengage Learning Modified by Dr. Bader Alhashel

Yield to Call 3.568% represents the periodic semiannual yield to call. YTCNOM = rNOM = 3.568% x 2 = 7.137% is the rate that a broker would quote. The effective yield to call can be calculated. YTCEFF = (1.03568)2 – 1 = 7.26% © Cengage Learning Modified by Dr. Bader Alhashel

If you bought these callable bonds, would you be more likely to earn the YTM or YTC? The coupon rate = 10% compared to YTC = 7.137%. The firm could raise money by selling new bonds which pay 7.137%. Could replace bonds paying $100 per year with bonds paying only $71.37 per year. Investors should expect a call, and to earn the YTC of 7.137%, rather than the YTM of 8%. © Cengage Learning Modified by Dr. Bader Alhashel

When is a call more likely to occur? In general, if a bond sells at a premium, then (1) coupon > rd, so (2) a call is more likely. So, expect to earn: YTC on premium bonds. YTM on par and discount bonds. © Cengage Learning Modified by Dr. Bader Alhashel

If you buy a callable bond and interest rates decline, will the value of your bond rise as much as it would have risen if the bond was not callable? © Cengage Learning Modified by Dr. Bader Alhashel

Problem 7-12 © Cengage Learning Modified by Dr. Bader Alhashel

Problem 7-14 © Cengage Learning Modified by Dr. Bader Alhashel

What is interest rate (or price) risk? The risk of a decline in a bond’s price due to an increase in interest rates. $1000 bond with 10% coupon rate: 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% Why does the value of the bond decrease if interest rates go up © Cengage Learning Modified by Dr. Bader Alhashel

Why does a longer-term bond have more sensitivity to interest rate movements (higher interest rate risk) than shorter-term bonds? Because given higher interest rates the paid principal at the end is discounted over many years so its worth less given the higher interest rates Alternatively, it is worth less because I can take the money and invest instead in a higher interest rate bond © Cengage Learning Modified by Dr. Bader Alhashel

Illustrating Interest Rate Risk 10-Year Bond 1-Year Bond © Cengage Learning Modified by Dr. Bader Alhashel

Problem 7-7 © Cengage Learning Modified by Dr. Bader Alhashel

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. EXAMPLE: Suppose you just won $500,000 playing the lottery. You intend to invest the money and live off the interest. © Cengage Learning Modified by Dr. Bader Alhashel

Reinvestment Rate Risk Example You may invest in either a 10-year bond or a series of ten 1- year bonds. Both 10-year and 1-year bonds currently yield 10%. If you choose the 1-year bond strategy: After Year 1, you receive $50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000. If you choose the 10-year bond strategy: You can lock in a 10% interest rate, and $50,000 annual income for 10 years, assuming the bond is not callable. © Cengage Learning Modified by Dr. Bader Alhashel

Conclusions about Interest Rate and Reinvestment Rate Risk Which risk should we choose to be exposed to more? Depends on your investment horizon If you are a retiree living off your interest income, you want to minimize your reinvestment risk Someone who needs the money one year from now is not concerned with reinvestment risk, but the value of his bond when he wants to sell it © Cengage Learning Modified by Dr. Bader Alhashel

Default Risk If an issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate bonds is less than the promised return. The higher the probability of default the higher the higher the compensation investors demand. Influenced by the issuer’s financial strength and the terms of the bond contract. © Cengage Learning Modified by Dr. Bader Alhashel

Types of Bonds Mortgage bonds: A bond backed by fixed assets. Debentures: A long-term bond that is not secured by a mortgage on specific property. Subordinated debentures: bond having a claim on assets only after the senior debt has been paid off in the event of liquidation. Mortgage bonds are bonds backed by collateral Debenture are unsecured bonds (used by established companies with strong and clear cash flow) © Cengage Learning Modified by Dr. Bader Alhashel

Bond ratings Bond ratings reflect the probability of default on the bond. Three major rating agencies: Moody’s, Standard & Poor, and Fitch. Investment-grade bonds: bonds with ratings above BB. Institutional investors and banks are permitted by law to hold only investment grade bonds. Junk bonds: Bonds with a BB or lower rating.

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 C Bond ratings are designed to reflect the probability of a bond issue going into default. © Cengage Learning Modified by Dr. Bader Alhashel

Factors Affecting Default Risk and Bond Ratings Financial performance Debt ratio TIE ratio Current ratio Qualitative factors: Bond contract provisions Secured vs. Unsecured debt Senior vs. subordinated debt Guarantee and sinking fund provisions Debt maturity © Cengage Learning Modified by Dr. Bader Alhashel

Other Factors Affecting Default Risk Earnings stability Regulatory environment Potential antitrust or product liabilities Pension liabilities Potential labor problems © Cengage Learning Modified by Dr. Bader Alhashel

Bankruptcy When a company is insolvent (can’t pay its obligations): Reorganization Liquidation Typically, a company wants Reorganization, while creditors may prefer Liquidation. Why does the company and its stock holders want Reorganization? © Cengage Learning Modified by Dr. Bader Alhashel

Bankruptcy Company must demonstrate in its reorganization plan that it is “worth more alive than dead”. The debt could be restructured Reduce interest rate Postpone the maturity date Debt is exchanged for equity Restructuring is done to reduce the firm’s debt level (leverage) to a reasonable level that can be met with its projected cash flows © Cengage Learning Modified by Dr. Bader Alhashel

Priority of Claims in Liquidation Secured creditors from sales of secured assets. Trustee’s costs Wages, subject to limits Taxes Unfunded pension liabilities Unsecured creditors Preferred stock Common stock © Cengage Learning Modified by Dr. Bader Alhashel

Reorganization 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. © Cengage Learning Modified by Dr. Bader Alhashel

Bond Markets Primarily traded in the over-the-counter (OTC) market. Most bonds are owned by and traded among large financial institutions. Bond market in Kuwait © Cengage Learning Modified by Dr. Bader Alhashel