e CHAPTER 7 Valuation and Characteristics of Bonds Orientation: This chapter introduces the concepts that underlie asset valuation. We are specifically concerned with bonds. We also look at the concept of the bondholder's expected rate of return on an investment. I. Types of bonds A. B. C. D. Debentures: unsecured long-term debt. Subordinated debentures: bonds that have a lower claim on assets in the event of liquidation than do other senior debtholders. Mortgage bonds: bonds secured by a lien on specific assets of the firm, such as real estate. Eurobonds: bonds issued in a country different from the one in whose currency the bond is denominated; for instance, a bond issued in Europe or Asia that pays interest and principal in U.S. dollars. Zero and low coupon bonds allow the issuing firm to issue bonds at a substantial discount from their $1,000 face value with a zero or very low coupon. 1. The disadvantages are, when the bond matures, the issuing firm will face an extremely large nondeductible cash outflow much greater than the cash inflow they experienced when the bonds were first issued. Discount bonds are not callable and can be retired only at maturity. E. 2. 87 3. F. II. On the other hand, annual cash outflows associated with interest payments do not occur with zero coupon bonds. Junk bonds: bonds rated BB or below. Terminology and characteristics of bonds A. A bond is a long-term promissory note that promises to pay the bondholder a predetermined, fixed amount of interest each year until maturity. At maturity, the principal will be paid to the bondholder. In the case of a firm's insolvency, a bondholder has a priority of claim to the firm's assets before the preferred and common stockholders. Also, bondholders must be paid interest due them before dividends can be distributed to the stockholders. A bond's par value is the amount that will be repaid by the firm when the bond matures, usually $1,000. The contractual agreement of the bond specifies a coupon interest rate that is expressed either as a percent of the par value or as a flat amount of interest which the borrowing firm promises to pay the bondholder each year. For example: A $1,000 par value bond specifying a coupon interest rate of nine percent is equivalent to an annual interest payment of $90. The bond has a maturity date, at which time the borrowing firm is committed to repay the loan principal. A convertible bond allows the investor to exchange the bond for a predetermined number of the firm's shares of common stock. A bond is callable or redeemable when it provides the firm with the right to pay off the bond at some time before its maturity date. These bonds frequently have a call protection period which prevents the firm from calling the bond for a pre-specified time period. An indenture (or trust deed) is the legal agreement between the firm issuing the bonds and the bond trustee who represents the bondholders. It provides the specific terms of the bond agreement such as the rights and responsibilities of both parties. The current yield on a bond refers to the ratio of annual interest payment to the bond's market price. 88 B. C. D. E. F. G. H. I. J. Bond ratings 1. Bond ratings are simply judgments about the future risk potential of the bond in question. Bond ratings are extremely important in that a firm's bond rating tells much about the cost of funds and the firm's access to the debt market. Three primary rating agencies exist--Moody's, Standard &amp; Poor's, and Fitch Investor Services. The different ratings and their implications are described. 2. 3. III. Definitions of value A. B. C. D. Book value is the value of an asset shown on a firm's balance sheet which is determined by its historical cost rather than its current worth. Liquidation value is the amount that could be realized if an asset is sold individually and not as part of a going concern. Market value is the observed value of an asset in the marketplace where buyers and sellers negotiate an acceptable price for the asset. Intrinsic value is the value based upon the expected cash flows from the investment, the riskiness of the asset, and the investor's required rate of return. It is the value in the eyes of the investor and is the same as the present value of expected <a href="/keyword/future-cash-flows/" >future cash flows</a> to be received from the investment. IV. Valuation: An Overview A. Value is a function of three elements: 1. 2. 3. B. The amount and timing of the assets' expected cash flows The riskiness of these cash flows The investors' required rate of return for undertaking the investment Expected cash flows are used in measuring the returns from an investment. 89 V. Valuation: The Basic Process The value of an asset is found by computing the present value of all the <a href="/keyword/future-cash-flows/" >future cash flows</a> expected to be received from the asset. Expressed as a general present value equation, the value of an asset is found as follows: V where Ct V = = = $C1 1 (1 k ) $C 2 $Cn 2 n (1 k ) (1 k ) k N VI. Bond Valuation A. = = the cash flow to be received at time t the intrinsic value or present value of an asset producing expected <a href="/keyword/future-cash-flows/" >future cash flows</a> , Ct, in years 1 through N the investor's required rate of return the number of periods The value of a bond is simply the present value of the future interest payments and maturity value discounted at the bondholder's required rate of return. This may be expressed as: Vb where It M kb N = = = = = $I 1 $I 2 $ In $M 1 2 n n (1 kb ) (1 kb ) (1 kb ) (1 kb ) the dollar interest to be received in each payment the par value of the bond at maturity the required rate of return for the bondholder the number of periods to maturity In other words, we are discounting the expected <a href="/keyword/future-cash-flows/" >future cash flows</a> to the present at the appropriate discount rate (required rate of return). B. If interest payments are received semiannually (as with most bonds) the valuation equation becomes: Vb = $I 1 / 2 k 1 b 2 1 $I 2 / 2 1 kb 2 2 $I 2n / 2 1 kb 2 2n $M 1 kb 2 2n 90 VII. Yield to Maturity A. The bondholder's expected rate of return is the rate the investor will earn if the bond is held to maturity, provided of course that the company issuing the bond does not default on the payments. This rate is also known as the yield to maturity. We compute the bondholder's expected rate of return by finding the discount rate that gets the present value of the future interest payments and principal payment just equal to the bond's current market price. B. VIII. Bond Value: Three Important Relationships A. First relationship A decrease in interest rates (required rates of return) will cause the value of a bond to increase; an interest rate increase will cause a decrease in value. The change in value caused by changing interest rates is called interest rate risk. B. Second relationship 1. If the bondholder's required rate of return (current interest rate) equals the coupon interest rate, the bond will sell at par, or maturity value. If the current interest rate exceeds the bond's coupon rate, the bond will sell below par value, or at a &quot;discount.&quot; If the current interest rate is less than the bond's coupon rate, the bond will sell above par value, or at a &quot;premium.&quot; 2. 3. C. Third relationship A bondholder owning a long-term bond is exposed to greater interest rate risk than when owning a short-term bond. 91 Study Problems 1. Gents Clothiers, Inc. has bonds maturing in 6 years and pays 6% interest semiannually on a $1000 face value. a. b. SOLUTION a. Value of bond if interest is paid semiannually: (1) Present value of interest payments: = $30 (PVIFA12,5%) = $30 (8.863) = $265.89 (2) Present value of principal: = $1,000 (PVIFA12,5%) = $1,000(0.557) = $557 (3) Present value of the interest and principal Present value of the interest $265.89 Present value of the principal 557.00 Value of the bond $822.89 Present value of the interest payments: = $60 (PVIFA6,10%) = $60(4.355) = $261.30 (2) Present value of the principal: = $1,000 (PVIFA6,10%) = $1,000(0.564) = $564 (3) Present value of the interest and principal Present value of the interest $261.30 Present value of the principal 564.00 Value of the bond $825.30 If your required rate of return is 10%, what is the value of the bond? How would your answer change if the interest were paid annually? b. Value of bond if interest is paid annually: (1) 92 2. Edge Manufacturing Corporation's bonds are selling in the market for $1,193.96. These 15-year bonds pay 8% interest (annually) on a $1,000 par value. If they are purchased at the market price, what is the expected rate of return? SOLUTION Expected Rate of Return: $1,193.96 = $80 (PVIFA 15, k b ) + $1,000 (PVIFA 15, k b ) where kb is the expected rate of return to be solved for by trial and error. Try a 6% rate of return. At 6% the present value of the interest and principal is equal to $80(9.712) + $1,000(0.417) = $1,193.96 The expected rate of return is 6%. (Note: With a financial calculator, there is no need to guess as to the rate. The rate may be determined by the calculator.) 3. The market price is $865.60 for a 5-year, 12% bond ($1,000 face value) that pays interest semiannually. What is the expected rate of return? SOLUTION $865.60 = $60 (PVIFA 10, k b ) + $1,000 (PVIF 10, k b ) where kb is the expected rate of return (to be solved by trial and error). Try 8%: $60(6.710) + $1,000(0.463) = $865.60 The required rate of return is 8% (on a semiannual basis) or 16% (on an annual basis). 93 Self Tests TRUE-FALSE 1. The par value of a bond is essentially independent of the market value of a bond. 2. The only variable that can cause the value of a bond to increase or decrease is a change in the bondholder's required rate of return. 3. In an efficient marketplace, the intrinsic value of a security will equal its market value. 4. If the market price of a security is larger than the value assigned to the security by an investor, then the expected rate is greater than the required rate of return. 5. Bond ratings indicate the chance that the bondholder will experience interest rate risk with a given bond. 6. The intrinsic value of an asset can be defined as the present value of the asset's expected <a href="/keyword/future-cash-flows/" >future cash flows</a> . 7. The yield to maturity of a bond is the current value of the bond. 8. The three items that directly affect the cash flows from owning a bond are the bond's par value, maturity date, and the coupon rate of interest. 9. The expected rate of return is equal to the required rate of return of bondholders who are willing to pay the present market price for the bonds. 10. An increase in interest rates will cause the value of a bond to increase. 11. An increase in interest automatically drives bonds' stated rates up. 12. Changes in interest rates have a greater impact on the value of short-term bonds as opposed to the value of long-term bonds. 13. The stated coupon rate of interest has no effect on the market price of a bond. 94 14. Investors are attracted to zero coupon bonds by their high periodic interest payments. 15. In the case of insolvency, bondholders are honored before common stock but after preferred stock. 16. A bond denominated by yen, issued in Japan, and not registered with the SEC, could not be classified as a Eurobond. 17. Junk bonds differ from high-yield bonds in that junk bonds will almost always carry a lower rating than high-yield bonds. 18. In an efficient marketplace, the intrinsic value of a security will equal its market value. MULTIPLE CHOICE 1. For a $1,000 par-value bond carrying an 8% coupon (interest paid quarterly) and having a 10% yield to maturity, the quarterly interest payments would be a. b. c. d. e. 2. $20. $30. $25. $50. $10. The value of a security may be expressed as a function of a. b. c. d. e. expected cash flows. riskiness of cash flows. the investor's required rate of return. a and b only. a, b, and c. 3. If the market is in equilibrium, the expected rate of return and the required rate of return a. b. c. will be the same. will be different. have no relationship to each other. 95 4. If everything else is assumed to be constant, as the investor's required rate of return decreases, the value of a security a. b. c. d. stays the same. increases. decreases. has no relationship to the investor's required rate of return. 5. In the basic security valuation model V = $C1 1 (1 k ) $C 2 $Cn 2 n (1 k ) (1 k ) C1 stands for a. b. c. d. 6. the investor's required rate of return. cash flow to be received in year 1. the intrinsic value of an asset producing expected <a href="/keyword/future-cash-flows/" >future cash flows</a> . none of the above. The _________________ of an asset is the observed value for the asset in the marketplace. a. b. c. d. intrinsic value liquidation value market value none of the above 7. The is the legal agreement that provides the specific terms of the loan agreement. a. b. c. d. mortgage debenture indenture prospectus 8. A(n) ____________ is a bond secured by a lien on real property. a. b. c. d. mortgage bond subordinated debenture Eurobond coupon bond 96 9. Junk bonds have all the following characteristics except a. b. c. d. rated BB or lower. low rates of return. highly speculative. no security. 10. Bond valuation depends on all but a. b. c. d. the amount of cash flows to be received. the maturity date of the loan. the investor's required rate of return. when the loan was issued. 11. When a bond is worth more than its face value, it is said to sell a. b. c. d. at a discount. at a premium. at its maturity value. above its market return. 12. When the market interest rate rises above the stated interest rate of a bond, the bond a. b. c. d. will sell at a discount. will sell at a premium. will sell at its par or stated value. will not sell because investors can receive a better return from the market. 13. The risk of changing bond values due to the variability of future interest rates is a. b. c. d. time value of money. interest-rate risk. timing risk. investment risk. 97 14. The current yield on a bond refers to a. b. c. d. the interest payments due within the next year. the ratio of the annual interest payment to the bond's market price. the interest earned in the current period. the coupon rate of interest. 15. Bond ratings are favorably affected by all except a. b. c. d. profitable operations. large firm size. low variability in past earnings. taking more advantage of financial leverage. 16. When bond prices are quoted, they are generally expressed at a. b. c. d. par value. face value. a percentage of par value. current yield. 17. The current interest rate can also be called a. b. c. d. e. the yield to maturity. the coupon interest rate. the expected rate of return. the risk premium. a and c 98