A. What are the key features of a bond? answer:if possible, begin this lecture by showing students an actual bond certificate. We show a real coupon bond with physical coupons. These can no longer be issued–it is too easy to evade taxes, especially estate taxes, with bearer bonds. All bonds today must be registered, and registered bonds don’t have physical coupons. 1. Par or face value. We generally assume a $1,000 par value, but par can be anything, and often $5,000 or more is used.
With registered bonds, which is what are issued today, if you bought $50,000 worth, that amount would appear on the certificate. 2. Coupon rate. The dollar coupon is the “rent” on the money borrowed, which is generally the par value of the bond. The coupon rate is the annual interest payment divided by the par value, and it is generally set at the value of k on the day the bond is issued. To illustrate, the required rate of return on one of southern bell’s bonds was 11 percent when they were issued, so the coupon rate was set at 11 percent.Order now
If the company were to float a new issue today, the coupon rate would be set at the going rate today (october 1998), which would be about 7. 4%. 3. Maturity. This is the number of years until the bond matures and the issuer must repay the loan (return the par value). The southern bell bonds had a 30-year maturity when they were issued, but the maturity declines by 1 year each year after their issue. 4. Issue date. The southern bell bonds were issued in 1977, when interest rates were higher than they are today. 5.
Default risk is inherent in all bonds except treasury bonds–will the issuer have the cash to make the promised payments? Bonds are rated from aaa to d, and the lower the rating the riskier the bond, the higher its default risk premium, and, consequently, the higher its required rate of return, k. Southern bell is rated aaa. B. What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky? Answer:a call provision is a provision in a bond contract that gives the issuing corporation the right to redeem the bonds under specified terms prior to the normal maturity date.
The call provision generally states that the company must pay the bondholders an amount greater than the par value if they are called. The additional sum, which is called a call premium, is typically set equal to one year’s interest if the bonds are called during the first year, and the premium declines at a constant rate of int/n each year thereafter. A sinking fund provision is a provision in a bond contract that requires the issuer to retire a portion of the bond issue each year. A sinking fund provision facilitates the orderly retirement of the bond issue.
The call privilege is valuable to the firm but potentially detrimental to the investor, especially if the bonds were issued in a period when interest rates were cyclically high. Therefore, bonds with a call provision are riskier than those without a call provision. Accordingly, the interest rate on a new issue of callable bonds will exceed that on a new issue of noncallable bonds. Although sinking funds are designed to protect bondholders by ensuring that an issue is retired in an orderly fashion, it must be recognized that sinking funds will at times work to the detriment of bondholders.
On balance, however, bonds that provide for a sinking fund are regarded as being safer than those without such a provision, so at the time they are issued sinking fund bonds have lower coupon rates than otherwise similar bonds without sinking funds. D. How is the value of a bond determined? What is the value of a 10-year, $1,000 par value bond with a 10 percent annual coupon if its required rate of return is 10 percent? Answer:a bond has a specific cash flow pattern consisting of a stream of constant interest payments plus the return of par at maturity. The annual coupon payment is the cash flow: pmt = (coupon rate) ? par value) = 0. 1($1,000) = $100. For a 10-year, 10 percent annual coupon bond, the bond’s value is found as follows: 0 1 2 3 9 10 | | | | • • • | | 100 100 100 100 100 90. 91 + 1,000 82. 64 . . . 38. 55 385. 54 1,000. 00 Expressed as an equation, we have: Or: vb = $100(pvifa10%,10) + $1,000(pvif10%,10) = $100 ((1- 1/(1+. 1)10)/0. 10) + $1,000 (1/(1+0. 10)10). The bond consists of a 10-year, 10% annuity of $100 per year plus a $1,000 lump sum payment at t = 10: v annuity = $ 614. 46 pv maturity value = 385. 54 value of bond = $1,000. 00 The mathematics of bond valuation is programmed into financial calculators which do the operation in one step, so the easy way to solve bond valuation problems is with a financial calculator. Input n = 10, kd = i = 10, pmt = 100, and fv = 1000, and then press pv to find the bond’s value, $1,000. Then change n from 10 to 1 and press pv to get the value of the 1-year bond, which is also $1,000. K. Suppose a 10-year, 10 percent, semiannual coupon bond with a par value of $1,000 is currently selling for $1,135. 0, producing a nominal yield to maturity of 8 percent. However, the bond can be called after 5 years for a price of $1,050. K. 1. What is the bond’s nominal yield to call (ytc)? Answer:if the bond were called, bondholders would receive $1,050 at the end of year 5. Thus, the time line would look like this: 0 1 2 3 4 5 | | | | | | 50 50 50 50 50 50 50 50 50 50 1,050 pv1 . pv4 pv5c pv5cp 1,135. 90 = sum of pvs The easiest way to find the ytc on this bond is to input values into your calculator: n = 10; pv = -1135. 90; pmt = 50; and fv = 1050, which is the par value plus a call premium of $50; and then press the k = i button to find i = 3. 765%. However, this is the 6-month rate, so we would find the nominal rate on the bond as follows: Knom = 2(3. 765%) = 7. 5301% ? 7. 5%. This 7. 5% is the rate brokers would quote if you asked about buying the bond. You could also calculate the ear on the bond: Ear = (1. 03765)2 – 1 = 7. 672%.
Usually, people in the bond business just talk about nominal rates, which is ok so long as all the bonds being compared are on a semiannual payment basis. When you start making comparisons among investments with different payment patterns, though, it is important to convert to ears. K. 2. If you bought this bond, do you think you would be more likely to earn the ytm or the ytc? Why? Answer:since the coupon rate is 10% versus ytc = kd = 7. 53%, it would pay the company to call the bond, get rid of the obligation to pay $100 per year in interest, and sell replacement bonds whose interest would be only $75. 0 per year. Therefore, if interest rates remain at the current level until the call date, the bond will surely be called, so investors should expect to earn 7. 53%. In general, investors should expect to earn the ytc on premium bonds, but to earn the ytm on par and discount bonds. (bond brokers publish lists of the bonds they have for sale; they quote ytm or ytc depending on whether the bond sells at a premium or a discount. ) L. Disney’s bonds were issued with a yield to maturity of 7. 5 percent. Does the yield to maturity represent the promised or expected return on the bond?
Answer:the yield to maturity is the rate of return earned on a bond if it is held to maturity. It can be viewed as the bond’s promised rate of return, which is the return that investors will receive if all the promised payments are made. The yield to maturity equals the expected rate of return only if (1) the probability of default is zero and (2) the bond cannot be called. For bonds where there is some default risk, or where the bond may be called, there is some probability that the promised payments to maturity will not be received, in which case, the promised yield to maturity will differ from the expected return.
M. Disney’s bonds were rated aa- by s. Would you consider these bonds investment grade or junk bonds? Answer:the disney bonds would be investment grade bonds. Triple-a, double-a, single-a, and triple-b bonds are considered investment grade. Double-b and lower-rated bonds are considered speculative, or junk bonds, because they have a significant probability of going into default. Many financial institutions are prohibited from buying junk bonds.