Finance 320F Unit 8 Application

Zero Coupon Bonds: You find a zero coupon bond with a par value of $10,000 and 17 years to maturity. If the yield to maturity on this bond is 4.9 percent, what is the price of the bond? Assume semiannual compounding periods.

"Zeros" play a major role in financial markets and are issued by some entities, such as school boards in Texas. To find the price of a zero coupon bond, we need to find the value of the future cash flows. With a zero coupon bond, the only cash flow is the par value at maturity. We find the present value assuming semiannual compounding to keep the YTM of a zero coupon bond equivalent to the YTM of a coupon bond, so: P = $10,000(PVIF2.45%,34) P = $4,391.30 Going to the calculator guide: Section 2: Basic Time Value Calculations, Calculation1: Solve for present value.

Bonds as Equity: The 100-year bonds we discussed in the chapter have something in common with junk bonds. Critics charge that, in both cases, the issuers are really selling equity in disguise. What are the issues here? Why would a company want to sell "equity in disguise"?

. A 100-year bond looks like a share of preferred stock. In particular, it is a loan with a life that almost certainly exceeds the life of the lender, assuming that the lender is an individual. With a junk bond, the credit risk can be so high that the borrower is almost certain to default, meaning that the creditors are very likely to end up as part owners of the business. In both cases, the "equity in disguise" has a significant tax advantage.

Municipal Bonds: Why is it that municipal bonds are not taxed at the federal level, but are taxable across state lines? Why is it that U.S. Treasury bonds are not taxable at the state level? (You may need to dust off the history books for this one.)

. As a general constitutional principle, the federal government cannot tax the states without their consent if doing so would interfere with state government functions. At one time, this principle was thought to provide for the tax-exempt status of municipal interest payments. However, modern court rulings make it clear that Congress can revoke the municipal exemption, so the only basis now appears to be historical precedent. The fact that the states and the federal government do not tax each other's securities is referred to as "reciprocal immunity." You will certainly not have this issue on a quiz or exam in this course, but municipals are increasingly in the news and it's useful to understand them.

Treasury Bonds

Bonds are financial security representing debt payments. Bonds in general face to major risks. Default risk is the chance that the issuer of the bond may default, and not make promised payments or accomplish other provisions of the bond. Interest rate risk arises as the bond promises a certain rate of return. Even if the bond doesn't default, fluctuation in market interest rates may change the market value of the bond. Government bonds are not of themselves default free. Bonds of some local governments and some national bonds, such as those issued by Greece, have a chance of defaulting. However, debt securities issued by the U.S. Federal Government are generally considered to be default free. However, as with all fixed-interest debt securities, as interest rates fluctuate, the value of a Treasury security will fluctuate. While this risk is not a major factor in short-term U.S. securities such as Treasury Bills, long-term Treasury securities have substantial interest rate risk.

Coupon Rates: Barnes Enterprises has bonds on the market making annual payments, with 12 years to maturity, a par value of $1,000, and a price of $963. At this price, the bonds yield 6.14 percent. What must the coupon rate be on the bonds?

By now you can see that there are several basic calculations for bonds: the bond price, the bond yield, and the bond's coupon payment. Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $963 = C(PVIFA6.14%,12) + $1,000(PVIF6.14%,12) Solving for the coupon payment, we get: C = $56.95 The coupon payment is the coupon rate times the par value. Using this relationship, we get Coupon rate = $56.95 / $1,000 Coupon rate = .0570, or 5.70%

Bond Ratings: Companies pay rating agencies such as Moody's and S&P to rate their bonds, and the costs can be substantial. However, companies are not required to have their bonds rated in the first place; doing so is strictly voluntary. Why do you think they do it?

Companies pay to have their bonds rated because unrated bonds can be difficult to sell. Many large investors are prohibited from investing in unrated issues, such as pension funds which can usually invest only in bonds with investment-grade ratings.

Bond Yield: Stein Co. issued 15-year bonds two years ago at a coupon rate of 5.4 percent. The bonds make semiannual payments. If these bonds currently sell for 94 percent of par value, what is the YTM?

Here, we are finding the YTM of a semiannual coupon bond. The bond price equation is: P = $940 = $27(PVIFAR%,26) + $1,000(PVIFR%,26) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find: R = 3.037% Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so: YTM = 23.037% YTM = 6.07%

Coupon Rates: Volbeat Corporation has bonds on the market with 10.5 years to maturity, a YTM of 6.2 percent, a par value of $1,000, and a current price of $945. The bonds make semiannual payments. What must the coupon rate be on the bonds?

Here, we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $945 = C(PVIFA3.1%,21) + $1,000(PVIF3.1%,21) Solving for the coupon payment, we get: C = $27.40 Since this is the semiannual payment, the annual coupon payment is: 2 × $27.40 = $54.80 And the coupon rate is the coupon payment divided by par value, so: Coupon rate = $54.80 / $1,000 Coupon rate = .0548, or 5.48%

Bond Ratings: Often, junk bonds are not rated. Why?

Junk, or speculative grade, bonds are increasingly in the news, and not just for businesses, but also for local governments and perhaps soon even for states. Junk bonds often are not rated because there would no point in an issuer paying a rating agency to assign its bonds a low rating (it's like paying someone to kick you!). As discussed in the course, these bonds provide a higher rating, but also have higher risk.

Bond Yield: The Timberlake-Jackson Wardrobe Co. has 7 percent coupon bonds on the market with 9 years left to maturity. The bonds make annual payments and have a par value of $1,000. If the bonds currently sell for $961.50, what is the YTM?

One of the most important relationships in time value is the inverse relationship between present values and interest rates. In a well-functioning bond market the price of the bond is the present value of the bond's coupon payments and par value. Here, we need to find the YTM of a bond: the rate we'd receive if we bought the bond today. . The equation for the bond price is: P = $961.50 = $70(PVIFAR%,9) + $1,000(PVIFR%,9) Notice the equation cannot be solved directly for R. Using a spreadsheet, a financial calculator, or trial and error, we find: R = YTM = 7.61% I really think you should use a calculator to calculate R, and will provide an example below, but am providing this to show you how approximation works. If you are using trial and error to find the YTM of the bond you should pick an interest rate to start the process. First, we know the YTM has to be higher than the coupon rate since the bond is a discount bond. That still leaves a lot of interest rates to check. One way to get a starting point is to use the following equation, which will give you an approximation of the YTM: Approximate YTM = [Annual interest payment + (Par value - Price) / Years to maturity] / [(Price + Par value) / 2] Solving for this problem, we get: Approximate YTM = [$70 + ($38.50 / 9)] / [($961.50 + 1,000) / 2] Approximate YTM = .0757, or 7.57% This is not the exact YTM, but it is close, and it will give you a place to start. (Chapter 6, 4) Now for the calculator. Go to Section 2: Basic Time Value Calculations, Calculation 6: Solve for present value of an ordinary annuity. Again, our five favorite buttons will solve the above question N = 9 years PMT = The coupon payment: 7% x $1,000 = $70 FV = The par value of the bond = $1,000 (Bonds are generally priced at $1,000) PV = The price of the bond, which is the present value of the coupon payments and face value = - $961.50. Note, as this is what the investor pays for the bond, it's entered as a"-". With the four pieces of information entered, we just press I/YR = the YTM of 7.61%

Bond Prices: Lycan, Inc., has 7 percent coupon bonds on the market that have 9 years left to maturity. The bonds make annual payments and have a par value of $1,000. If the YTM on these bonds is 8.4 percent, what is the current bond price?

The price of any bond is the PV of the interest payment, plus the PV of the par (face) value. Notice this problem assumes an annual coupon. The price of the bond will be: P = $70({1 - [1/(1 + .084)]9} / .084) + $1,000[1 / (1 + .084)9] P = $913.98 We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as: PVIFR,t = 1 / (1 + R)t which stands for Present Value Interest Factor PVIFAR,t = ({1 - [1/(1 + R)]t } / R) which stands for Present Value Interest Factor of an Annuity These abbreviations are shorthand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in the remainder of the solutions key. The bond price equation for this problem would be: P = $70(PVIFA8.4%,9) + $1,000(PVIF8.4%,9) P = $913.98 The PVIF notation is used in many of our examples. You can find the PVIF factors in time value tables at the end of the text, in Appendix A. (Chapter 6, 3) However, the most efficient way to calculate bond prices is a financial calculator. Go to Section 2: Basic Time Value Calculations, Calculation 6: Solve for present value of an ordinary annuity. Here we have our five favorite buttons that will solve the above question N = 9 years I/YR = the YTM of 8.4% PMT = The coupon payment: 7% x $1,000 = $70 FV = The par value of the bond = $1,000 (Bonds are generally priced at $1,000) Push PV, which gives us the value of the bond today + $913.98

Interpreting Bond Yields. Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the coupon rate on the bond now? The YTM?

The yield to maturity is the rate of return an investor would get if she bought the bond today and held it to maturity. As bond market prices reflect the economic value of the bond's future cash flows, the YTM should match the bond's required rate of return when the bond is purchased. For noncallable bonds, the yield to maturity and required rate of return are interchangeable terms. The coupon rate is the stated nominal annual rate of interest that the bond will pay, and is set when the bond is issued. The amount of the periodic interest payment is determined by multiplying the bond's face, or par, value by the coupon rate. The coupon is the contractual rate, whereas the YTM is the current market required rate of return on the bond. The bond in this question has a coupon rate of 10%. This means that the bond promises to pay 10% interest per year. As bonds are set a face values of $1,000, the annual coupon paid would be 10% x $1,000 = $100. When a bond is first issued, it is generally issued at par, which means Market value = Face value RR/YTM = Coupon rate. If in two years the YTM drops to 8%, this means that the required rates of return on equivalent bonds has dropped to 8%. While newly issued bonds would have a coupon rate of 8%, our bond's coupon rate is fixed at 10%. However, given our bond offers $100, whereas other newly issued bonds now offer only $80, our 10% bond is more attractive and investors will pay more for it—it would sell at a premium. This higher price would produce a current YTM of 8%. This discussion is based on the time value techniques from Units 5 and 6. Our discussion uses nominal, not inflation-adjusted interest rates, and is set on an annual basis. To compute the actual prices and coupon payments we'd have to switch to semiannual compounding, as bonds pay interest semiannually.

Call Provisions: A company is contemplating a long-term bond issue. It is debating whether or not to include a call provision. What are the benefits to the company from including a call provision? What are the costs? How do these answers change for a put provision? There are two benefits.

There are two benefits. First, the company can take advantage of interest rate declines by calling in an issue and replacing it with a lower coupon issue. For example, if TMI issues a bond when YTMs, and thus coupon rates, are 8%, and then rates drop to 4%, they could call the bond that pays a $80 coupon and replace it with a new bond that pays a $40 coupon, giving it a substantial savings on its cost of borrowing! Second, a company might wish to eliminate a covenant for some reason. Calling the issue does this. The cost to the company is a higher coupon. A put provision, where the bondholder may require the company to buy back it's bond, is desirable from an investor's standpoint, so it helps the company by reducing the coupon rate on the bond. The cost to the company is that it may have to buy back the bond at an unattractive price.

Bond Prices: Harrison Co. issued 15-year bonds one year ago at a coupon rate of 6.1 percent. The bonds make semiannual payments. If the YTM on these bonds is 5.3 percent, what is the current dollar price assuming a $1,000 par value?

To find the price of this bond, we need to realize that the maturity of the bond is 14 years. The bond was issued one year ago, with 15 years to maturity, so there are 14 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is: P = $30.50(PVIFA2.65%,28) + $1,000(PVIF2.65%,28) P = $1,078.37 However, the most efficient way to calculate bond prices is a financial calculator. Go to Section 2: Basic Time Value Calculations, Calculation 6: Solve for present value of an ordinary annuity plus the present value of the terminal payment.. (Chapter 6, 6) While we can still use our favorite buttons to solve the above question, we are facing semiannual compounding and must adjust the numbers we enter into the calculator. N = 14 years, which converts to 28 periods. I/YR = the YTM of 5.3%, which converts to a semiannual rate of 2.65% PMT = The coupon payment: 6.1% x $1,000 = $61, which converts to semiannual coupon payments of $30.50 FV = The par value of the bond = $1,000 (Bonds are generally priced at $1,000) Push PV, which gives us the value of the bond today $1,078.37.

Bond Prices Vs. Yield

a. The bond price is the present value when discounting the future cash flows from a bond; YTM is the interest rate used in discounting the future cash flows (coupon payments and principal) back to their present values. In efficient markets (which you'll begin to learn about in the Unit 7 assignment) the bond price represents the economic value of the bond—its promised cash flows (coupon payment and face value) discounted by its opportunity cost (YTM). b. If the coupon rate is higher than the required return on a bond, the bond will sell at a premium, since it provides periodic income in the form of coupon payments in excess of that required by investors on other similar bonds. If the coupon rate is lower than the required return on a bond, the bond will sell at a discount, since it provides insufficient coupon payments compared to that required by investors on other similar bonds. For premium bonds, the coupon rate exceeds the YTM; for discount bonds, the YTM exceeds the coupon rate, and for bonds selling at par, the YTM is equal to the coupon rate. c. Current yield is defined as the annual coupon payment divided by the current bond price. Current yield thus focuses on the return provided by coupon payments and does not factor in the principle payment when the bond matures. For premium bonds, the current yield exceeds the YTM, for discount bonds the current yield is less than the YTM, and for bonds selling at par value, the current yield is equal to the YTM. In all cases, the current yield plus the expected one-period capital gains yield of the bond must be equal to the required return. (Chapter 6, 6.15)