P6-5 Nominal interest rates and yield curves A recent study of inflationary expectations has revealed that the consensus among economic forecasters yields the following average annual rates of inflation expected over the periods noted. (Note: Assume that the risk that future interest rate movements will affect longer maturities more than shorter maturities is zero; that is, assume that there is no maturity risk.)
a. If the real rate of interest is currently 2.5%, find the nominal rate of interest on each of the following U.S. Treasury issues: 20-year bond, 3-month bill, 2-year note, and 5-year bond.
b. If the real rate of interest suddenly dropped to 2% without any change in inflationary expectations, what effect, if any, would it have on your answers in part a? Explain.
c. Using your findings in part a, draw a yield curve for U.S. Treasury securities. Describe the general shape and expectations reflected by the curve.
d. What would a follower of the liquidity preference theory say about how the preferences of lenders and borrowers tend to affect the shape of the yield curve drawn in part c? Illustrate that effect by placing on your graph a dotted line that approximates the yield curve without the effect of liquidity preference.
e. What would a follower of the market segmentation theory say about the supply and demand for long-term loans versus the supply and demand for short-term loans given the yield curve constructed for part c of this problem?
P6-11 Bond prices and yields Assume that the Financial Management Corporation's $1,000-par-value bond had a 5.700% coupon, matures on May 15, 2023, has a current price quote of 97.708, and has a yield to maturity (YTM) of 6.034%. Given this information, answer the following questions:
a. What was the dollar price of the bond?
b. What is the bond's current yield?
c. Is the bond selling at par, at a discount, or at a premium? Why?
d. Compare the bond's current yield calculated in part b to its YTM and explain why they differ.
P6-17 Bond value and changing required returns Midland Utilities has outstanding a bond issue that will mature to its $1,000 par value in 12 years. The bond has a coupon interest rate of 11% and pays interest annually.
a. Find the value of the bond if the required return is (1) 11%, (2) 15%, and (3) 8%.
b. Plot your findings in part a on a set of "required return (x axis)-market value of bond (y axis)" axes.
c. Use your findings in parts a and b to discuss the relationship between the coupon interest rate on a bond and the required return and the market value of the bond relative to its par value.
d. What two possible reasons could cause the required return to differ from the coupon interest rate?
P6-18 Bond value and time: Constant required returns Pecos Manufacturing has just issued a 15-year, 12% coupon interest rate, $1,000-par bond that pays interest annually.
The required return is currently 14%, and the company is certain it will remain at 14% until the bond matures in 15 years.
a. Assuming that the required return does remain at 14% until maturity, find the value of the bond with (1) 15 years, (2) 12 years, (3) 9 years, (4) 6 years, (5) 3 years, and (6) 1 year to maturity.
b. Plot your findings on a set of "time to maturity (x axis)-market value of bond (y axis)" axes constructed similarly to Figure 6.5 on page 252.
c. All else remaining the same, when the required return differs from the coupon interest rate and is assumed to be constant to maturity, what happens to the bond value as time moves toward maturity? Explain in light of the graph in part b.
P6-22 Yield to maturity Each of the bonds shown in the following table pays interest annually.
a. Calculate the yield to maturity (YTM) for each bond.
b. What relationship exists between the coupon interest rate and yield to maturity and the par value and market value of a bond? Explain.