# Yield Curves; Expectations theory; Bond valuation; Yield to maturity; Yield to call

6-1: YIELD CURVES The following yields on U.S. Treasury securities were taken from a recent financial publication:

Term Rate

6 months 5.1%

1 year 5.5

2 years 5.6

3 years 5.7

4 years 5.8

5 years 6.0

10 years 6.1

20 years 6.5

30 years 6.3

a. Plot a yield curve based on these data?

b. What type of yield curve is shown?

c. What information does this graph tell you?

d. Based on this yield curve, if you needed to borrow money for longer than 1 year, would it make sense for you to borrow short-term and renew the loan or borrow long-term?

6-15: EXPECTATIONS THEORY Assume that the real risk-free rate is 2% and that the maturity risk premium is zero. If the 1-year bond yield is 5% and a 2-year bond (of similar risk) yields 7%, what is the 1-year interest rate that is expected for Year 2? What inflation rate is expected during Year 2? Comment on why the average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2.

7-5: BOND VALUATION An investor has two bonds in his portfolio that have a few value of $1,000 and pay a 10% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year.

a. What will the value of each bond be if the going interest rate is 5%, 8%, and 12%? Assume that only one more interest payments is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L.

b. Why does the longer-term bond's price vary more than the price of the shorter-term bond when interest rates change?

7-10: CURRENT YIELD, CAPITAL GAINS YIELD, AND YIELD TO MATURITY Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 8% annual coupon rate and were issued 1 year ago at their par value of $1,000. However, due to changes in interest rates, the bond's market price has fallen to $901.40. The capital gains yield last year was -9.86%.

a. What is the yield to maturity?

b. For the coming year, what are the expected current and capital gains yields?

c. Will the actual realized yields be equal to the expected yields if interest rates change? IF not, how will they differ?

7-19: YIELD TO MATURITY AND YIELD TO CALL Kaufman Enterprises has bonds outstanding with a $1,000 face value and 10 years left until maturity. They have an 11% annual coupon payment, and their current price is $1,175. The bonds may be called in 5 years at 109% of face value (Call price = 41,090).

a. What is the yield to maturity?

b. What is the yield to call if they are called in 5 years?

c. Which yield might investors expect to earn on these bonds? Why?

d. The bond's indenture indicates that the call provision gives the firm the right to call the bonds at the end year beginning in Year 5. In Year 5, the bonds may be called at 109% of face value; but in each of the next 4 year, the call percentage will decline by 1%. Thus, in Year 6, they may be called at 108% of face value; in Year 7, they may be called at 107% of face value; and so forth. If the yield curve is horizontal and interest rates remain at their current level, when is the latest that investors might expect the firm to call the bonds?