# Bonds stocks and reserve requirements

1. Johnson Motors' bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1000 par value, and the coupon rate is 8%. The bonds have a yield to maturity of 9%. What is the current market price of these bonds?

2. A 10-year, 12% semiannual coupon bond with a par value of $1000 sells for $1100. What is the bond's yield to maturity?

3. Galen Corporation has a bond issue outstanding with an annual coupon rate of 7 percent paid quarterly and 4 years remaining until maturity. The par value of the bond is $1000. Determine the current value of the bond if market conditions justify a 14 percent, compound quarterly, required rate of return.

4. A bond you are evaluating has a 10 percent coupon rate (compounded semiannually), a $1000 face value, and is 10 years from maturity.

a. If the required rate of return on the bond is 6%, what is its present value?

b. If the required rate of return on the bond is 8%, what is its present value?

c. What do your answers to parts a and b say about the relation between required rates of return and fair values.

5. Calculate the fair present value of the following bonds, all of which have a 10% coupon rate (paid semiannually), face value of $1000, and a required rate of return of 8 percent.

a. The bond has 10 years remaining to maturity.

b. The bond has 15 years remaining to maturity.

c. The bond has 20 years remaining to maturity.

d. What do your answers to parts a and c say about the relation between time to maturity and present values.

6. Repeat parts a through c of question 5 using a required rate of return on the bond of 11 percent. What do your calculations imply about the relation between time to maturity and bond price volatility?

7. A. What is the duration of a two year bond that pays an annual coupon of 10 percent and has a current yield to maturity of 12 percent? Use $1000 as the face value.

B. What is the duration of a two-year zero-coupon bond that is yielding 11.5%? Use $1000 as the face value.

C. Given these answers, how does duration differ from maturity?

8. Consider the following.

a. What is the duration of a five year Treasury bond with a 10% semiannual coupon selling at par?

b. What is the duration of the above bond if the yield to maturity increases to 14 percent? What if the ytm increases to 16 percent?

c. What can you conclude about the relationship between duration and yield to maturity?

9. An insurance company is analyzing the following three bonds, each with 5 years to maturity, and is using duration as its measure of interest rate risk:

a. $10000 par value, coupon rate = 8%, ytm = .10

b. $10000 par value, coupon rate = 10%, ytm = .10

c. $10000 par value, coupon rate = 10%, ytm = .10

10. Calculate the present value on a stock that pays $5 in dividends per year (with no growth) and has a required rate of return of 10 percent.

11. Bank Three currently has $600 million in transaction deposits on its balance sheet. The federal reserve has currently set the reserve requirement at 10 percent of transaction deposits.

a. If the federal reserve decreases the reserve requirement to 8 percent, show the balance sheet of Bank Three and the Federal Reserve System just before and after the full effect of the reserve department change. Assume Bank Three withdraws all excess reserves and gives out loans, and that borrowers eventually return all of these funds to Bank Three in the form of transaction deposits.

b. Redo part (a) using a 12 percent reserve requirement.

#### Solution Summary

Answers questions on bonds on bonds (current market price, yield to maturity, required rate of return, duration, interest rate risk), stocks (present value) and reserve requirements.