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# A 20-year bond with a 7.50% semi-annual coupon bond

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I. A 20-year bond with a 7.50% semi-annual coupon bond was sold at par 10 years ago. Now the 10-year semi-annual payment corporate bond has a required return (or YTM) of 8.25%. Calculate the bond's market price. The par level of bonds is \$1000.
II. a) What is the duration of a 2-year bond with an 8.5% semi-annual coupon and a required return (YTM) of 8.00%?
b)What is the duration of a 20-year zero-coupon bond with a required return (YTM) of 8.00%?
c)You expect a sudden decrease in market rates due to a macroeconomic change. Would you rather have in your portfolio the item from a) above or b) above?
Which item would you prefer, and specifically explain the reasons why?

#### Solution Preview

I. A 20-year bond with a 7.50% semi-annual coupon bond was sold at par 10 years ago. Now the 10-year semi-annual payment corporate bond has a required return (or YTM) of 8.25%. Calculate the bond's market price. The par level of bonds is \$1000.
We need to calculate how much the bonds have been issued by using the formula as follows: -

where B is the issued price
C is the coupon payment
r is the current interest rate
n is the period

Since the bond issues 10 years ago, its remaining life is 10 years. You need to multiply the remaining life by 2 because the company pays interest semiannually.
Coupon payment is equal to \$1,000 x 7.5% = 75/2 = \$37.50
The current interest ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer what is the duration of a 2-year bond with an 8.5% semi-annual coupon and a required return (YTM) of 8.00%, what is the duration of a 20-year zero-coupon bond with a required return (YTM) of 8.00%, would you rather have in your portfolio the item from a) or b), and which item would you prefer, and specifically explain the reasons why.

\$2.19

## Bonds- Rate of Return, Price at different time periods

1. Six years ago, the Singleton Company sold a 20-year bond issue with a 14 percent annual coupon rate and a 9 percent call premium. Today, Singleton called the bonds. The bonds were originally sold at their face value of \$1,000. Compute the realized rate of return for investors who purchased the bond when they were issued and who surrender them today in exchange for the call price.

2. An investor has two bonds in his portfolio. Each bond matures in four years, has a face value of \$1,000, and has a yield to maturity equal to 9.6 percent. One bond, Bond C, pays an annual coupon of 10 percent; the other bond, Bond Z, is a zero coupon bond.

a. Assuming that the yield to maturity of each bond remains at 9.6 percent over the next 4 years, what will be the price of each of the bonds at the following time periods? Fill in the following table:

t PRICE OF BOND C PRICE OF BOND Z
____________________________________________________________
0
1
2
3
4
____________________________________________________________

b. Plot the time path of the prices for each of the two bonds.

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