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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