Assume you have a one-year investment horizon and are trying to choose among thr

Question

Assume you have a one-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 7.2% coupon rate and pays the $72 coupon once per year. The third has a 9.2% coupon rate and pays the $92 coupon once per year.

a. If all three bonds are now priced to yield 7.2% to maturity, what are their prices? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Zero 7.2% Coupon 9.2% Coupon

Current prices $

b-1. If you expect their yields to maturity to be 7.2% at the beginning of next year, what will their prices be then? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Zero 7.2% Coupon 9.2% Coupon

Price one year from now $ $ $

b-2. What is your rate of return on each bond during the one-year holding period? (Do not round intermediate calculations.Round your answers to 2 decimal places.) Zero 7.2% Coupon 9.2% Coupon

Rate of return % % %

Explanation / Answer

a) Bond 1

Price = par value/(1 +YTM)^N = 1000/(1+0.072)^10 = 498.944

Bond 2

K = N           
BOND PRICE= [(Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N
                   k=1

                    K = 10           
BOND PRICE= [(7.2*1000/100)/(1 + 7.2/100)^k]     +   1000/(1 + 7.2/100)^10
                   k=1

= 1000

Bond 3

K = N           
BOND PRICE= [(Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N
                   k=1

                    K = 10           
BOND PRICE= [(9.2*1000/100)/(1 + 7.2/100)^k]     +   1000/(1 + 7.2/100)^10
                   k=1

=1139.18

2) Price after 1 year

Bond 1

Price = par value/(1 +YTM)^N = 1000/(1+0.072)^9 = 534.87

Bond 2

K = N           
BOND PRICE= [(Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N
                   k=1

                    K = 9   
BOND PRICE= [(7.2*1000/100)/(1 + 7.2/100)^k]     +   1000/(1 + 7.2/100)^9
                   k=1

= 1000

Bond 3

K = N           
BOND PRICE= [(Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N
                   k=1

                    K = 9   
BOND PRICE= [(9.2*1000/100)/(1 + 7.2/100)^k]     +   1000/(1 + 7.2/100)^9
                   k=1

=1129.2

Rate of return:

((end of year price + coupon)/beginning of year price)-1)*100

Bond 1

((534.87+0)/498.944)-1)*100 = 7.2%

Bond 2

((1000+72)/1000)-1)*100 = 7.2%

Bond 3

((1129.2+92)/1139.18)-1)*100 = 7.2%

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