Question

A 3.375%, 10-year bond with semi-annual coupon payments and a face value of $10,000 has just been sold at par. a. What are the cash flows to the bond? b. What is the (annual) required return on the bond? Hint: 1. Hint: APR vs EAR c. If a 10-year zero-coupon bond were marketed at the same required return as in part b), what would be the price of a $10,000 face value bond? d. Immediately after issuance, if the required return increases by 0.50% per year, compounded semi-annually, what will be the new price of the coupon bond? (Note: this is a one-time increase of 0.50%, not a continuing series of increases.) e. What would happen to the price of the 10-year zero-coupon bond with a face value of $10,000 given this change in interest rate? f. What is the percentage change in the coupon bond, given the change in interest rates? g) What is the percentage change in the zero-coupon bond, given the change in interest rates? h) What causes the difference in the answers to part f) and part g)?

Answer 1

a) coupon payment:

10,000 x 3.375% / 2 = $168.75 per coupon

b) the rate of return is:

0.034034766 = 3.40%

c) $7,155.6418

d) $9,588.7378

e) it would also decrease his value. To $ 6,984.9173

f) 10,000 / 9,588.74 - 1 = 4.29%

g) 9,588.74 / 6,984.92 - 1 = 37.27%

h) The zero bond coupon only considers the maturity value which is completely influence by the change in rate. The normal bond also has coupon payment which are less affected for the change in rate as they are spread over the life of the bond. The next coupon payment is only affected by 6 month not the complete 10 years period for example.

Step-by-step explanation:

b)

`(1+r_n/2)^2 -1 = r_e\\Where:\\r_n = $ the bond coupon rate\\r_e = $ effective rate`

(1+0.03375/2)^2-1 = 0.034034766

c)

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 10,000.00

time 10.00

rate 0.03403

`(10000)/((1 + 0.034034766)^(10) ) = PV`

PV 7,155.6418

d) we recalcualte the present value considering the new rate

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 168.750

time 20

rate 0.019375

`168.75 * (1-(1+0.019375)^(-20) )/(0.019375) = PV\\`

PV $2,776.0195

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 10,000.00

time 20.00

rate 0.019375

`(10000)/((1 + 0.019375)^(20) ) = PV`

PV 6,812.72

PV c $2,776.0195

PV m $6,812.7183

Total $9,588.7378

e)

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 10,000.00

time 10.00

rate 0.03653

`(10000)/((1 + 0.036534766)^(10) ) = PV`

PV 6,984.9173