Question

1. Price each bond and explain how the number of years to maturity and the coupon rate affect the current price of bonds. Assume a YTM of 7%.
   1. A 4-year bond with a 9% annual coupon
   2. A 4-year bond with a zero coupon
   3. A 15-year bond with a 9% annual coupon
   4. A 15-year bond with a zero coupon

The following content is partner prov

Answer 1

Price of each bond = present value of the future cash flows of the bond using its YTM as the discount rate.

(1): Annual coupon = 9% of 1000 = $90. Thus price = 90/1.07 + 90/1.07^2 + 90/1.07^3 + 1090/1.07^4

= $1,067.74

(2): Here there will be no coupons and so price = 1000/1.07^4

= $762.90

(3): Annual coupon = 9% of 1000 = $90. Thus price = 90/1.07 + 90/1.07^2 + 90/1.07^3+..........90/1.07^15 + 1000/1.07^15

= $1,182.16

(4): Here price = 1000/1.07^15

= $362.45

There is a direct relationship between coupon rate and price of bonds. The higher is the coupon rate the higher will be the price of a bond. This is because higher coupons will lead to higher amount of cash flows. With regards to number of years to maturity it should be noted that for coupon paying bonds the higher the number of years to maturity the higher will be the price. However in case of zero coupon bonds the higher the number of years to maturity the lower will be the price.