Question

Consider two 5-year bonds: one has an 5% coupon rate and sells for $98; the other has an 8% coupon rate and sells for $109. What is the price of a 5-year zero coupon bond? (Assume that coupons are paid annually, and the face values of all the bonds are $100.)

(Keep your answer to 2 decimal places, e.g. xx.12.)

Answer 1

Bond 1:

Par Value = $ 100, Coupon Rate = 5% and Coupon Frequency = Annual, Tenure = 5 years and price = $ 98

Annual Coupon = 0.05 x 100 = $ 5

Let the yield to maturity be y1

Therefore, 98 = 5 x (1/y1) x [1-{1/(1+y1)^(5)}] + 100 / (1+y1)^(5)

Using EXCEL's Goal Seek Function/hit and trial method/a financial calculator to solve the above equation, we get:

y1 = 0.05468 or 5.468 %

Bond 2:

Par Value = $ 100, Coupon Rate = 8% and Coupon Frequency = Annual, Tenure = 5 years and price = $ 109

Annual Coupon = 0.08 x 100 = $ 8

Let the yield to maturity be y2

Therefore, 109 = 8 x (1/y2) x [1-{1/(1+y2)^(5)}] + 100 / (1+y2)^(5)

Using EXCEL's Goal Seek Function/hit and trial method/a financial calculator to solve the above equation, we get:

y2 = 0.05871 or 5.871 %

Average Yield of a 5 year bond = (5.871 + 5.468) / 2 = 5.6695 %

Price of a 5 year zero coupon bond = 100 / (1.056695)^(5) = $ 75.9017 ~ $ 75.90