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Suppose that 5-year government bonds are selling at a yield of 4%. What is the value of a 5-year bond with a 6 percent coupon? Start by assuming that the bond makes annual coupon payments. Then reworks your answer assuming that the bonds pay semi-annual coupons and the yield refers to a semi-annual compounded rate. How would the bond value you found above change if interest rates fall to 3 percent?
Solution:
Annual Coupon Payments
Assuming the face-value is $1000 for a Period of 5 years and bond yield = 4%
(Annual) coupon payments = 1000 * 6% = 60
Now, we use the Price of bond formula to calculate the present value of the coupons and then sum the present value of the face value:
Price of Bond = PV(bond) =PV(coupons)+PV (Final Payment of Face Value)
PV (bond) = 60 * [ 1/.04 – 1/.04*(1.04) ^5] + 1000/ (1.04) ^5
= $1089.04
Suppose instead these bonds pay semi-annually coupons and the yield is the semi-annual compounded ratePeriod = 5 years to 10 semesters
Yield = 4% to 2% semi-annual
Coupon payments = semi-annual = 1,000*3% = 30
Price of bond = PV (Bond) = 30* [1/.02-1/.02*(1.02) ^10)] + 1000/ (1.02) ^10 =
= $1089.83
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