Question

Prices of zero-coupon bonds reveal the following pattern of forward rates: Year Forward Rate 1 5 % 2 6 3 7 In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $50 with par value $1,000. a. What is the price of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

The price of the coupon bond is $ 1,232.30

Step-by-step explanation:

The forward rates are:

year 1 5%

year 2 6%

year 3 7%

In determining the price of the bond,we discount the coupon and the face value of the bond as below:

price=coupon/(1+f1)+coupon/(1+f1)*(1+f2)+(coupon+face value)/(1+f1)*(1+f2)*(1+f3)

price=50/(1+5%)+50/(1+5%)*(1+6%)+1050/(1+5%)*(1+6%)*(1+7%)=$1,232.30

The price of the bond using the forward rates provided is $ 1,232.30

This implies that an increasing forward rates led to the bond been issued at a premium of $232.30 when compared to its face value of $1000 i.e $ 1,232.30-$1,000.00