Question

A bond that matures in 17 years has a ​$1 000 par value. The annual coupon interest rate is 14 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 17 percent.

What would be the value of this bond if it paid interest​ annually? ______

What would be the value of this bond if it paid interest​ semiannually? _______

Answer 1

Calculation for annual interest payment:

Par value is $1000
Time period is 17 years
Annual coupon rate is 14%
Annual coupon payment =(Coupon rate)*(Par value)=(14%)*(1000)=140
Yield to maturity=17%

We can determine the present value using excel as:

Answer: If the interest is paid annually, then the value of the bond will be equal to $835.76.

B 1000 17 А 1 Par value 2 Time period 3 Payment 4 Yield to maturity 5 Present value= 6 Formula used: 140 17% ($835.76 PV(B4,B2,B3,B1)

Calculation for semiannual interest payment:

Par value is $1000
Time period is 17 years, as the interest is paid semiannually, the number of periods=17*2=34

Semi annual coupon payment=(Annual coupon payment)/2=140/2=70
Annual yield to maturity=17%
Semiannual yield to maturity=17%/2=0.085
We can determine the present value using excel as:

F 1000 34 E 1 Par value 2 Time period 3 Payment 4 Yield to maturity 5 Present value= 6 Formula used: 70 0.085 ($834.55) PV(F4,F2, F3,F1)

Answer: If the interest is paid semi annually, then the value of the bond will be equal to $834.55