Question

Company A’s bonds have 10 years to maturity with $1000 par value, assume that this bond pays coupon interest of 9% with semiannual compounding. YTM is 10%. What is bond’s current price?   Answer to the nearest cent, xxx.xx and enter without the dollar sign.

Answer 1

Given the following information,

Coupon rate = 9% = 0.09

Number of compounding periods = semiannual = 2

Years to maturity = 10

Semi annual periods = N = Years to maturity*Number of compounding periods

= 10*2

= 20

Face value = $1000

YTM = yield to maturity = 10% = 0.10

Semiannual rate = y = 0.10/2 = 0.05

Method 1:

We know that, price of the bond is calculated by using the following formula,

P = CPN*(1/y)*(1-(1/(1+y)^N)) + FV/ (1+y)^N

Where,

CPN = Coupon Payment = (Coupon rate*Face value)/ Number of coupon payments in a year

CPN = (0.09*1000)/ 2

CPN = 45

Substituting the above given values in the equation we get,

P = 45*(1/0.05)*(1-(1/(1+0.05)^20)) + 1000/ (1+0.05)^20

P = 45*(1/0.05)*(1-(1/(1.05)^20)) + 1000/ (1.05)^20

P = 45*(20)*(1-(1/2.6533)) + 1000/ 2.6533

P = 45*(20)*(1-0.3769) + 1000*0.3769

P = 45*(20)*(0.6231) + 1000*0.3769

P = 560.80 + 376.89

P = 937.69

Method 2:

Calculation of bonds current price using excel,

Therefore, by either method, the current price of the bond is 937.69