Use the information for the question(s) below. The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 15 years. The bond certificate indicates that the stated coupon rate for this bond is 8% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 7.5%, then the price that this bond trades for will be closest to:

$1,044.57

Explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond. We calculate the present value of both the coupon payment and the maturity payment.

According to given data

Face value of the bond is $1,000

Coupon payment = C = $1,000 x 8% = $80 annually = $40 semiannually

Number of periods = n = 15 years x 2 = 30 period

YTM =  7.5% annually = 3.75% semiannually

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond = $40 x [ ( 1 - ( 1 + 3.75% )^-30 ) / 3.75% ] + [ $1,000 / ( 1 + 3.75% )^30 ]

Price of the Bond = $713.17 + $331.40 = $1,044.57

The price of the bond will be closest $1,0445

Explanation:

Face value $1000, years to maturity 15 years , coupon rate 8% paid semi annually, YTM 80%

Semiannual

n = 15*2 = 30

coupon payments = 8%*1000/2 = $40

YTM = 7.5%/2 = 3.75%

Value of a bond is equal the present value of coupon payments and present value of face value at maturity

Bond Price = C* [1-(1+r)^-n/r] + FV/ (1+r)^n

                  = 40 * [1-(1+0.375)^-30/0.0375] + 1000/(1+0.0375)^30

                  =713.1698 +331.4033

                  = $1,044.57

     Therefore when rounding of the price of this bond is closest to $1,0445          

the correct option is c