Question

Yan Yan Corp. has a $10,000 par value bond outstanding with a coupon rate of 4.8 percent paid semiannually and 22 years to maturity. The yield to maturity on this bond is 4.2 percent. What is the price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

$10,856

Step-by-step 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.

According to given data

Face value of the bond is $10,000

Coupon payment = C = $10,000 x 4.8% = $480 annually = $240 semiannually

Number of periods = n = 22 years x 2 = 44 period

YTM = 4.2% annually = 2.1% 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 = $240 x [ ( 1 - ( 1 + 2.1% )^-44 ) / 2.1% ] + [ $10,000 / ( 1 + 2.1% )^44 ]

Price of the Bond = $6,848.64 + $4007.4 = $10,856.04