Southampton Inc. issued 8% bonds with a face amount of $100 million on January 1, 2018. The bonds mature on December 31, 2032 (15 years). The market rate is 10%. Interest is paid semi-annually on June 30 and December 31. What is the present value of the bonds on January 1, 2018 (rounded to the nearest thousand)?

The present value of the bonds on January 1, 2018 is $84.63 million

Explanation:

8% coupon payment of bond for a period of 15 year at a discount rate of 10% is the an annuity. Value of this bond will be calculated by following formula

Coupon payment = 100 x 8% = $8 million annually = $4 million semiannually

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

Yield to maturity = 10% annually = 5% semiannually

Price of bond is the present value of future cash flows, to calculate Price of the bond use following formula

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

Price of the Bond = $4 million x [ ( 1 - ( 1 + 5% )^-30 ) / 5% ] + [ $100 million / ( 1 + 5% )^30 ]

Price of the Bond = $4 million x [ ( 1 - ( 1 + 0.05 )^-30 ) / 0.05 ] + [ $100 million / ( 1 + 0.05 )^30 ]

Price of the Bond = $4 million x [ ( 1 - ( 1.05 )^-30 ) / 0.05 ] + [ $100 million / ( 1.05 )^30 ]

Price of the Bond = $61.49 + $23.14 = $84.63 million

See the attached table for answer.

Explanation: