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