Answer:
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
