In: Accounting
Sage Hill Inc. issues $7,750,000 of 6% bonds due in 9 years with interest payable at year-end. The current market rate of interest for bonds of similar risk is 8%. What amount will Sage Hill receive when it issues the bonds?
Solution :
The amount that Sage Hill will receive when it issues the bonds is
= Present value of Interest payments for Years 1 to 9 + Present value of the Face value or Principal value of the bond
As per the information given in the question
Face value or Principal value of the bond = $ 7,750,000 ;
Interest rate or coupon rate of the bonds = 6 % ;
Thus Annual coupon payment = $ 7,750,000 * 6 % = $ 465,000 ;
The current market rate of interest for bonds of similar risk is 8% ; Thus the present value of Annual coupon payments and the present value of face value of the bonds shall be calculated by discounting them at 8 % .
Thus the amount that Sage Hill will receive when it issues the bonds shall be equal to
= $ 465,000 * PVIFA(8 %,9 ) + $ 7,750,000 * PVF(8%,9)
= ( $ 465,000 * 6.246888 ) + ( $ 7,750,000 * 0.500249 )
= $ 2,904,802.92 + $ 3,876,929.75
= $ 6,781,732.67
Therefore the amount that Sage Hill will receive when it issues the bonds = $ 6,781,732.67