Snap Slug Sound Engineering Company needs to raise some funds to pay for expansion. They issue $12,000,000 worth of 9 year debentures paying interest at 12.25% pa payable semi-annually. When the debentures are issued, interest rates in the debt-capital market are j2 = 12.5% pa compounded semi-annually. Calculate the amount of capital raised.
A "debenture" is essentially a "bond" and is priced as such:
1 - Find the PV of the $12,000,000 par value using the market rate of 12.50%.
2 - Find the PV of the semi-annual coupons at the market rate of 12.50%
3 - Add the two together to get the amount of money raised.
PV of the par value of $100 at maturity =$33.580.
PV of the semi-annual coupons =$65.092
Price of the debenture =$33.580 + $65.092 =$98.672 per $100.
$98.672/100 x $12,000,000 =$11,840,640 - amount of capital raised.