Question

Recently, the vice president of operations of the company has requested construction of a new plant to meet the increasing demand for the company’s bicycles. After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing $3,000,000 of 11 percent corporate bonds on April 1, 2019, due on April 1, 2033. Interest is payable annually on April 1 each year. At the time the bonds were issued, the market interest rate for similar financial securities is 10 percent. Determine the selling price of the bonds.

The company, having issued the bonds in part (b), is committed to make annual sinking fund deposits of $90,000. The deposits are made on the last day of each year and yield a return on 10 percent. Will the fund at the end of 15 years be sufficient to retire the bonds? If not, what is the amount of the deficiency?

Answer 1

(b) Formula for the interest payments:
PV-OA = R (PVF-OA_n,i)
PV-OA = $165,000 (PVF-OA_14,10%)
PV-OA = $165,000 (7.3667)
PV-OA = $1,215,505.50
Formula for the principal:
PV = FV (PVF_n,i)
PV = $3,000,000 (PVF_14,10%)
PV = $3,000,000 (0.26333)
PV = $789,990
The selling price of the bonds = $1,215,505.50 + $789,990 = $2,005,495.50.
(c) Future value of an ordinary annuity of $90,000
at 10% for 14 years ($90,000 × 27.9750) = $2,517,750
Deficiency ($3,000,000 ? $2,517,750) = $482,250