Question

Complete the below table to calculate the price of a $1.9 million bond issue under each of the following independent assumptions (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.):

1. Maturity 12 years, interest paid annually, stated rate 10%, effective (market) rate 12%.
2. Maturity 9 years, interest paid semiannually, stated rate 10%, effective (market) rate 12%.
3. Maturity 6 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%.
4. Maturity 20 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%.
5. Maturity 10 years, interest paid semiannually, stated rate 12%, effective (market) rate 12%.

Answer 1

1. Maturity 12 years, interest paid annually, stated rate 10%, effective (market) rate 12%:

Interest payment = $1,900,000 x 10% = $190,000

Present value of interest payment	$1,176,930
[$190,000 x 6.19437 present value annuity factor (12%, 12 years)]
Present value of face value of the bonds payable	$487,692
[$1,900,000 x 0.25668 present value factor (12%, 12 years)]
Issue price of the bonds	$1,664,622

2. Maturity 9 years, interest paid semiannually, stated rate 10%, effective (market) rate 12%:

Interest payment = $1,900,000 x 10% x 6/12 = $95,000

Present value of interest payment	$1,028,622
[$95,000 x 10.82760 present value annuity factor (6%, 18 years)]
Present value of face value of the bonds payable	$665,646
[$1,900,000 x 0.35034 present value factor (6%, 18 years)]
Issue price of the bonds	$1,694,268

3. Maturity 6 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%.:

Interest payment = $1,900,000 x 12% x 6/12 = $114,000

Present value of interest payment	$880,277
[$114,000 x 7.72173 present value annuity factor (5%, 12 years)]
Present value of face value of the bonds payable	$1,166,429
[$1,900,000 x 0.61391 present value factor (5%, 12 years)]
Issue price of the bonds	$2,046,706

4. Maturity 20 years, interest paid semiannually, stated rate 12%, effective (market) rate 10%.:

Interest payment = $1,900,000 x 12% x 6/12 = $114,000

Present value of interest payment	$1,956,136
[$114,000 x 17.15909 present value annuity factor (5%, 40 years)]
Present value of face value of the bonds payable	$269,895
[$1,900,000 x 0.14205 present value factor (5%, 40 years)]
Issue price of the bonds	$2,226,031

5. Maturity 10 years, interest paid semiannually, stated rate 12%, effective (market) rate 12%.:

Stated rate and effective interest rate is same. So, No change in bond issue price

Thus, issue price of the bonds is $1,900,000