Question

Karen Austin Inc. has issued three types of debt on January 1, 2017, the start of the company’s fiscal year.

1. \(10 million, 10-year, 15% unsecured bonds, interest payable quarterly. Bonds were priced to yield 12%.
2. \)25 million par of 10-year, zero-coupon bonds at a price to yield 12% per year.
3. $20 million, 10-year, 10% mortgage bonds, interest payable annually to yield 12%.

Instructions

Prepare a schedule that identifies the following items for each bond: (1) maturity value, (2) number of interest periods over life of bond, (3) stated rate per each interest period, (4) effective-interest rate per each interest period, (5) payment amount per period, and (6) present value of bonds at date of issue.

Short answer

Particulars	15% Unsecured Bonds (a)	Zero-coupon Bonds (b)	10% Mortgage Bonds (c)
Present value	$11,733,639	$8,049,250	$17,739,840

Step-by-step solution

Meanings of Bonds

Bonds refer to a type of investment security where an investor provides money or loan to the company for a particular period and, in return, gets the fixed interest rate (coupon) and the principal amount at the maturity date.

Preparing a Schedule for 15% unsecured bonds, zero-coupon bonds, and 10% mortgage bonds.

Sr. no.	Particular	15% Unsecured Bonds	Zero-coupon Bonds	10% Mortgage Bonds
1	Maturity value	$10,000,000	$25,000,000	$20,000,000
2	Number of interests periods	40	10	10
3	Stated rate per period	$\left(\frac{15\%}{4}\right)$ 3.75 %	0	10%
4	Effective rate per period	$\left(\frac{12\%}{4}\right)$ 3%	12%	12%
5	Payment amount per period	$375,000	0	$2,000,000
6	Present value	$11,733,639	$8,049,250	$17,739,840

Working notes:

Calculation of payments amount per bond for 15% unsecured bond.

$\begin{array}{rcl}\mathbf{Payments}\mathbf{}\mathbf{amount}\mathbf{}\mathbf{per}\mathbf{}\mathbf{period}& \mathbf{=}& \mathbf{Maturity}\mathbf{}\mathbf{value}\mathbf{\times }\mathbf{Bond}\mathbf{}\mathbf{rate}\mathbf{\times }\mathbf{Interest}\mathbf{}\mathbf{payable}\mathbf{}\mathbf{quaterly}\\ & \mathbf{=}& \mathbf{\$}\mathbf{10}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{15}\mathbf{\%}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{4}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{375}\mathbf{,}\mathbf{000}\end{array}$

Calculation of payments amount per bond for 10% mortgage bond.

$\begin{array}{rcl}\mathbf{Payments}\mathbf{}\mathbf{amount}\mathbf{}\mathbf{per}\mathbf{}\mathbf{period}& \mathbf{=}& \mathbf{Maturity}\mathbf{}\mathbf{value}\mathbf{\times }\mathbf{Bond}\mathbf{}\mathbf{rate}\mathbf{}\\ & \mathbf{=}& \mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{10}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{000}\end{array}$

Calculation of Present value for 15% unsecured bond

Present value of an annuity of $375,000 discounted at 3% per period for 40 periods $\left(\$375,000\times 23.11477\right)$	$8,668,039
Present value of $10,000,000 discounted at 3% per period for 40 periods at 3% per periods for 40 periods $\left(\$10,000,000\times 0.30656\right)$	3,065,600
	$11,733,639

Calculation of Present value for a zero-coupon bond

Present value of $25,000,000 discounted at 12% per period for 10 periods at 12% for 10 periods data-custom-editor="chemistry" $\left(\$25,000,000\times 0.32197\right)$	$8,049,250

Calculation of Present value for a 10% mortgage bond

Present value of an annuity of $2,000,000 discounted at 12% per for 10 periods $\left(\$2,000,000\times 5.65022\right)$	$11,300,440
Present value of $20,000,000 discounted at 12% per period for 10 years $\left(\$20,000,000\times 0.32197\right)$	6,439,400
	$17,739,840