Chapter 16, Problem 21P

1. and 2.

To determine

Prepare a schedule to show the impact of the assumed conversion of each convertible security on diluted earnings per share and also show the manner by which the securities that are included in the diluted earnings per share are ranked.

Explanation of Solution

Earnings per share (EPS): The amount of net income available to each shareholder per common share outstanding is referred to as earnings per share (EPS).

Prepare a schedule to show the impact of the assumed conversion of each convertible security on diluted earnings per share.

Convertible security	Impact in ($)	Ranking
10.2% bonds (1)	$2.55	5
12.0% bonds (3)	$1.71	3
9.0% bonds (5)	$1.51	2
8.3% preferred stock (6)	$2.13	4
7.5% preferred stock (7)	$1.25	1

(Table 1)

Working notes:

(1) Calculate the impact of the 10.2% bonds on diluted earnings per share.

$\begin{array}{c}\text{Diluted earnings per share =}\frac{\left(\begin{array}{l}\text{Net income obtained on 10}\text{.2\% bonds}\times \\ \text{Corporation income tax rate}\end{array}\right)}{\left(\begin{array}{l}\text{Number of shares of bonds}\\ \text{ convertible into common stock }\end{array}\right)}\\ =\frac{\left(\$200,000\times 10.2\%\right)\times \left(1-30\%\right)}{200\times 28}\\ =\frac{\$20,400}{5,600}\\ =\$2.55\end{array}$

(2) Calculate the Premium on amortized bond for 20 year life:

$\begin{array}{c}\begin{array}{l}\text{Premium on amortized }\\ \text{bond for 20 year life}\end{array}\}\text{ =Carrying value }-\text{Face}\text{value}\\ =\$160,000\times 110\%-\$160,000\\ =\$176,000-\$160,000\\ =\$16,000\end{array}$

(3) Calculate the impact of the 12.0% bonds on diluted earnings per share.

$\begin{array}{c}\text{Diluted earnings per share =}\frac{\left(\left(\begin{array}{l}\text{Net income on 12}\text{.0\%}\\ \text{ bonds}-\text{Value of bonds}\\ \text{ when premium }\\ \text{is amortized (2)}\end{array}\right)\times \left[\begin{array}{l}\text{Corporation income}\\ \text{ tax rate}\end{array}\right]\right)}{\left(\begin{array}{l}\text{Number of shares of bonds}\\ \text{ convertible into common stock }\end{array}\right)}\\ =\frac{\left(\$160,000\times 12.0\%-(\$800)\right)\times \left(1-30\%\right)}{160\times 47}\\ =\frac{\left(\$19,200-\$800\right)\times 0.7}{7,520}\\ =\frac{\$12,880}{7,520}\end{array}$

$\text{ = \$1}\text{.71}$

(4) Calculate the discount on amortized bond for 10 year life:

$\begin{array}{c}\begin{array}{l}\text{Discount on amortized }\\ \text{bond for 10 year life}\end{array}\}\text{ = Carrying value }-\text{ Face value}\\ =\$200,000\times 95\%-\$200,000\\ =\$10,000\end{array}$

(5) Calculate the impact of the 9.0% bonds on diluted earnings per share.

$\begin{array}{c}\text{Diluted earnings per share =}\frac{\left(\left(\begin{array}{l}\text{Net income on 9}\text{.0\%}\\ \text{ bonds+Value of bonds}\\ \text{ when discount}\\ \text{is amortized (4)}\end{array}\right)\times \left[\begin{array}{l}\text{Corporation income}\\ \text{ tax rate}\end{array}\right]\right)}{\left(\begin{array}{l}\text{Number of shares of bonds}\\ \text{ convertible into common stock }\end{array}\right)}\\ =\frac{\left(\$200,000\times 9.0\%+(\$1,000)\right)\times \left(1-30\%\right)}{200\times 44}\\ =\frac{\left(\$18,000+\$1,000\right)\times 0.7}{8,800}\\ =\frac{\$13,300}{8,800}\end{array}$

$\text{ = \$1}\text{.51}$

(6) Calculate the impact of the 8.3% preferred stock on diluted earnings per share.

$\begin{array}{c}\text{Diluted earnings per share =}\frac{\text{Net income obtained on preferreds stock of 8}\text{.3\%}}{\left(\begin{array}{l}\text{Number of shares of preferred }\\ \text{stock converted into common stock }\end{array}\right)}\\ =\frac{120,000\times 8.3\%}{1,200\times 3.9}\\ =\frac{\$9,960}{4,680}\\ =\$2.13\end{array}$

(7) Calculate the impact of the 7.5% preferred stock on diluted earnings per share.

$\begin{array}{c}\text{Diluted earnings per share =}\frac{\text{Net income obtained on preferreds stock of 7}\text{.5\%}}{\left(\begin{array}{l}\text{Number of shares of preferred }\\ \text{stock converted into common stock }\end{array}\right)}\\ =\frac{180,000\times 7.5\%}{1,800\times 6}\\ =\frac{\$13,500}{10,800}\\ =\$1.25\end{array}$

3. and 4.

To determine

Calculate the basic earnings per share and diluted earnings per share.

Explanation of Solution

Calculate the basic earnings per share and diluted earnings per share.

(Figure 1)

Working notes:

(8) Calculate the numerator for the basic earnings per share:

$\begin{array}{c}\text{Numerator earnings per share = Net income }-\text{Preferred dividend}\\ =\$119,460-(\$9,960+\$13,500)\\ =\$96,000\end{array}$

5.

To determine

Identify the amount that will be reported as basic and diluted earnings per share for the year 2016.

Explanation of Solution

The Company W must report an amount of $2.40 as basic earnings per  share and $2.20 as diluted earnings  per share in its 2016 income statement.