Question

DeSoto Tools Inc. is planning to expand production. The expansion will cost \(300,000, which can be financed either by bonds at an interest rate of 14 percent or by selling 10,000 shares of common stock at \)30 per share. The current income statement before expansion is as follows:

DeSOTO TOOLS, INC.
Sales		\(1,500,000
Less: Variable cost	\)450,000
Fixed cost	550,000	1,000,000
Earning before interest and taxes		\(500,000
Less: Interest expenses		100,000
Earning before taxes		\)400,000
Less: Taxes @34%		136,000
Earning after taxes		\(264,000
Shares		100,000
Earning per shares		\)2.64

After the expansion, sales are expected to increase by \(1,000,000. Variable costs will remain at 30 percent of sales, and fixed costs will increase to \)800,000. The tax rate is 34 percent.

a. Calculate the degree of operating leverage, the degree of financial leverage,

and the degree of combined leverage before expansion. (For the degree of

operating leverage, use the formula developed in footnote 2; for the degree

of combined leverage, use the formula developed in footnote 3. These

instructions apply throughout this problem.)

Short answer

Before expansion, the degree of operating leverage, financial leverage and the combined leverage is 2.10, 1.25 and 2.625, respectively.

Step-by-step solution

Degree of operating leverage

$\begin{array}{rcl}\mathrm{Degree}\mathrm{of}\mathrm{operating}\mathrm{leverage}& =& \frac{\mathrm{Sales}-\mathrm{Total}\mathrm{variable}\mathrm{cost}}{\mathrm{Sales}-\mathrm{Total}\mathrm{variable}\mathrm{cost}-\mathrm{Fixed}\mathrm{cost}}\\ & =& \frac{\$1,500,000-\$450,000}{\$1,500,000-\$450,000-\$550,000}\\ & =& 2.10\end{array}$

Degree of financial leverage

$\begin{array}{rcl}\mathrm{Degree}\mathrm{of}\mathrm{financial}\mathrm{leverage}& =& \frac{\mathrm{EBIT}}{\mathrm{EBT}}\\ & =& \frac{\$500,000}{\$400,000}\\ & =& 1.25\end{array}$

Degree of combined leverage

$\begin{array}{rcl}\mathrm{Degree}\mathrm{of}\mathrm{combined}\mathrm{leverage}& =& \frac{\mathrm{Sales}-\mathrm{Total}\mathrm{variable}\mathrm{cost}}{\mathrm{Sales}-\mathrm{Total}\mathrm{variable}\mathrm{cost}-\mathrm{Fixed}\mathrm{cost}-\mathrm{Interest}}\\ & =& \frac{\$1,500,000-\$450,000}{\$1,500,000-\$450,000-\$550,000-\$100,000}\\ & =& 2.625\end{array}$