Mr. Gold is in the widget business. He currently sells 1.5 million widgets a year at \(6 each. His variable cost to produce the widgets is \)4 per unit, and he has \(1,550,000 in fixed costs. His sales-to-assets ratio is six times, and 30 percent of his assets are financed with 10 percent debt, with the balance financed by common stock at a \)10 par value per share. The tax rate is 35 percent. His brother-in-law, Mr. Silverman, says he is doing it all wrong. By reducing his price to \(5.00 a widget, he could increase his volume of units sold by 60 percent. Fixed costs would remain constant, and variable costs would remain \)4 per unit. His sales-to-assets ratio would be 7.5 times. Furthermore, he could increase his debt-to-assets ratio to 50 percent, with the balance in common stock. It is assumed that the interest rate would go up by 1 percent, and the price of stock would remain constant.

a. Compute earnings per share under the Gold plan.

Step by step solution

01

Total assets of the company

$\begin{array}{rcl}\mathbf{Totalassets}& \mathbf{=}& \frac{\mathbf{Sales}}{\mathbf{Saletoassetratio}}\\ & \mathbf{=}& \frac{\left(\mathbf{1}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{\$}\mathbf{6}\right)}{\mathbf{6}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}\end{array}$

02

Interest on debt

$\begin{array}{rcl}\mathbf{Interestondebts}& \mathbf{=}& \mathbf{Debtamount}\mathbf{\times }\mathbf{Interestrate}\\ & \mathbf{=}& \left(\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{30}\mathbf{\%}\right)\mathbf{\times }\mathbf{10}\mathbf{\%}\\ & \mathbf{=}& \mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000}\end{array}$

03

Number of shares

$\begin{array}{rcl}\mathbf{Numberofshares}& \mathbf{=}& \frac{\mathbf{Sharecapital}}{\mathbf{Parvalue}}\\ & \mathbf{=}& \frac{\left(\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{70}\mathbf{\%}\right)}{\mathbf{\$}\mathbf{10}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{105}\mathbf{,}\mathbf{000}\end{array}$

04

EPS

Particulars	Amount ($)
Sales (1,500,000 x $6)	9,000,000
Less: Variable cost (1,500,000 x $4)	6,000,000
Contribution	3,000,000
Less: fixed cost	1,550,000
EBIT	1,450,000
Less: Interest cost	45.000
EBT	1,405,000
Less: Tax @35%	491,750
EAT	913,250
Number of shares	105,000
EPS	8.70

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