Question

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 \(1,550,000 in fixed costs. His sales-to-assets ratio is six times, and 30 percent of his assets are financed with 10 percent debt, with the balance financed by common stock at \)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.

b. Compute earnings per share under the Silverman plan.

Short answer

EPS of the company under the silverman plan is $0.62

Step-by-step solution

Sale under silver man plan

$$\begin{gathered} \mathbf{Sales}\mathbf{=}\mathbf{Existingsaleunit}\left(\mathbf{1}\mathbf{+}\mathbf{Increament}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{1}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}\left(\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{60}\right) \\ \mathbf{=}\mathbf{2}\mathbf{,}\mathbf{400}\mathbf{,}\mathbf{000} \end{gathered}$$

Total assets of the company

$$\begin{gathered} \mathbf{Totalassets}\mathbf{=}\frac{\mathbf{Sales}}{\mathbf{Saletoassetratio}} \\ \mathbf{=}\frac{\left(\mathbf{2}\mathbf{,}\mathbf{400}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{\$}\mathbf{5}\right)}{\mathbf{7}\mathbf{.}\mathbf{50}} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000} \end{gathered}$$

Interest on debt

$$\begin{gathered} \mathbf{Interestondebts}\mathbf{=}\mathbf{Debtamount}\mathbf{\times }\mathbf{Interestrate} \\ \mathbf{=}\left(\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{50}\mathbf{\%}\right)\mathbf{\times }\mathbf{11}\mathbf{\%} \\ \mathbf{=}\mathbf{\$}\mathbf{88}\mathbf{,}\mathbf{000} \end{gathered}$$

Number of shares

$$\begin{gathered} \mathbf{Numberofshares}\mathbf{=}\frac{\mathbf{Sharecapital}}{\mathbf{Parvalue}} \\ \mathbf{=}\frac{\left(\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{50}\mathbf{\%}\right)}{\mathbf{\$}\mathbf{10}} \\ \mathbf{=}\mathbf{800}\mathbf{,}\mathbf{000} \end{gathered}$$

EPS

Particulars	Amount ($)
Sales (2,400,000 x $5)	12,000,000
Less: Variable cost (2,400,000 x $4)	9,600,000
Contribution	2,400,000
Less: fixed cost	1,550,000
EBIT	850,000
Less: Interest cost	88,000
EBT	762,000
Less: Tax @35%	266,700
EAT	495,300
Number of shares	800,000
EPS	0.62