91Ó°ÊÓ

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.

c. Mr. Gold’s wife, the chief financial officer, does not think that fixed costs

would remain constant under the Silverman plan but that they would go up

by 15 percent. If this is the case, should Mr. Gold shift to the Silverman

plan, based on earnings per share?

Step by step solution

01

Sale under silverman plan

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

02

Total assets of the company

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

03

Interest on debt

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

04

Number of shares

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

05

Fixed cost

$$\begin{gathered} \mathbf{Fixedcost}\mathbf{=}\mathbf{Existingfixedcost}\left(\mathbf{1}\mathbf{+}\mathbf{Increament}\mathbf{\%}\right) \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{550}\mathbf{,}\mathbf{000}\left(\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{15}\right) \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{782}\mathbf{,}\mathbf{500} \end{gathered}$$

06

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	1,782,500
EBIT	617,500
Less: Interest cost	88,000
EBT	529,500
Less: Tax @35%	185,325
EAT	344,175
Number of shares	800,000
EPS	0.43

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