# Leverage and EPS

Mr. Katz is in the widget business. He currently sells 2 million widgets a year at $4 each. His variable cost to produce the widgets is $3 per unit, and he has $1,500,000 in fixed costs. His sales-to-assets ratio is four times, and 40 percent

of his assets are financed with 9 percent debt, with the balance financed by common stock at $10 per share. The tax rate is 30 percent. His brother-in-law, Mr. Doberman, says Mr. Katz is doing it all wrong. By reducing his price to $3.75 a widget, he could increase his volume of units sold by 40 percent. Fixed costs would remain constant, and variable costs would

remain $3 per unit. His sales-to-assets ratio would be 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.

Instructions

a. Compute earnings per share under the Katz plan.

b. Compute earnings per share under the Doberman plan.

c. Mr. Katz's wife does not think that fixed costs would remain constant under the Doberman plan but that they would go up by 20 percent. If this is the case, should Mr. Katz shift to the Doberman plan, based on earnings per share?

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#### Solution Preview

a. Compute earnings per share under the Katz plan.

Katz Plan

Sales

# of units= 2,000,000

Selling Price= $4.00

Sales (amount) = $8,000,000 =2000000x4

Variable Cost per unit= $3.00

Total Variable cost= $6,000,000 =2000000x3

Total fixed cost= $1,500,000

Sales to assets ratio= 4

Therefore assets required= $2,000,000 =8000000/4

Assets financed by debt 40% $800,000 =0.4x2000000

Assets financed by equity= 60% $1,200,000 =0.6x2000000

Share price= $10.00

Therefore # of shares= 120,000

Interest rate on debt= 9%

Interest expense= $72,000 =0.09x800000

Sales= $8,000,000

Variable cost= $6,000,000

Fixed cost= $1,500,000

EBIT 500,000

-Interest (72,000) =0.09x800000

EBT 428,000 ...

#### Solution Summary

The solution calculates EPS under different financing plans. Calculations and answers are provided as a plain text response as well as formatted in the attached Excel spreadsheet.