Mr Katz is in the widget business. He currently sells 2 million widgets a year a

Question

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-asset 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 cost 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.

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a. Compute earnings per share under the Katz plan.

b. Compute earnings per share under the Dobermab 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?

Explanation / Answer

Mr katz

Sales = 2milllion * $4 = $8 Million

Sales to asset ratio = four times

Asset = $8million / 4 = $2million

Asset financed with debt = $2 million * 40% = $ 0.8 million

Interest on debt = 0.8million * 9% = $72000

Asset financed with common stock = $2 million - $0.8 million = $1.2 million

Number of shareholders = $1.2million / $10 = 120000

Computation of Profit

Sales = $8000000

Less-variable cost= $6000000

Less– fixed cost= $1500000

EBIT = $500000

Less–interest expense = $72000

EBT = $428000

Less- tax = 128400

Earnings available for equity shareholders= 299600

Earnings per share = earnings available for equity shareholders / number of equity share

Earnings per share under katz paln = 299600/120000

= $2.5 (approx)

Mr. Doberman

Sales = 2milllion(1+0.4) * $3.75 = $10.5 Million

Sales to asset ratio = five times

Asset = $10.5million / 5 = $2.1million

Asset financed with debt = $2.1 million * 50% = $ 1.05 million

Interest on debt = 1.05million * 10% = $105000

Asset financed with common stock = $2.1 million - $1.05 million = $1.05 million

Number of shareholders = $1.05million / $10 = 105000

Computation of Profit

Sales = $10500000

Less-variable cost= $6000000

Less– fixed cost= $1500000

EBIT = $3000000

Less–interest expense = $105000

EBT = $2895000

Less- tax = 869500

Earnings available for equity shareholders= 2026500

Earnings per share = earnings available for equity shareholders / number of equity share

Earnings per share under Doberman paln = 2026500/105000

= $19.3

c) Mr. Katz's wife

Fixed costs would remain constant under the Doberman plan but that they would go up by 20 percent

EBT = 2595000

Less- tax = 778500

Earnings available for equity shareholders= 1816500

Earnings per share = earnings available for equity shareholders / number of equity share

Earnings per share under katz paln = 1816500/105000

= $17.3

Yes, Mr. Katz should shift to the Doberman plan, based on earnings per share

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