A company has variable costs of $22.50, total fixed costs of $21,700,000 and pla

Question

A company has variable costs of $22.50, total fixed costs of $21,700,000 and plans to sell its product for $38.00. In 2015 it sold 2,200,000 units of product. Required: a) breakeven in units and dollars; b) assume management wants to earn $5,000,000 in operating income, how many units must be sold; c) assume income tax rates are 35% of pre-tax income and management wants to earn $3,000,000 after tax- how many units are required; d) for 2015 what is the margin of safety in dollars and percentage; e) what is the operating leverage in 2015.

Explanation / Answer

Contrubution margin = Selling price per unit - variable cost per unit = 38 - 22.50 = $15.50 per unit

(A)

Break even (in units) = Fixed cost / contribution magin per unit = 21,700,000 / 15.50 = 1,400,000 units

Break even in dollars = Break even in units * selling price = 1,400,000 * 38 = $53,200,000

(B) Units to be sold = (Fixed cost + operating income )/ Contribution margin

Units to be sold = (21,700,000 + 5,000,000) / 15.50 = 1,722,580.65 units or 1,722,581 units (approx)

(C) Pre tax Income tax = 3,000,000 / .65 = $4,615,384.62

Units to be sold = (Fixed cost + Pre tax income )/ Contribution margin

Units to be sold = (21,700,000 + 4,615,384.62) / 15.50 = 1,697,766.75 units or 1,697,767 units (approx)

(D) Margin of safety in $= Actual sales - Breakeven sales

Margin of safety in $ =2,200,000 * 38 - $53,200,000 =$30,400,000

Margin of safety in percentage = margin of safety in Dollar / actual sales

= $30,400,000 / 83,600,000 = 36.36%

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