The Sterling Tire Company’s income statement for 2013 is as follows: STERLING TI
ID: 2450038 • Letter: T
Question
The Sterling Tire Company’s income statement for 2013 is as follows: STERLING TIRE COMPANY Income Statement For the Year Ended December 31, 2013 Sales (32,000 tires at $84 each) $ 2,688,000 Variable costs (32,000 tires at $42) 1,344,000 Fixed costs 520,000 Earnings before interest and taxes (EBIT) $ 824,000 Interest expense 56,000 Earnings before taxes (EBT) $ 768,000 Income tax expense (30%) 230,400 Earnings after taxes (EAT) $ 537,600 Given this income statement, compute the following: a. Compute the degree of operating leverage. (Round your answer to 2 decimal places.) Degree of operating leverage b. Compute the degree of financial leverage. (Round your answer to 2 decimal places.) Degree of financial leverage c. Compute the degree of combined leverage. (Round your answer to 2 decimal places.) Degree of combined leverage d. Compute the break-even point in units. (Round your answer to the nearest whole number.) Break-even point units
Explanation / Answer
Question: The Sterling Tire Company's income statement for 2013 is as follows: STERLING TIRE COMPANY Income Statement For the Year Ended December 31, 2013 Sales (32,000 tires at $84 each) = $2,688,000 Less: Variable costs (32,000 tires at $42) = 1,344,000 Fixed costs = 520,000 Earnings before interest and taxes (EBIT) = $824,000 Interest expense = 56,000 Earnings before taxes (EBT) = $768,000 Income tax expense (30%) = 230,400 Earnings after taxes (EAT) = $537,600 Given this income statement, compute the following: a. Degree of operating leverage. b. Degree of financial leverage. c. Degree of combined leverage. d. Break-even point in units. Solution: a. Degree of operating leverage. Degree of operating leverage (DOL): - It measures the EBIT's percentage change as a result of a change of one percent in the level of output. - It helps in measuring the business risk. To compute it just use the following formula: Degree of operating leverage = Sales revenue less total variable cost divided by sales revenue less total cost: DOL = (Sales-Variable Costs) / (Sales-Variable Costs-Fixed Costs) For this problem: DOL = ($2,688,000-$1,344,000) / ($2,688,000-$1,344,000-$520,000) = = $1,344,000 / $8,24,000 = = 1.63 ---------------- b. Degree of financial leverage. The degree of financial leverage (DFL) is defined as the percentage change in earnings per share [EPS] that results from a given percentage change in earnings before interest and taxes (EBIT): DFL = Percentage change in EPS divided by Percentage change in EBIT The above equation can be worked to get the following equivalent one: DFL = EBIT / (EBIT-I), where I is the interest expense. For this problem: DFL = $824000 / ($824000-$56,000) = = $824000 / $768,000 = = 1.073 ---------------- c. Degree of combined leverage. The degree of combined leverage is also known as degree of total leverage (DTL). To compute it use the following formula: DCL = DOL * DFL For this problem: DCL = 1.63* 1.073 = 1.74899 -------------------- d. Break-even point in units( numbers of skates). Break-even point in Units = Fixed Costs / Contribution margin per unit where: Contribution margin per unit = (Revenues - Variable Costs) / Units sold = = Price per unit - Variable cost per unit In effect: The break-even level of sales is the sales point at which EBIT = 0 ; or in other words: break-even point in units = level of sales necessary to cover operating costs. At the break-even level of sales: EBIT = Sales - Variable costs - Fixed costs = 0 then: Sales - Variable costs = Fixed costs If we call: q = quantity sold; p = price per unit; v = variable cost per unit, then Revenues = q.p and Variable costs = q.v We will have: Revenues - Variable costs = q.p - q.v = q.(p - v) Then for the break-even point is: q.(p - v) = Fixed costs ==> q = Fixed costs / (p - v) For this problem is: Variable costs per unit = $42 Contribution margin per unit = Price per unit - Variable cost per unit = = $84 - $42 = = $42 Break-even point in Units = Fixed Costs / Contribution margin per unit = = $824000/$42 = = 19,619 The break even point in units is 19,619.
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