15-13A (Break-even point and operating leverage) Allison Radios manufactures a c
ID: 2663583 • Letter: 1
Question
15-13A(Break-even point and operating leverage) Allison Radios manufactures a complete line of radio and communication equipment for law enforcement agencies. The average selling price of its finished product is $180 per unit. The variable cost for these same units is $126. Allison Radios incurs fixed costs of $540,000 per year.
a. What is the break-even point in units for the company?
b. What is the dollar sales volume the firm must achieve in order to reach the break-even point?
c. What would be the firm’s profit or loss at the following units of production sold:
12,000 units? 15,000 units? 20,000 units?
d. Find the degree of operating leverage for the production and sales levels given in part (c).
Explanation / Answer
(a) Break-even point occurs when contribution equals fixed cost. Contribution per unit = selling price /unit - variable cost /unit ($) => = 180 - 126 = 54 ($) Let beak-even quantity be Q units. Total contribution = 54*Q ($) fixed cost is $ 540.000 So, for break-even point, 54Q = 540,000 => Q = 10,000 units (ANSWER) (b) Dollars sales volume in $ = Price /unit * Q at break-even => = 180 * 10,000 => = 1,800,000 (ANSWER) (c) Profit = Contribution - Fixed cost (i) At 12,000 units, Profit = 54*12,000 - 540,000 => = 648,000 - 540,000 = 108,000 ($) (ANSWER) (II) At 15,000 units, Profit = 54*15,000 - 540,000 => = 810,000 - 540,000 = 270,000 ($) (ANSWER) (III) At 20,000 units, Profit = 54*20,000 - 540,000 => = 540,000 ($) (ANSWER) (d) Operating leverage OL = FC/ TC (akin to debt/(debt+equity) = 540,000/(126 Q+540,00) = 540,000/(126*12000 + 540,000) = 0.2632 (for Q = 12,000) OL = 540,000/(126*15,000+540,000) = 0.2222 (for Q = 15,000) OL = 540,000/(126*20,000+540,000) = 0.1765 (for Q = 20,000) Another measure of OL is VC/FC (akin to debt/ equity) and can be calculated from above data,
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