Question

Ion Generating, Inc., produces ion generators and control (detection) devices for industrial applications such as chemical labs. It is contemplating an expansion into the home security market by producing a smoke detector based off of the same technology that would sell at a price of $50. The production of each smoke detector would require $20 in materials, and 0.4 hours of labor at the rate of $25 per hour. Energy, supervisory and other variable overhead costs would amount to $10 per unit. The accounting department has derived an allocated fixed overhead charge of $7.50 per smoke detector (at a projected volume of 300,000 units) to account for the expected increase in fixed costs.

a. Calculate the degree of operating leverage at a projected volume of 300,000 units and explain what the DOL means. Then calculate the DOL at the breakeven sales level. What happens to DOL when output approaches breakeven level?

Answer 1

(a)

(I) When Q = 300,000:

Contribution margin (CM) = Quantity x (Price - Total average variable cost = Price - Material - Labor - Overhead)

= 300,000 x [50 - 20 - (0.4 x 25) - 10]

= 300,000 x (20 - 10)

= 300,000 x 10

= 3,000,000

Total fixed cost (FC) = (7.5 x 300,000) = 2,250,000

Degree of operating leverage (DOL) = CM / (CM - FC)

= 3,000,000 / (3,000,000 - 2,250,000)

= 3,000,000 / 750,000

= 4

This means that if sales increase (decrease) by 1%, Operating income will increase (decrease) by 4%.

(II) At break-even,

TR = TVC + FC

50 x Q = Q x 10 + FC

40 x Q = FC, where CM = 40 x Q

DOL = 40Q / (40Q - 40Q)

= 40Q / 0

=

Therefore, as output approaches breakeven level, DOL approaches infinity.