Question

OceanGate sells external hard drives for $288 each. Its total fixed costs are $45 million, and its variable costs per unit are $173. The corporate tax rate is 41%. If the economy is strong, the firm will sell 2 million drives, but if there is a recession, it will sell only half as many.

a. What will be the percentage decline in sales if the economy enters a recession? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

b. What will be the percentage decline in profits if the economy enters a recession? (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

c. Calculate the operating leverage of this firm? (Round your answer to 2 decimal places.)

Answer 1

a) Sale Price per unit = $288, Units sold in strong economy = 2 million

Units sold in recession = Units sold in strong economy / 2 = 2million / 2 = 1 million

Sales in strong economy = Units sold in strong economy x sale price per unit = 2million x $288 = $576 million

Sales in recession = Units sold in recession x sale price per unit = 1million x $288 = $288 million

Percentage decline in sales = (Sales in recession / Sales in strong economy) - 1 = (288/576) - 1 = 0.50 - 1 = - 0.50 = -50.00%

Percentage decline in sales = -50.00%

b) Variable cost per unit = $173

Variable cost in strong economy = Units sold in strong economy x Variable cost per unit = 2million x $173 = $346 million

Profit in strong economy = (Sales - Variable cost - fixed cost)(1-tax rate) = (576 - 346 - 45)(1-41%) = 185 x 59% = 109.15

Variable cost in recession = Units sold in recession x Variable cost per unit = 1 million x $173 = $173

Profit in recession = (Sales - Variable cost - fixed cost)(1-tax rate) = (288 - 173 - 45)(1-41%) = 70 x 59% = 41.30

Percentage decline in Profit = (Profit in recession / Profit in strong economy) - 1 = (41.30/109.15) - 1 = 0.37837837 - 1 = -0.62162163 = -62.162163% = -62.16% (rounded to two decimal places)

Hence Percentage decline in profit = -62.16%

c) EBIT in strong economy = Sales - Variable cost - fixed cost= 576 - 346 - 45 = 185

EBIT in recession = Sales - Variable cost - fixed cost = 288-173-45 = 70

Percentage change in EBIT = (EBIT in recession/EBIT in strong economy) - 1 = (70/185) - 1 = 0.37837837 - 1 = -0.62162163 = -62.162163%= -62.16%

Percentage change in sales = -50%

Degree of operating leverage = Percentage change in EBIT / Percentage change in sales = -62.16% / -50.00% = 1.2432 = 1.24 (rounded to two decimal places)

Hence Operating leverage = 1.24