Question

OceanGate sells external hard drives for $173 each. Its total fixed costs are $26 million, and its variable costs per unit are $121. The corporate tax rate is 47%. If the economy is strong, the firm will sell 8 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?

b. What will be the percentage decline in profits if the economy enters a recession?

c. Calculate the operating leverage of this firm?

Answer 1

Answer a:

If the economy is strong,

Quantity of drives sold by the firm = 8 million

Sales = Quantity sold * Price = 8 million * $173 = $1384 million

If there is a recession,

It will sell only half as many = 8/2 =4 million

Sales = Quantity sold * Price = 4 million * $173 = $692 million

Percentage decline in sales if the economy enters a recession = (1384 - 692) /1384 = 50%

Percentage decline in sales if the economy enters a recession = 50%

Answer b:

Contribution per unit = Price per unit - Variable cost per unit = $173 - $121 =$52 per unit

Profit = (Contribution per unit * Quantity sold - Fixed cost) * (1 - Tax rate)

If the economy is strong,

Quantity of drives sold by the firm = 8 million

Profit = (52 * 8 - 26) * (1 - 47%) = $206.70 million

If there is a recession,

It will sell only half as many = 8/2 =4 million

Profit = (52 * 4 - 26) * (1 - 47%) = $96.46 million

Percentage decline in profits if the economy enters a recession = (206.70 - 96.46) / 206.70 = 53.33333% = 53.33%

Percentage decline in profits if the economy enters a recession = 53.33%

Answer c:

Operating leverage = % change in EBIT / % change in Sales.

If the economy is strong,

EBIT = (Contribution per unit * Quantity sold - Fixed cost) = $52 * 8 - 26 = $390 million

If there is a recession,

EBIT = (Contribution per unit * Quantity sold - Fixed cost) = $52 * 4 - 26 = $182 million

Percentage change in EBIT = (390 - 182) /390 = 53.3333%

Operating leverage = 53.3333% / 50% = 1.066667 = 1.07

Operating leverage = 1.07