Question

OceanGate sells external hard drives for $152 each. Its total fixed costs are $48 million, and its variable costs per unit are $106. The corporate tax rate is 45%. If the economy is strong, the firm will sell 4 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.

If the economy is strong, sales = 4 million

If the economy enters a recession, sales = 2 million

Percentage decline in sales = Decline in sales / Original sales = (2 - 4) / 4 = -0.5 = - 50%

b.

If the economy is strong, sales = 4 million units

or, sales = $ 152 * 4 million = $ 608 million

Fixed cost = $ 48 million

Variable cost = $ 106 * 4 million = $ 424 million

Profit before tax = Sales - Fixed cost - Variable cost = $ 136 million

Profit after tax = $ 136 *(1-45%) million = $ 74.8 million

If the economy enters a recession, sales = 2 million

or, sales = $ 152 * 2 million = $ 304 million

Fixed cost = $ 48 million

Variable cost = $ 106 * 2 million = $ 212 million

Profit before tax = Sales - Fixed cost - Variable cost = $ 44 million

Profit after tax = $ 44 *(1-45%) million = $ 24.2 million

The percentage decline in profits if the economy enters a recession

= ($ 24.2 - $ 74.8) / $ 74.8 = -0.67647 = - 67.65%

c.

Operating leverage = Q(P-VC) / [Q(P-VC) - FC] = 4*(152-106) / [ 4*(152-106) - 48] = 1.35