Question

OceanGate sells external hard drives for $294 each. Its total fixed costs are $23 million, and its variable costs per unit are $191. The corporate tax rate is 32%. 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.)

OceanGate sells external hard drives for $294 each. Its total fixed costs are $23 million, and its variable costs per unit are $191. The corporate tax rate is 32%. 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. if the economy enters a recession, sales will be only half of what it would be when economy is strong. When economy is strong sell will be 2 million devices. when economy is in recession, sell will be 2 million*50% = 1 million devices.

Decline in sales = (sell when recession/sell when economy strong) - 1 = (1 million/2 million) - 1 = 0.5 -1 = -0.5 or -50.00%

b. percentage decline in profits = (profits when recession/profits when economy strong) - 1

Profits when economy strong = [((sell price per unit - variable cost per unit)*quantity sold) - total fixed costs]*(1-tax rate)

Profits when economy strong = [(($294 - $191)*2,000,000) - $23,000,000]*(1-0.32)

Profits when economy strong = [($103*2,000,000) - $23,000,000)*0.68 = ($206,000,000 - $23,000,000)*0.68

Profits when economy strong = $183,000,000*0.68 = $124,440,000

Profits when economy in recession = [(($294 - $191)*1,000,000) - $23,000,000]*(1-0.32)

Profits when economy in recession = [($103*1,000,000) - $23,000,000)*0.68 = ($103,000,000 - $23,000,000)*0.68

Profits when economy in recession = $80,000,000*0.68 = $54,400,000

percentage decline in profits = ($54,400,000/$124,440,000) -1 = 0.4371584699453552 - 1 = -0.5628 or -56.28%

c. Operating leverage = [quantity*(selling price - variable price)]/[quantity*(selling price - variable price) - fixed costs]

Operating leverage = [2,000,000*($294 - $191)]/[2,000,000*($294 - $191) - $23,000,000]

Operating leverage = (2,000,000*$103)/(2,000,000*$103) - $23,000,000 = $206,000,000/$183,000,000 = 1.125 or 1.13