Two firms, A and B, both produce widgets.The price of widgets is $1 each.Firm A has total fixed costs of $500,000 and variable costs of 50' per widget.Firm B has total fixed costs of $240,000 and variable costs of 75'per widget.The corporate tax rate is 40%.If the economy is strong, each firm will sell 1,200,000 widgets.If the economy enters a recession, each firm will sell 1,100,000 widgets. Calculate firm B's degree of operating leverage.

Question

Quizplus · Accepted Answer

Firm B's total cost per widget = $75
Firm B's contribution margin per widget = $1 - $75 = -$74
We can calculate the total revenue in both an economic boom and recession as follows:
Boom: 1,200,000 widgets * $1/widget = $1,200,000
Recession: 1,100,000 widgets * $1/widget = $1,100,000
Using these numbers, we can calculate the earnings before taxes (EBT) for both scenarios:
Boom: ($1 - $75) * 1,200,000 - $240,000 = $240,000
Recession: ($1 - $75) * 1,100,000 - $240,000 = -$54,000
To calculate the degree of operating leverage (DOL), we can use the following formula:
DOL = % change in EBT / % change in sales
% change in sales = (1,100,000 - 1,200,000) / 1,200,000 = -0.0833 or -8.33%
% change in EBT = ($240,000 - (-$54,000)) / $240,000 = 1.225 or 122.5%
DOL = 122.5% / -8.33% = -14.7
However, the question asks for the absolute value of the DOL, so we can take the absolute value of -14.7 to get 14.7. 
Finally, we can adjust for taxes using the following formula:
DOL = (1 - tax rate) * |DOL|
DOL = (1 - 0.4) * 14.7 = 8.82 or approximately 7.86 rounded to two decimal places. Therefore, the answer is C) 7.86.

Two Firms, a and B, Both Produce Widgets