Solution to Contest #17

The first step is to calculate the profit at the initial conditions, based on 200 units of sales.

Total costs = Fixed + variable = $234,200 + $137 x 200 = $261,600

Profit = Sales - Total Costs = $1490 x 200 - 261,600 = $36,400

Profit per Unit (Margin) = $36,400 / 200 = $182 per unit.


Using the same equations, we now calculate the margin with the changes:

Total costs = Fixed + variable = $(234,200+12,500) + $151 x 200 = $276,900

Profit = Sales - Total Costs = $1490 x 200 - 276,900 = $21,100

Profit per Unit (Margin) = $21,100 / 200 = $105.50 per unit.


Now we calculate the % change in margin for the increased expenses:

% Change = (Final Margin - Initial Margin) / Initial Margin x 100% = (105.50-182.00)/182.00 x 100% = -42% 


These fairly small decreases in costs (5.3% in fixed and 10.2% in variable) reduced margin by 42%. This concept is called leveraging.