3-36 CVP Analysis and Price Changes

a. Compute the volume in units and the dollar sales level necessary to maintain the present profit level, assuming that the maximum price increase is implemented.

1. First I need to determine the profit.

Profit = (Price – Variable Costs) * Unit of Output – Fixed Costs
Profit = ($30 - $15) * 60,000 - 0 - $700,000 ($15) * 60,000 = $900,000 - $700,000 = $200,000
Profit = $200,000

2. Next I need to determine the variable costs associated.
Variable costs = $15, however they are broken into three separate categories and all have increases expected.
Labor = (15% increase expected), so 115% * $15 = $17.25
Materials = (10% increase expected), so 110% * $15 = $16.50
Overhead = (20% increase expected), so 120% * $15 = $18.00

These increases must be further evaluated because they combine to make up 100%. Broken down we are told that 50% of the variable costs are from labor and both materials and overhead make up 25%. Because of this we must adjust our dollar amounts accordingly.

Labor = $17.25 / 50% = $8.625
Materials = $16.50 / 25% = $4.125
Overhead = $18.00 / 25% = $4.50
Variable cost per unit total = $17.25

3. Lastly I need to determine the new price maximum and adjustment to fixed costs, given the increases of 10% in price and 5% in fixed costs.

Price = 110% (10% increase) * $30 (maximum price) = $33.00
Fixed Costs = 105% (5% increase) * $700,000 = $735,000

4. Now I can plug in my adjusted numbers in to the original profit equation and solve.

Profit = (Price – Variable Costs) * Units of Output – Fixed Costs
$200,000 = ($33 - $17.25) * X - $735,000
X = ($935,000 ($200k + $735k) / ($33 - $17.25)
X = ($935,000 / $15.75) = 59,365
59,365 Units needed. In Sales we simply multiply the units required by the $33 amount and get $1,959,045

Sales = $1,959,045 and