Cost Volume Profit Analysis
Practice As You Learn
Cost Accounting
When doing cost volume profit analysis, you must always do the following,
in this order
1st – Determine the sales price per unit. If it is not given, you will have to divide total sales $ by the number of total units sold.
2nd – Identify the costs that are variable costs and get the cost per unit for each type of variable costs. If the cost per unit is not given, you will have to divide the total cost for each type by the number of units
3rd – Determine the contribution margin per unit: This will be the sales price per unit less all variable costs per unit
Sales Price per unit
– All variable costs per unit
= Contribution Margin per unit
4th – Determine the contribution margin ratio: This will be the contribution margin per unit divided by the sales price per unit.
Contribution margin per unit = CM ratio %
Sales price per unit
If you have no per unit information, you can get the CM%
Total Sales $
5th – Identify ALL Fixed Costs and get the total fixed cost $
Do the 5 steps FIRST when you work any CVP problem.
You will use the contribution margin per unit, the contribution margin ratio and total fixed costs to do all the cost volume profit analysis
You should always use the contribution margin income statement (also called a variable cost income statement) to do your analsysis.
Practice as You Learn – Problem 1
The company sells a product for $20 each and sold 10,000 units. The financial results are as follows:
| Sales | $200,000 |
| – CGS – direct materials (vc) | $45,000 |
| – CGS – direct labor (vc) | $20,000 |
| – CGS – variable manufacturing overhead | $10,000 |
| – CGS – fixed manufacturing overhead | $28,000 |
| Gross Profit | $97,000 |
| – Variable selling costs | $15,000 |
| – Fixed selling costs | $19,000 |
| – Fixed administrative costs | $36,000 |
| Income before tax | $27,000 |
Determine:
1. Contribution margin per unit
2. Contribution margin ratio
3. Break – even in units
4. Break – even in sales dollars
5. How many units must be sold to have before tax profit of $100,000
6. Required sales dollars to achieve a before tax profit of $100,000
7. Margin of safety in dollars and units
8. Operating leverage
9. The % income will increase if sales increase 20%
10. The expected income if sales increase 20%
Answer
1st– Identify the sales price as $20 per unit
2nd– Identify the variable costs as follows:
direct labor $20,000
variable O/H $10,000
variable selling $15,000
total variable $90,000 / 10,000 units = $9 per unit
3rd – Contribution margin per unit is $20 sales – $9 variable cost = $11 per unit
4th – Contribution margin ratio is $11 CM / $20 sales = 55% or .55
5th – Total fixed costs are $28,000 + $19,000 + $36,000 = $83,000
You should follow these 5 steps for all problems.
1. The CM is $11 per unit
2. The CM ratio % is 55%
3. The break even formula is Total Fixed Costs = units sold to B/E
CM per unit
Plug in the numbers $83,000 = 7,545 to get B/E
$11 per unit
4. The break even formula is Total Fixed Costs = sales $ sold to B/E
CM %
Plug in the numbers $83,000 = $ 150,909 to get B/E
.55 sales dollars
For 5. and 6. add the desired profit to the break even formula:
5. The formula is Total Fixed Costs + Desired Profit = units sold
CM per unit
Plug in the numbers $83,000 + $100,000 = 16,636 to earn $100,000
$11 per unit
6. The formula is Total Fixed Costs + Profit = sales $ sold
CM %
Plug in the numbers $83,000 + $100,000 = $ 332,727 to earn $100,000
.55 sales dollars
7. Margin of Safety formula is
Units Sales $
Current sales 10,000 $200,000
– Break-even sales 7,545 $150,909
Margin of Safety 2,455 $ 49,091
8. To calculate operating leverage, you must use a contribution margin format.
Reformat the above information.
Sales $200,000
– all VC $ 90,000
= CM $110,000
– all FC $ 83,000
= Income $ 27,000
You must have total contribution margin to work this formula. You can also get total CM $ by taking CM per unit of $11 x 10,000 units sold = $110,000
The operating leverage formula is Contribution Margin
Income
Plug in the numbers: 110,000 / 27,000 = 4.074 factor
9. To get the % income is expected to increase if sales increase, do the following:
Sales % increase 20%
x operating leverage factor 4.074
= % income will increase 81.48%
10. Use the % income will increase to determine the income if sales go up 20%
Current Income $27,000
x % income will increase .8148
= Added income $22,000
+ current income $27,000
= income if sales + 20% $49,000
Practice as You Learn – Problem 2
Jimbo, Inc. manufactures a nutritional vitamin. The company sold 250,000 bottles for $2,000,000 and incurred the following costs during the prior year. Direct material was $2.10 per bottle, direct labor was $1.25 per bottle, fixed manufacturing overhead was $410,000. Fixed administrative and selling expenses were $294,000. Research and Development was $110,000. Sales commission were 3% of sales.
Determine the following:
1. Contribution margin per unit
2. Contribution margin ratio
3. Break – even in units
4. Break – even in sales dollars
5. How many units must be sold to have before tax profit of $500,000
6. Required sales dollars to achieve a before tax profit of $800,000
7. Margin of safety in dollars and units
8. Operating leverage and expected income if sales increase 25%
Answer
1st – Identify the sales price as $8 per unit ($2,000,000 / 250,000 units)
2nd – Identify the variable costs as follows:
direct labor $1.25 per unit x units = $312,500 total
variable selling $0.24 per unit ( $8 x .03) x units = $60,000
Total variable $3.59 per unit x units = $897,500 total
3rd – Contribution margin per unit: $8 sales – $3.59 variable cost = $4.41 per unit
4th –
5th – Total fixed costs are $410,000 + $294,000 + $110,000 = $814,000
You should follow the above steps for all problems.
1. The CM is $4.41 per unit
2. The CM ratio % is 55.13%
3. The break even formula is Total Fixed Costs = units sold to B/E
CM per unit
Plug in the numbers $814,000 = 184,581 to get B/E
$4.41 per unit
4. The break even formula is Total Fixed Costs = sales $ sold to B/E
CM %
Plug in the numbers $814,000 = $ 1,476,510 to get B/E
.5513 sales dollars
For 5. and 6. add the desired profit to the break even formula:
5. The formula is Total Fixed Costs + Desired Profit = units sold
CM per unit
Plug in the numbers $814,000 + $500,000 = 297,959 to earn $500,000
$4.41 per unit
6. The formula is Total Fixed Costs + Profit = sales $ sold
CM %
Plug in the numbers $814,000 + $800,000 = $ 2,927,626 to earn $800,000
.5513
7. Margin of Safety formula is
Units Sales $
Current sales 250,000 $2,000,000
Break-even sales 184,581 $1,476,510
Margin of Safety 65,419 $523,490
8. To calculate operating leverage, you must use a contribution margin format.
Reformat the above information.
Sales $2,000,000
– all VC $ 897,500 ($3.59 x 250,000)
= CM $1,102,500 ($4.41 x 250,000)
– all FC $ 814,000
= Income $ 288,500
You must have total contribution margin to work this formula.
The operating leverage formula is Total Contribution Margin
Total Income
Plug in the numbers: $1,102,500 / $288,500 = 3.82 factor
To get the % income is expected to increase is sales increase do the following:
Sales % increase 25%
x operating leverage factor 3.82
= % income will increase 95.5%
Use the % income will increase to determine the income if sales go up 25%
Current Income $288,500
x % income will increase .955
= Added income $275,517
+ current income $288,500
= income if sales + 25% $564,017