CVP and Breakeven Analyses
6.2 Contribution Margin
The difference between unit selling price and variable cost is called the contribution margin per unit, denoted by CM.
[asciimath]CM=SP-VC[/asciimath]Formula 6.7
The contribution margin represents the amount that contributes to covering fixed costs and generating profit. For each unit sold beyond the break-even point, profit increases by the amount of the unit contribution margin. On the other hand, for each unit sold less than the break-even quantity, there is a loss equivalent to the unit contribution margin.
If we collect the X terms in Formula 6a, we obtain
[asciimath]NI=(SP-VC)*X-FC[/asciimath]
Substituting CM into Formula 6.7 and rearranging for X, we get
[asciimath]NI=CM*X-FC[/asciimath]
[asciimath]X=(NI+FC)/(CM)[/asciimath]Formula 6.8a
Formula 6.8a can be used to find the quantity (volume) for a desired net income. To find the quantity at break-even (BE), we let [asciimath]NI=0[/asciimath] and the formula becomes
[asciimath]X_(BE)=(FC)/(CM)[/asciimath]Formula 6.8b
Another helpful variable is the contribution margin rate. Expressed as a percentage, the contribution margin rate provides insights into the profitability of products and the ability to cover fixed costs. For example, if the contribution margin rate is 40%, this means that 40 cents of every sales dollar is available to cover fixed costs and contribute to profit, after accounting for variable costs.
[asciimath]CM(%) = (CM)/(SP)[/asciimath]Formula 6.9a
If only the total revenue and total variables are known, the contribution margin rate can be found by
[asciimath]CM(%) = (TCM)/(TR)[/asciimath]Formula 6.9b
Here TCM is the total contribution margin, which is the difference between the total revenue and total variable costs.
[asciimath]TCM=TR-TVC[/asciimath]
Future Technology can make a maximum of 2957 webcams per month and sell them for $134 each. The company’s fixed costs per month are $111,690, and the variable costs are $32 per unit. a) Find the contribution margin per unit. b) Find the contribution margin rate. c) Calculate the number of webcams the company needs to sell per month to break even. d) Calculate the number of webcams the company needs to sell per month to achieve a profit of $36,210.
Show/Hide Solution
- The selling price is $134, so [asciimath]SP=$134[/asciimath]
- The variable cost per unit is $32, so [asciimath]VC=$32[/asciimath]
- The fixed costs are $111,690, so [asciimath]FC=$111,690[/asciimath]
- The capacity is 2957.
a) Contribution margin:
[asciimath]CM=SP-VC[/asciimath]
[asciimath]=134-32[/asciimath]
[asciimath]=$102[/asciimath]
b) The contribution margin rate:
[asciimath]CM(%)=(CM)/(SP)[/asciimath]
[asciimath]=102/134 xx 100%[/asciimath]
[asciimath]~~76%[/asciimath]
c) The quantity at break-even is given by Formula 6.8b:
[asciimath]X_(BE)=(FC)/(CM)[/asciimath]
[asciimath]=(111,690)/102[/asciimath]
[asciimath]=1095[/asciimath] Webcams
d) The quantity at any given profit is given by Formula 6.8a:
[asciimath]NI=$36,210[/asciimath]
[asciimath]X=(NI+FC)/(CM)[/asciimath]
[asciimath]=(36,210+111,690)/(102)[/asciimath]
[asciimath]=(147,900)/102[/asciimath]
[asciimath]=1450[/asciimath] Webcams
Try an Example
If we only know the total dollar values and not the specific unit selling price or variable costs, we can determine the break-even point in terms of dollars instead of units using the contribution margin rate.
[asciimath]TR=(FC)/(CM(%))[/asciimath] Formula 6.10
BestDeal Inc. had a total revenue of $146,400 last month. Its total variable costs and fixed costs for the period were $25,150 and $31,500, respectively. Compute its break-even point in sales dollars.
Show/Hide Solution
- Total revenue is $146,400, so [asciimath]TR=$146,400[/asciimath]
- Total variable costs are $25,150 so [asciimath]TVC=$25,150[/asciimath]
- Fixed costs are $31,500 so [asciimath]FC=$31,500[/asciimath]
Since unit selling price and variable cost are unknown, we find the contribution margin rate from Formula 6.8b and use Formula 6.10 to find the revenue at break-even.
[asciimath]TCM=TR-TVC[/asciimath]
[asciimath]=146,400-25,150[/asciimath]
[asciimath]=$121,250[/asciimath]
So the contribution margin rate is
[asciimath]CM(%) = (TCM)/(TR)[/asciimath]
[asciimath]=(121,250)/(146,400)xx100%[/asciimath]
[asciimath]~~82.82%[/asciimath]
Plugging CM(%) and FC into Formula 6.10 yields
[asciimath]TR=(FC)/(CM(%))[/asciimath]
[asciimath]=(31,500)/(82.82%)[/asciimath]
[asciimath]~~$38,034.29[/asciimath] Rounded to the nearest cents
Try an Example
Section 6.2 Exercises
- Qual Electronics can make a maximum of 2636 tablets per month and sell them for $121 each. The company’s fixed costs per month are $90,942, and the variable costs are $52 per unit. a) Compute the contribution margin per unit. b) Compute the contribution margin rate. c) Calculate the number of tablets the company needs to sell per month to break even.
Show/Hide Answer
a) CM = $69
b) CM Rate = 57%
c) X = 1318 Tablets
- A manufacturing plant had a total revenue of $143,800 last year. Its total variable costs and fixed costs for the period were $23,700 and $30,900, respectively. Compute the break-even point in sales dollars.
Show/Hide Answer
TR = $36,997.66
- Future Technology sells webcams for $134 each. The company’s fixed costs per month are $111,690, and the variable costs are $32 per unit. a) Compute the contribution margin per unit. b) Compute the contribution margin rate. c) Calculate the total revenue at the break-even point.
Show/Hide Answer
a) CM = $102
b) CM Rate = 76%
c) TR = $146,730.00
