CVP and Breakeven Analyses
6.3 Cost-Volume-Profit (CVP) Analysis
The cost-volume-profit formula (Formula 6.6a) we introduced in the first section shows how cost, volume, and profit are connected. You can use it to solve for any of the variables or determine changes to any of the variables in the formula. The latter is referred to as what-if analysis or sensitivity analysis. Sensitivity analysis involves adjusting these variables to see how changes impact the break-even point, overall profit, and other financial outcomes.
Best Tech. can produce a maximum of 4305 tablets per month and sell them for $220 each. The company’s fixed costs per month are $193,110, and the variable costs are $63 per unit. a) Calculate the number of tablets the company needs to sell per month to break even. b) If the company wants to make a profit of $60,288 per month, how many tablets does it need to sell? c) If the company sold 3800 tablets in a month, how much would its net income be? d) If the company were to spend an additional $25,120 in a month for advertising, how much would it need to sell to break even?
Show/Hide Solution
- The selling price is $220, so [asciimath]SP=$220[/asciimath]
- The variable cost per unit is $63, so [asciimath]VC=$63[/asciimath]
- The fixed costs are $193,110 per month, so [asciimath]FC=$193,110[/asciimath]
- The capacity is 4305.
a) Contribution margin approach:
[asciimath]CM=SP-VC[/asciimath] [asciimath]=220-63[/asciimath] [asciimath]=$157[/asciimath]
The quantity at break-even is given by Formula 6.8b:
[asciimath]X_(BE)=(FC)/(CM)[/asciimath]
[asciimath]=(193,110)/157[/asciimath]
[asciimath]=1230[/asciimath] Tablets
b) The quantity at any given profit is given by Formula 6.8a:
[asciimath]NI=$60,288[/asciimath]
[asciimath]X=(NI+FC)/(CM)[/asciimath]
[asciimath]=(60,288+193,110)/(157)[/asciimath]
[asciimath]=(253,398)/157[/asciimath]
[asciimath]=1614[/asciimath] Tablets
c) We are looking for NI given X = 3800 Tablets. We use Formula 6.6a to calculate NI:
[asciimath]NI=SP*X-(VC*X+FC)[/asciimath]
[asciimath]=220(3800)-(63(3800)+193,110)[/asciimath]
[asciimath]=836,000 - (239,400+193,110)[/asciimath]
[asciimath]=836,000-432,510[/asciimath]
[asciimath]=$403,490[/asciimath] Profit
d) The advertising cost is considered a fixed cost as it is per time period and independent of the quantity. So the fixed costs are increased by $25,120.
[asciimath]FC_(New) = 193,110 + $25,120[/asciimath] [asciimath]= $218,230[/asciimath]
The new quantity at break-even is given by Formula 6.8b:
[asciimath]X_(BE)=(FC_(New))/(CM)[/asciimath]
[asciimath]=(218,230)/157[/asciimath]
[asciimath]=1390[/asciimath] Tablets
Try an Example
Sparkling Shoes is a small company that sells designer shoes. Its fixed costs, including rent, salaries, and utilities, are $10,000 per month. The variable costs (like materials, labor, and packaging) are $40 per pair. Each pair of shoes is sold for $100. Answer the following independent parts.
a) How many pairs of shoes does the company need to sell to break even?
b) What is the break-even point in sales dollars?
c) If Sparkling Shoes wants to achieve a monthly profit of $5,000, how many pairs of shoes should they sell?
d) If Sparkling Shoes decides to reduce the selling price to $90 per pair, how many shoes do they need to sell to break even?
e) If the fixed costs increase by $1,900 due to a rent hike, how will that impact the break-even point in units?
Show/Hide Solution
- The selling price per pair is $100, so [asciimath]SP=$100[/asciimath]
- The variable cost per pair is $40, so [asciimath]VC=$40[/asciimath]
- The fixed costs are $10,000 per month, so [asciimath]FC=$10,000[/asciimath]
a) Contribution margin approach:
[asciimath]CM=SP-VC[/asciimath] [asciimath]=100-40[/asciimath] [asciimath]=$60[/asciimath]
The quantity at break-even is given by Formula 6.8b:
[asciimath]X_(BE)=(FC)/(CM)[/asciimath]
[asciimath]=(10,000)/60[/asciimath]
[asciimath]=166.66...[/asciimath]
[asciimath]~~167[/asciimath] Pairs (Rounded up to the nearest whole number)
b) The Break-even point in dollars is the total revenue at the break-even point in units:
[asciimath]TR=SP*X_(BE)[/asciimath]
[asciimath]=100(167)[/asciimath]
[asciimath]=$16,700[/asciimath]
c) The quantity at any given profit is given by Formula 6.8a:
[asciimath]NI=$5,000[/asciimath]
[asciimath]X=(NI+FC)/(CM)[/asciimath]
[asciimath]=(5000+10,000)/(60)[/asciimath]
[asciimath]=(15,000)/60[/asciimath]
[asciimath]=250[/asciimath] Pairs
d) The new selling price is $90, so [asciimath]SP_(New)=$90[/asciimath]
The quantity at break-even is given by Formula 6.8b:
[asciimath]X_(BE)=(FC)/(CM_(New))[/asciimath]
[asciimath]=(10,000)/50[/asciimath]
[asciimath]=200[/asciimath] Pairs
e) If FC increases by $1900, [asciimath]FC_(New)=10,000+$1900[/asciimath] [asciimath]=$11,900[/asciimath]. Note that the part questions are independent, so we use the original selling price to answer Part (e).
The quantity at break-even is given by Formula 6.8b:
[asciimath]X_(BE)=(FC)/(CM)[/asciimath]
[asciimath]=(11,900)/60[/asciimath]
[asciimath]=198.33...[/asciimath] Pairs
[asciimath]~~199[/asciimath] Pairs (Rounded up to the nearest whole number)
Note: When calculating the number of units, it is important to always round up to the nearest whole number, irrespective of the decimal value. This ensures that the business remains on the profitable side of the break-even point.
Try an Example
Section 6.3 Exercises
- GreatSound Technology manufactures and sells headsets for $84 each. Annually, the company incurs fixed costs totaling $54,234. Additionally, each headset incurs variable costs of $20 for manufacturing and $18 for labor. a) Determine the yearly sales volume of headsets required for GreatSound Technology to break even. b) If GreatSound Technology produced and sold 2245 headsets in a year, calculate the company’s profit or loss for that year. c) To achieve an annual profit of $143,658, how many headsets must the company sell?
Show/Hide Answer
a) X = 1179 Headsets
b) NI = $49,036; Profit
c) X = 4302 Headsets
- Wearit is a small company that sells designer shoes. Its fixed costs, including rent, salaries, and utilities, are $22,045.40 per month. The variable costs (like materials, labor, and packaging) are $85.4 per pair. Each pair of shoes is sold for $244. a) How many pairs of shoes does Wearit need to sell each month to break even? b) If Wearit wants to achieve a monthly profit of $13,322.40, how many pairs of shoes should they sell? c) If Wearit decides to reduce the selling price to $234 per pair, how many shoes do they need to sell to break even? d) If the fixed costs increase by $6,613.62 due to a rent hike, how will that impact the break-even point in units? Each part is independent.
Show/Hide Answer
a) X = 139 Pairs
b) X = 223 Pairs
c) X = 149 Pairs
d) X = 181 Pairs
- XYZ Electronics is a company that manufactures and sells wireless speakers. The selling Price per Speaker is $150. The variable costs per speaker are $90, which includes costs of materials, labor, and variable overhead. The company’s fixed costs include rent, salaries of permanent staff, and fixed overhead totaling $300,000. a) Calculate the break-even point in units and in total sales dollars. b) If XYZ Electronics aims to achieve a profit of $200,000 for the year, how many speakers must they sell? c) How would an increase in variable costs to $100 per speaker affect the break-even point? d) If fixed costs increase by 10%, how many units need to be sold to achieve the original profit target of $200,000? Each part is independent.
Show/Hide Answer
a) X = 5000 Speakers; TR = $750,000
b) X = 8334 Speakers
c) X = 6000 Speakers
d) X = 8834 Speakers
