Unit 5: Cost-Volume-Profit (CVP) Analysis Module 9 - CVP Analysis - Basics

Variable costs

Costs that change in total in direct proportion to changes in activity level

Example would be food materials cost in a restaurant

Cost-volume-profit analysis (CVP)

Techniques for determining how changes in revenue, costs, and level of activity affect the profitability of an organization

CVP answers the question

How much do I need to sell to earn a proft

Cost behavior

The way a cost is affected by changes in activity levels

Fixed costs

Costs that remain constant in total, regardless of activity level, at least over a certain range of activity

Example would be cost of a rent

Key factors involved in CVP analysis

-revenues from the sales prices charged for goods and services

-fixed and variable costs

-sales volume

-mix of products

-resulting profits

Relevant range

The range of operating level, or volume of activity, over which the relationship between total costs (variable plus fixed) and activity level is approximately linear

Why are variable costs applicable only with relevant ranges

Because if activity increases or decreases significantly, cost relationships will probably change. If production volume sours factors like overtime work and bulk purchase discounts may cause direct labor and materials costs per unit to change

Economies of scale

A proportionate saving in costs gained by an increased level of production. Similarly, as the level of activity decreases, the fixed cost per unit increases

Stepped costs

Costs that change in total in stairstep fashion (in large amounts) with changes in volume of activity

Mixed costs

Costs that contain both variable and fixed costs components

What is the purpose of using CVP analysis?

To study the interrelationships among revenues, costs, levels of activity, and profits

What is a mixed cost?

A cost that includes both a fixed portion and a variable portion

What kind of cost is property taxes on a factory building?

Fixed cost

What kind of cost is rent in a retail mall when the rental agreement requires the tenant to pay a base amount plus a percentage of sales?

Mixed cost

What kind of cost is cheese in a pizza restaurant?

Variable cost

The more pizzas sold, the more cheese needed. Since the amount of cheese needed varies with the number of pizzas sold, it is strictly a variable cost.

CVP Equation

sales revenue - variable costs - fixed costs = profit

CVP equation can be used to

compute net income, break-even number of units, and the number of units required to reach a given target profit

Contribution margin income statement

An income statement in which costs are separated by behavior (variable and fixed) instead of by functional classification (CoGS, admin expenses etc), this allows managers to see the impact that various changes in activity volume can have on profit

Contribution margin

The difference between total sales and variable costs; the portion of sales revenue available to cover fixed costs and provide a profit

Per-unit contribution margin

The excess of the sales price of one unit over its variable costs

Break-even point

The amount of sales at which total costs of the number of units sold equal total revenues; the point at which there is no profit or loss

Contribution margin ratio

The percentage of net sales revenue left after variable costs are deducted; the contribution margin divided by net sales revenue

CVP equation modified for the break-even point

Sales revenue-variable costs-fixed costs=$0

Profit graph

A graph that shows how profits vary with changes in volume

What is contribution margin?

Sales minus variable cost

Brown Beaver Company reported the following data:

Price per unit: $12

Variable cost per unit: $7

Fixed cost: $1,500

What is Brown Beaver's computed breakeven number of units?

300 units

$1,500 fixed cost/($12 selling price per unit − $7 variable cost per unit) = 300 units. In this case, the contribution margin is $5 per unit.

In a CVP graph, what is represented by the vertical-axis intercept of the total cost line?

Price per unit

Erma Rock supplies crushed rock for various construction customers. The company's fixed cost per month is $60,000. The variable cost of producing a ton of crushed rock is $4. The current selling price is $6 per ton.

What is Erma Rock's breakeven point in both tons and dollars?

30k tons and $180k

Sales revenue − Variable costs − Fixed costs = Target income $6x − $4x − $60,000 = $0 $2x = $60,000 X = 30,000 tons; 30,000 tons × $6 per unit = $180,000

Erma Rock supplies crushed rock for various construction customers. The company's fixed cost per month is $60,000. The variable cost of producing a ton of crushed rock is $4. The current selling price is $6 per ton.

How many tons of crushed rock does Erma Rock need to sell to make a monthly profit of $75,000?

67,500

Erma Rock has a contribution margin of $2 ($6 selling price minus $4 variable costs). At $2 per ton, breakeven is 30,000 tons or $60,000 fixed costs divided by $2. Because the contribution margin is $2, it would take $75,000/2 or 37,500 more tons from breakeven, or a total of 30,000, to reach breakeven and 37,500 to make the profit of $75,000.

Sales mix

The relative proportion of total sales dollars (or total units sold) that is represented by each of a company's products

Computing the break-even level of sales in a multiproduct environment involves

dividing total fixed cost by the overall contribution margin ratio

Contribution margin ratio is determined by

the exact sales mix

If the sales mix changes

then the overall contribution margin ratio changes, which changes the break-even point

What is sales mix

Proportion of sales revenue from each product

Mowing Motors sells two different products. Here are the monthly revenues and costs:

Product A

Sales quantity: 12,000 units

Price per unit: $5.50

Variable costs per unit: $1.15

Product B

Sales quantity: 18,000 units

Price per unit: $3.00

Variable costs per unit: $0.90

Total fixed costs: $225,000

Assuming the sales mix stays the same, what is the breakeven point for this company in units?

Product A: 30,000; Product B: 45,000

Percentage of Product A:

(12,000)/(12,000 + 18,000) = 12/30 = .4 = 40%

Percentage of Product B:

(18,000)/(12,000 + 18,000) = 18/30 = .6 = 60%

Contribution per Unit:

Product A: (5.50 - 1.15) * .4 = 4.35(.4) = $1.74

Product B: (3 - 0.90) * .6 = 2.1(.6) = $1.26

1.74 + 1.26 = $3.00

Breakeven Point by Units:

$225,000/$3.00 = 75,000 units

Breakeven Point for Product A:

75,000(.4) = 30,000 units

Breakeven Point for Product B:

75,000(.6) = 45,000 units

Yummy Food Drive-In sells burgers and fries. Yummy Food had the following sales revenues and profit for March:

Burgers:

Sales rev - $200k

Variable cost - (80k)

Contribution margin - $120k

Fries:

Sales rev - $50k

Variable cost - (5k)

Contribution margin - $45k

Total:

Sales rev - $250k

Variable cost - (85k)

Contribution margin - $165k

Fixed Cost - (100k)

Profit - $65k

What is Yummy Food's monthly breakeven point in sales dollars?

$151,515

Fixed costs/Average contribution margin ratio average = Breakeven sales dollars

Contribution margin ratio: $165,000/$250,000 = 66%

Breakeven sales dollars = $100,000/66% = $151,515

Yummy Food Drive-In sells burgers and fries. Yummy Food had the following sales revenues and profit for March:

Burgers:

Sales rev - $200k

Variable cost - (80k)

Contribution margin - $120k

Fries:

Sales rev - $50k

Variable cost - (5k)

Contribution margin - $45k

Total:

Sales rev - $250k

Variable cost - (85k)

Contribution margin - $165k

Fixed Cost - (100k)

Profit - $65k

What must their total sales be to have a target income of $30k?

$196,970

Target Sales = (Fixed Costs + Target Income) / Average Contribution Margin Ratio = ($100,000 + $30,000) / 66% = $196,970

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When calculating how much total sales would have to be for each product in a two-product firm to reach a target level income, why is it necessary to assume that the sales mix stays the same?

Because the current sales mix gives you a known average contribution margin percentage to make the CVP calculations; without a known contribution margin, it is impossible to calculate tarte net income or breakeven point

Sparkit Company recently leased retail space in a mall. The lease agreement states that Sparkit will pay $5,000 per month plus 2% of gross sales.

Which kinds of costs are represented in the lease agreement?

The lease cost would be a mixed cost

Erma Rock is considering buying an automated crusher, which would raise fixed costs to $80,000 per month but would lower the variable cost from $4 to $2 per ton.

What would Erma Rock's per month breakeven point be (in both tons and dollars) if the company were to acquire the automated crusher, assuming the price is $6 per ton?

20k tons and $120k

Erma Rock has fixed costs of $66,000, variable costs of $4.80 per ton, and a selling price of $5.10 per ton.

How many tons of crushed rock will Erma Rock need to sell to break even?

220k

Mickey & Mo Drive-In sells burgers and fries. The company had the following sales revenues and profit for June

Burgers:

Sales rev - $350k

Variable cost - 130k

Contribution margin - $220k

Fries:

Sales rev - $50k

Variable cost - 10k

Contribution margin - $40k

Total:

Sales rev - $400k

Variable cost - (140k)

Contribution margin - $260k

Fixed Cost - (00k

Profit - $160k Assuming the same sales mix, what must Mickey & Mo's Drive-In's total sales be to have a target income of $200,000?

$

$461,538

Eva Lee is a pediatric dentist setting up a practice in Des Moines, Iowa. She believes she can charge an average of $100 per patient and that her fixed costs are $35,000 per year. She believes that her variable costs are small and are only $10 per patient.

How many patients must Eva see per year to make $100,000?

1,500

This answer was derived by first calculating the contribution margin which is $90 per patient ($100-$10 per patient.) Second, the $90 contribution margin must be divided into the total of fixed costs and desired income or $135,000 ($100,000 desired profit + $35,000 fixed costs). When this calculation is made, the number of patients needed to be seen is 1,500 patients.