Chapter 13 - Cost-Volume-Profit (SoA)

LO 1 · What is cost behaviour analysis?

Studying how costs change as business activity changes. It helps managers plan and compare alternatives.

LO 1 · What is an activity index or volume index?

The activity measure used to explain a cost, such as miles driven, rooms occupied, sales dollars, or classes taught. A business can use multiple indexes.

LO 1 · How does total variable cost behave?

It changes in the same proportion as activity. If units rise 10%, total variable cost rises 10% within the relevant range.

LO 1 · How does variable cost per unit behave?

It stays constant within the relevant range. Total variable cost = variable cost per unit × activity.

LO 1 · What do variable cost graphs look like?

Total variable cost slopes up from zero. Variable cost per unit is a horizontal line.

LO 1 · Damon uses a $10 camera per phone. What does it spend on 2,000 and 10,000 phones?

$20,000 and $100,000 in total. The camera cost stays $10 per phone.

LO 1 · How does total fixed cost behave?

It stays the same as activity changes within the relevant range. Rent, insurance, property taxes, and straight-line depreciation are examples.

LO 1 · How does fixed cost per unit behave?

Fixed cost per unit = total fixed cost ÷ units. It falls as activity rises because the same total is spread over more units.

LO 1 · What do fixed cost graphs look like?

Total fixed cost is horizontal within the relevant range. Fixed cost per unit is a downward curve.

LO 1 · Damon pays $10,000 monthly rent. What is rent per phone at 2,000 and 10,000 phones?

$5 and $1 per phone. Total rent stays $10,000.

LO 1 · What is the relevant range?

The activity levels a company expects to operate within. Within that range, CVP treats total fixed costs and variable cost per unit as constant.

LO 1 · Why can cost graphs behave differently outside the relevant range?

The variable rate can change, such as with bulk discounts, and fixed costs can jump, such as when a second facility is needed.

LO 1 · What are examples of fixed costs managers can choose to change?

Research and development or management training budgets.

LO 1 · What is a mixed cost?

A cost with a fixed base plus a variable charge. Total cost changes with activity, but the entire bill does not change in the same proportion.

LO 1 · How do you recognize a mixed cost on a graph?

The total cost line starts above zero at the fixed cost. Its slope is the variable cost per unit of activity.

LO 1 · The truck rental graph starts at $50 and reaches $200 at 300 miles. What is the cost equation?

Total cost = $50 + ($0.50 × miles). The $150 increase over 300 miles gives the $0.50 rate.

LO 1 · Helena doubles production. Which costs in the slide are variable?

Direct materials, direct labour, and indirect materials. Their total costs double.

LO 1 · Which Helena costs are fixed and which are mixed?

Depreciation and rent are fixed because their totals stay the same. Maintenance and utilities are mixed because their totals rise by less than double.

LO 1 · What is the formula for total variable cost?

Total variable cost = variable cost per unit × activity.

LO 1 · What is the formula for fixed cost per unit?

Fixed cost per unit = total fixed costs ÷ units produced.

LO 1 · What is the formula for total mixed cost?

Total mixed cost = total fixed costs + (variable cost per unit × activity).

LO 2 · What does the high-low method estimate?

The variable rate and total fixed cost within a mixed cost.

LO 2 · How do you choose the high and low points?

Pick the highest and lowest activity levels and use their matching costs.

LO 2 · Why does subtracting the two total costs isolate variable cost?

Each total includes the same fixed amount, which cancels when you subtract.

LO 2 · How do you calculate the variable rate using high-low?

Variable cost per unit = (cost at high activity − cost at low activity) ÷ (high activity − low activity).

LO 2 · How do you calculate fixed cost after finding the variable rate?

Fixed cost = total cost − (variable rate × activity). Use either the high or low observation and keep its cost and activity together.

LO 2 · How do you write and use a mixed cost equation?

Estimated total cost = fixed cost + (variable rate × activity). Plug the activity you want to predict into the equation.

LO 2 · How do you read a cost scatter plot, and what is a limit of high-low?

Activity is on the x-axis and total cost is on the y-axis. High-low uses only two observations, so an unusual high or low point can affect the estimate.

LO 2 · Metro Transit has 50,000 miles at $63,000 and 20,000 miles at $30,000. What is the variable rate?

($63,000 − $30,000) ÷ (50,000 − 20,000) = $1.10 per mile.

LO 2 · What is Metro Transit’s fixed cost using the low point of 20,000 miles at $30,000 and a $1.10 rate?

$30,000 − ($1.10 × 20,000) = $8,000.

LO 2 · Estimate Metro Transit’s cost at 45,000 miles with $8,000 fixed and $1.10 per mile.

$8,000 + ($1.10 × 45,000) = $57,500.

LO 2 · Byrnes has 9,800 units at $14,740 and 7,000 units at $11,100. Find the variable rate.

($14,740 − $11,100) ÷ (9,800 − 7,000) = $1.30 per unit.

LO 2 · Write Byrnes’s cost equation and estimate cost at 8,000 units. Low point: 7,000 units at $11,100. Rate: $1.30.

Fixed cost = $11,100 − ($1.30 × 7,000) = $2,000. Total cost = $2,000 + ($1.30 × units). At 8,000 units it is $12,400.

LO 3 · What is cost-volume-profit (CVP) analysis?

Studying how sales volume, costs, and selling prices affect profit. Managers use it to plan profit and decide prices, product mix, and how to use production capacity.

LO 3 · What are the five inputs in CVP analysis?

Activity volume, unit selling prices, variable costs per unit, total fixed costs, and sales mix.

LO 3 · What does the linearity assumption mean in CVP?

Within the relevant range, selling price per unit, variable cost per unit, and total fixed costs are constant.

LO 3 · How does CVP classify costs, and what drives costs in the model?

Costs are split into fixed and variable components, including any mixed costs. Activity changes drive changes in total cost.

LO 3 · What does CVP assume about inventory and sales mix?

All units produced are sold. If several products are sold, the proportions sold stay constant.

LO 3 · How is a CVP income statement organized?

Sales − variable costs = contribution margin. Contribution margin − fixed costs = net income.

LO 3 · How does the CVP income statement differ from a traditional income statement?

The internal CVP statement groups costs by behaviour and shows contribution margin. The traditional statement shows gross profit after cost of goods sold. Vargo’s two statements report the same net income.

LO 3 · What is contribution margin and what does it cover?

Sales less variable costs. It covers fixed costs first, then any remaining amount is profit.

LO 3 · How do you calculate unit and total contribution margin?

Unit CM = selling price per unit − variable cost per unit. Total CM = sales − total variable costs, or unit CM × units sold.

LO 3 · How do you calculate contribution margin ratio?

Total CM ÷ total sales, or unit CM ÷ unit selling price. It measures how much of each sales dollar is left after variable costs.

LO 3 · How can you estimate the effect of a change in sales dollars?

Change in profit = change in sales dollars × CM ratio, assuming the CM ratio and total fixed costs stay constant.

LO 3 · Vargo sells phones for $500 with $300 unit variable costs. What are its unit CM and CM ratio?

$500 − $300 = $200 per phone. $200 ÷ $500 = 40%, or 40¢ left per sales dollar.

LO 3 · What makes up Vargo’s $300 in variable costs per phone and $200,000 in monthly fixed costs?

Variable: $185 materials, $100 labour, $15 commissions. Fixed: $40,000 manufacturing overhead, $150,000 CEO salary, $10,000 sales salaries.

LO 3 · Vargo sells 1,600 phones at $500, with $300 unit variable cost and $200,000 fixed costs. Prepare its CVP totals.

Sales $800,000 − variable costs $480,000 = CM $320,000. Subtract fixed costs $200,000 to get $120,000 net income.

LO 3 · Vargo has $200 unit CM and $200,000 fixed costs. What is profit at 1,000 and 1,001 phones?

At 1,000 phones, CM exactly covers fixed costs and profit is $0. One more phone adds $200 of CM and profit.

LO 3 · Vargo’s sales rise by $100,000 with a 40% CM ratio and constant fixed costs. What happens to profit?

Profit increases by $40,000.

LO 3 · Ampco sells 4,000 thermostats at $85 with $32 unit variable cost and $190,000 fixed costs. Find sales, variable costs, CM, and net income.

Sales $340,000. Variable costs $128,000. CM $212,000. Net income $22,000.

LO 3 · For Ampco, price is $85 and variable cost is $32. What are the per-unit and percent-of-sales figures?

Sales $85 (100%). Variable cost $32 (37.65%). CM $53 (62.35%).

LO 3 · What is the formula for sales revenue?

Sales revenue = selling price per unit × units sold.

LO 3 · What is the formula for total variable costs on a CVP income statement?

Total variable costs = variable cost per unit × units sold.

LO 3 · What is the formula for unit contribution margin?

Unit CM = selling price per unit − variable cost per unit.

LO 3 · What are the formulas for total contribution margin?

Total CM = sales − total variable costs = unit CM × units sold = sales × CM ratio.

LO 3 · What is the formula for net income on a CVP income statement?

Net income = total CM − total fixed costs. You can also write it as (unit CM × units sold) − total fixed costs or (sales × CM ratio) − total fixed costs.

LO 3 · How do you find variable costs as a percentage of sales?

Variable cost ratio = total variable costs ÷ total sales, or unit variable cost ÷ unit selling price. It also equals 1 − CM ratio when both ratios are decimals.

LO 4 · What happens at the break-even point?

Total sales revenue equals total variable plus fixed costs. Net income is zero, so total contribution margin equals fixed costs.

LO 4 · What are the three break-even methods?

Mathematical equation, contribution margin method, and CVP graph.

LO 4 · How do you find break-even units with the mathematical equation?

Set (price × units) − (variable cost per unit × units) − fixed costs = 0, then solve for units.

LO 4 · How do you find break-even units using contribution margin?

Total Fixed Costs divided by Contribution Margin per Unit.

LO 4 · How do you find break-even sales dollars?

Divide total fixed costs by the CM ratio as a decimal. You can also multiply exact break-even units by the selling price.

LO 4 · How do you read break-even from a CVP graph?

Find where sales revenue crosses total costs. Read units on the x-axis and sales dollars on the y-axis.

LO 4 · Where do the CVP graph lines start, and where are profit and loss?

Sales starts at zero. Total cost starts at fixed costs. Sales above total cost means profit, and sales below total cost means loss.

LO 4 · Vargo has $200,000 fixed costs, $200 unit CM, and a 40% CM ratio. Find break-even units and sales dollars.

$200,000 ÷ $200 = 1,000 phones. $200,000 ÷ 0.40 = $500,000 in sales.

LO 4 · Gossen breaks even selling 200,000 pliers at $4 with a 25% CM ratio. Find fixed costs.

Sales = 200,000 × $4 = $800,000. At break-even, fixed costs equal total CM: $800,000 × 0.25 = $200,000.

LO 4 · Lombardi charges $400, has $240 variable cost per unit and $180,000 fixed costs. Find break-even both ways.

Equation: 400Q − 240Q − 180,000 = 0, so Q = 1,125. Unit CM method: $180,000 ÷ ($400 − $240) = 1,125 units.

LO 4 · How do you find fixed costs when break-even sales are given?

Fixed costs = break-even sales dollars × CM ratio, or break-even units × unit CM.

LO 5 · What is target net income?

The profit management wants to earn. Total CM must cover fixed costs plus that profit.

LO 5 · What is the mathematical equation for target net income?

Sales − variable costs − fixed costs = target net income. Equivalently, required sales = variable costs + fixed costs + target net income.

LO 5 · How do you find required units for a target profit?

(fixed costs + target net income) divided by unit CM.

LO 5 · How do you find required sales dollars for a target profit?

Divide (fixed costs + target net income) by the CM ratio as a decimal.

LO 5 · How do you read a target profit on a CVP graph?

Find where the sales line is above the total cost line by the amount of the target profit. The vertical gap is profit.

LO 5 · Vargo charges $500, has $300 unit variable cost and $200,000 fixed costs. How many phones and how much sales revenue produce $80,000 profit?

500Q − 300Q − 200,000 = 80,000, so Q = 1,400 phones. Required sales = $280,000 ÷ 0.40 = $700,000.

LO 5 · At 1,400 phones, Vargo’s sales are $700,000 and total costs are $620,000. What is the vertical gap on the CVP graph?

$80,000 of profit.

LO 5 · What is the margin of safety?

How far actual or expected sales can fall before reaching break-even. A larger margin gives more room for sales to drop.

LO 5 · How do you calculate margin of safety in dollars?

Actual or expected sales dollars − break-even sales dollars.

LO 5 · How do you calculate the margin of safety ratio?

Margin of safety in dollars ÷ actual or expected sales dollars. The denominator is the level sales would fall from.

LO 5 · Vargo expects $750,000 of sales and breaks even at $500,000. Find both safety measures.

Margin of safety = $250,000. Ratio = $250,000 ÷ $750,000 ≈ 33.3%.

LO 5 · Marshall has $600,000 actual sales and $420,000 break-even sales. Find its margin of safety ratio.

($600,000 − $420,000) ÷ $600,000 = 30%.

LO 5 · Zootsuit charges $56 per bag, with $42 unit variable cost and $320,000 fixed costs. Find the CM ratio and break-even sales dollars.

CM ratio = ($56 − $42) ÷ $56 = 25%. Break-even sales = $320,000 ÷ 0.25 = $1,280,000.

LO 5 · Zootsuit has $1,382,400 actual sales and $1,280,000 break-even sales. Find its margin of safety and ratio.

$1,382,400 − $1,280,000 = $102,400. $102,400 ÷ $1,382,400 ≈ 7.4%.

LO 5 · Zootsuit has $320,000 fixed costs and a 25% CM ratio. What sales are needed for $410,000 profit?

($320,000 + $410,000) ÷ 0.25 = $2,920,000.

LO 5 · How do you write the target net income equation using units sold (Q)?

(Selling price per unit × Q) − (variable cost per unit × Q) − total fixed costs = target net income.