Chapter 15: Cost-volume-profit analysis

Cost-volume-profit (CVP) analysis is the managerial tool for questions such as: how many units must we sell to break even? What happens to profit if we cut the price, if suppliers raise their prices, or if rent goes up? How risky is our cost structure? The chapter starts with cost behaviour (variable, fixed and mixed costs), introduces the contribution margin, and then covers breakeven, target profit, sensitivity analysis, margin of safety, operating leverage and sales mix. This is one of the most calculation-heavy chapters for the exam.

Cost behaviour

• Variable costs change in total in proportion to volume, but are constant per unit. Batteries at $55 per tablet: 25 tablets cost $1,375, 100 tablets $5,500.
• Fixed costs stay the same in total over a wide range of volume, so the fixed cost per unit falls as volume rises. Fixed costs of $13,500 are $540 per tablet at 25 tablets and $135 at 100.
• Mixed costs have a fixed and a variable part, like a phone plan with a $100 subscription plus $0.10 per minute: $110 at 100 minutes, $150 at 500 minutes.

The relevant range is the range of volume within which total fixed costs and variable cost per unit stay constant. Outside it the assumptions break: to produce much more steel, Tata Steel must invest in new capacity, so fixed costs jump to a higher level and a new relevant range starts. Costs are also often sticky: they rise faster when volume grows than they fall when volume shrinks (cost stickiness).

The high-low method

The high-low method splits a mixed cost into its variable and fixed parts using the periods with the highest and lowest activity. Example: maintenance costs $1,960 at 480 tablets (highest) and $1,480 at 240 tablets (lowest).

The cost equation is total cost = $2 × tablets + $1,000; for 400 tablets: 800 + 1,000 = $1,800. Pick the highest and lowest activity levels, not the highest and lowest costs.

Contribution margin

The contribution margin is sales revenue minus variable costs: the amount that contributes to covering fixed costs and, after that, to operating income. Smart Touch Learning sells tablets at $500 with variable costs of $275:

At 200 tablets the contribution margin is 100,000 − 55,000 = $45,000. A contribution margin income statement classifies costs by behaviour (variable, then fixed): sales − variable costs = contribution margin − fixed costs = operating income. A traditional income statement classifies costs by function (product costs in cost of goods sold, period costs below gross profit).

CVP assumptions

• The price per unit does not change with volume.
• Every cost can be classified as variable, fixed or mixed.
• Volume is the only factor that changes total costs; fixed costs do not change.
• Inventory levels do not change (everything produced is sold).

Breakeven point and target profit

The breakeven point is the sales level where operating income is zero. Three approaches give the same answer:

• Equation approach: sales − variable costs − fixed costs = target profit. With fixed costs of $13,500: 500Q − 275Q − 13,500 = 0, so 225Q = 13,500 and Q = 60 tablets.
• Contribution margin approach (units):

• Contribution margin ratio approach (dollars):

Check: 60 × 500 = 30,000 revenue − 16,500 variable costs − 13,500 fixed costs = 0. For a target profit of $4,500 a month: (13,500 + 4,500) / 225 = 80 tablets. The case class did the same for Tata Steel slabs: price $500, variable cost $275, fixed costs $12,000 and a target profit of $6,000 give (12,000 + 6,000) / 225 = 80 slabs. A CVP graph shows the revenue line and the total cost line (starting at the fixed costs); they cross at the breakeven point, with the loss area below and the profit area above it.

Sensitivity analysis

Sensitivity analysis is a "what if" technique: how do profit and the breakeven point change if price, costs or volume change? Units are rounded up, because you cannot sell part of a tablet.

Once fixed costs are covered, each extra unit adds its full contribution margin to operating income. A clock company with a $17 unit contribution margin that sells 150 more clocks than planned earns 150 × 17 = $2,550 more.

Margin of safety

The margin of safety is the excess of expected sales over breakeven sales: how far sales can fall before the company makes a loss.

Expected sales of 100 tablets and breakeven at 60: margin of safety 40 tablets, or 40 × 500 = $20,000, and a ratio of 40%.

Operating leverage

The cost structure is the proportion of fixed to variable costs. Operating leverage predicts how strongly operating income reacts to a change in sales volume, and it is higher when fixed costs are a larger part of costs.

Two carriage-tour companies both carry 500 passengers and earn $4,000 operating income. Company A has high fixed costs: contribution margin $10,000, fixed costs $6,000, DOL = 10,000 / 4,000 = 2.50. Company B has mostly variable costs: contribution margin $5,000, fixed costs $1,000, DOL = 1.25. When a hurricane cuts passengers by 20% to 400, A's operating income falls by 2.50 × 20% = 50% (to $2,000) and B's by 1.25 × 20% = 25% (to $3,000). High operating leverage magnifies both rises and falls.

Sales mix

Most companies sell several products with different contribution margins. The sales mix is the combination that makes up total sales. Cool Cat sells cat beds (price $44, variable cost $24, margin $20) and scratching posts (price $100, variable cost $30, margin $70) in a ratio of 3 to 2.

1. Weighted-average unit contribution margin: (3 × 20 + 2 × 70) / 5 = 200 / 5 = $40.
2. Breakeven for the "package": fixed costs 40,000 / 40 = 1,000 units.
3. Split according to the mix: 1,000 × 3/5 = 600 cat beds and 1,000 × 2/5 = 400 scratching posts.

For a target profit of $20,000: 60,000 / 40 = 1,500 units, or 900 beds and 600 posts. If the mix shifts to the product with the higher margin, the breakeven point falls. Retailers such as Best Buy use data analytics to follow their sales mix and its effect on profit.