Managerial Accounting Chapter 3

Contribution margin

It’s what’s left from each sale after covering variable costs, and it contributes to paying fixed costs and then to profit.

It’s called “contribution” because it’s the amount left over to contribute toward covering fixed costs, and then toward profit. Once total CM exceeds fixed costs, the rest is profit.

CM (total)

Sales - Variable costs

CM per unit

= Price per unit - Variable cost per unit

It stays the same as long as price and variable cost per unit don’t change.

CM ratio

= CM ÷ Sales

OR

= CM per unit ÷ Price per unit

It shows how many cents of each sales dollar are left after variable costs.

Contribution margin income statement

Sales

- Variable costs

= Contribution Margin

- Fixed costs

= Operating Income

It sorts costs by behavior (variable vs. fixed)

Traditional vs. CM income statement

Traditional: Sales - COGS = Gross margin, then - selling and administrative = Operating income. It sorts costs by function (product vs. period)

CM format: sorts costs by behavior (variable vs. fixed).

Operating income is the same on both, because both subtract all costs. Only the middle subtotals differ.

Any increase in a variable cost, whether materials, labor, variable overhead, or variable selling costs, lowers contribution margin.

Break-even point

The sales level where total revenue = total costs, so operating income is exactly $0.

Break-even in units

Fixed costs ÷ CM per unit

Break-even in sales dollars

Fixed costs ÷ CM ratio

Target profit formula

Units = (Fixed costs + Target operating income) ÷ CM per unit

For dollars, divide by the CM ratio instead. Break-even is just the same formula with a target of $0.

How to check a break-even or target profit answer

Build a CM income statement at that volume. At break even, CM exactly equals fixed costs

Operating income above break-even

Operating income = CM per unit x (units sold - break-even units).

Once fixed costs are covered, every extra unit adds its full CM to profit. Use the CM per unit, not the ratio, when working in units.

Converting target net income to operating income

Operating income = Net income ÷ (1 - tax rate). The CVP formula always uses operating income (pre-tax).

Full target net income example

Price $20, CM ratio 60%, FC $25,000, net income target $15,000, tax 25%. CM per unit = $12.

Operating income needed = $15,000 ÷ 0.75 = $20,000

Units = ($25,000 + $20,000) ÷ $12 = 3,750

Total revenue line on the CVP graph

Starts at the origin (zero sales = zero revenue). Its slope is the selling price per unit.

Total cost line on the CVP graph

Starts at the level of fixed costs on the y-axis (costs exist even at zero volume). Its slope is the variable cost per unit. The fixed cost line is flat.

Where do the lines meet, and what is the area between them?

The revenue line crosses the total cost line at the break-even point. To the right of break-even the gap between the lines is operating profit. To the left, it’s an operating loss.

Sensitivity analysis

A way to test how changes in selling price, costs, or volume affect profit and break-even, answering “what if?” questions.

Price increases: effect on CM per unit and break-even

CM per unit goes up and break-even goes down (fewer units needed)

Example:

The price changing from $0.60 → $0.66 makes CM $0.30 and break-even 5,000 units (from 6,250). A price decrease does the opposite.

Variable cost per unit increases: effect

CM per unit goes down and break-even goes up. Example: VC $0.36 → #0.39 makes CM $0.21 and break-even 7,143 units (from 6,250). A decrease does the opposite.

Fixed costs increase: effect

CM per unit has no change, but break-even goes up. Example: FC $1,500 → $1,650 makes break-even 6,875 units (from 6,250). A decrease lowers break-even.

Does a change in sales volume change break-even?

No. Only a change in price, variable cost per unit, or fixed costs changes break-even.

Price and variable cost per unit both rise 10%: effect on CM per unit and CM ratio?

CM per unit increases, CM ratio is unchanged.

Example: $100 - $60 = $40 (40%) becomes $110 - $66 = $44 (still 40%)

Fixed costs rise and variable cost per unit falls (new machine): what happens to break-even?

You can’t tell without numbers, because the two effects pull in opposite directions (higher fixed costs raise it, a higher CM lowers it.

Margin of safety (MOS)

The amount by which expected sales exceed break-even sales. It shows how far sales can fall before the company starts losing money, so a bigger MOS means lower risk.

MOS in units and dollars

Units: expected units - break-even units

Dollars: expected sales $ - break-even sales $ (or MOS units X price)

MOS ratio

MOS ÷ expected sales

It expresses the cushion as a percentage so firms of different sizes can be compared.

MOS homework example

Expected sales $220,000, break-even 10,000 units at $20 (= $200,000 in sales). MOS = $220,000 - $200,000 = $20,000. It is not sales minus fixed costs, and it is not break-even sales itself.

Cost structure and operating leverage

Cost structure is the mix of fixed vs. variable costs. Operating leverage is how strongly operating income reacts to a change in sales. A company with high fixed costs and low variable costs has high operating leverage (more risk and more reward).

Degree of operating leverage (DOL)

Contribution margin ÷ operating income

Example: $10,000 ÷ $4,000 = 2.50

Predicting change in operating income

% change in operating income = DOL x % change in sales.

Example: DOL 2.50 and a 20% sales drop means operating income falls 2.50 × 20% = 50%

DOL at different sales levels

DOL changes at every sales level, so it is always calculated at a specific volume. It’s highest close to break-even, because operating income is tiny and CM ÷ OI becomes huge.

Sales mix

The combination (proportion) of products that make up total sales. Products have different prices and CMs, so the mix affects overall profit and break-even

Weighted-average CM per unit

Total CM of the mix ÷ total units in the mix.

Three steps for multi-product break-even

(1) Find the weighted-average CM per unit.

(2) Break-even total units = fixed costs ÷ weighted-average CM.

(3) Split the total by the mix.

Example: $1,820 ÷ $0.26 = 7,000 units; A = 9/10 × 7,000 = 6,300, B = 1/10 × 7,000 = 700.

Bundle method

Treat the mix as one “bundle.” CM per bundle = sum of (units in bundle x CM per unit).

Break-even bundles = fixed costs ÷ CM per bundle. Then multiply by each product’s units per bundle. Both methods give the same answer.

What happens when the sales mix changes?

Break-even and operating income change. Shifting toward the higher-CM product lowers break-even.

Example: a 4:1 mix (CM per bundle $60) breaks even at 37,500 bundles (187,500 units), versus 180,000 units at a 3:1 mix. The mix is always stated in units, not dollars, and the method assumes the mix stays constant.

CVP assumptions

Price per unit doesn’t change with volume; all costs can be classified as fixed, variable, or mixed; variable costs change only with volume; fixed costs don’t change with volume (within the relevant range); inventory levels don’t change.

Using CVP to make a decision

Calculate operating income with the change, compare it to operating income without it, and choose the higher one.

Example (Tiny’s Cabinets: price $600, VC $350, FC $20,000, currently 100 units = $5,000 income): a $5,000 ad campaign raising sales 10% gives 110 × $250 − $25,000 = $2,500, so no. If it raises sales 25%, it gives 125 × $250 − $25,000 = $6,250, so yes.