Accounting Mod 16

What is CVP analysis?

Cost-volume-profit analysis: how changes in volume, price, and costs affect profit

Profit equation (in units)

Profit = (Price - VC per unit) x Units - Fixed costs

Variable cost behavior

Total changes in proportion to volume; the cost per unit stays constant

Fixed cost behavior

Total stays constant within the relevant range; the cost per unit falls as volume rises

Contribution margin (CM)

Sales - variable costs; the amount available to cover fixed costs and then provide profit

Unit contribution margin (UCM)

Price - VC per unit; the CM earned on each unit sold

CM ratio formula

CM / Sales = UCM / Price; the CM earned per dollar of sales

VC ratio formula

Variable costs / Sales = 1 - CM ratio

Layout of a contribution income statement

Sales - variable costs = CM; CM - fixed costs = operating income

How is a contribution statement organized vs. a traditional one?

Contribution: by cost behavior (variable vs. fixed). Traditional: by function (production vs. selling and admin)

Why is gross profit not the same as CM?

Gross profit deducts fixed manufacturing overhead and ignores variable selling and admin costs; CM deducts all variable costs and no fixed costs

Break-even point

The sales level where profit = 0 and CM exactly covers fixed costs

Break-even units formula

Fixed costs / UCM

Break-even sales (dollars) formula

Fixed costs / CM ratio

Target profit units formula

(Fixed costs + desired profit) / UCM

Target profit sales (dollars) formula

(Fixed costs + desired profit) / CM ratio

Where does desired profit go in the target-profit formula?

In the numerator, added on top of fixed costs (never subtracted)

Which inputs does break-even depend on?

Fixed costs, price, VC per unit, and the sales mix; not current sales and not the tax rate

UCM x break-even units equals what?

Fixed costs (so profit = 0); use this as a zero-profit check

Divide by UCM or by CM ratio: which gives units and which gives dollars?

UCM gives units; CM ratio gives sales dollars

How do you convert a unit amount to sales dollars?

Multiply by the selling price (never by VC per unit)

Margin of safety (MOS)

Current sales - break-even sales; how far sales can fall before a loss occurs

MOS ratio

MOS / current sales

MOS in dollars from MOS in units

MOS units x selling price

Is MOS a level or a gap?

A gap; it can never exceed current sales

Common MOS error

Subtracting fixed costs instead of break-even sales (MOS is sales minus sales)

Why does a bigger MOS mean less risk?

Sales can fall further before the company reaches break-even and starts losing money

CVP graph: where does the revenue line start and what is its slope?

It starts at the origin; slope = price per unit

CVP graph: where does the total cost line start and what is its slope?

It starts at fixed costs on the vertical axis; slope = VC per unit

CVP graph: what does the fixed cost line look like?

A flat horizontal line at the fixed cost amount (slope = 0)

CVP graph: where is break-even?

Where the revenue line crosses the total cost line

CVP graph: what do the areas left and right of break-even show?

Left = loss area; right = profit area

CVP graph: what does the vertical gap between revenue and total cost show?

Profit (or loss) at that volume

Profit-volume graph: vertical-axis intercept

Negative fixed costs (at zero units you lose exactly FC)

Profit-volume graph: where does the line cross the horizontal axis?

At the break-even point

Profit-volume graph: slope

UCM if units are on the horizontal axis; CM ratio if sales dollars are

Fixed costs rise: effect on the CVP graph?

The total cost line shifts up in parallel (the intercept changes, the slope does not)

Fixed costs rise: effect on the profit-volume graph?

The line shifts down in parallel; break-even rises

VC per unit rises: effect on the CVP graph?

The total cost line gets steeper with the same intercept; break-even rises

VC per unit rises: effect on the profit-volume graph?

The line gets flatter with the same intercept; break-even rises

Price rises: effect on the CVP graph?

The revenue line gets steeper; break-even falls

Rule of thumb for graph shifts

A fixed cost change moves an intercept; a price or VC change moves a slope

CVP assumption 1 (cost behavior)

All costs can be classified cleanly as fixed or variable

CVP assumption 2 (linearity)

Price and VC per unit are constant within the relevant range, so revenue and cost lines are straight

CVP assumption 3 (sales mix)

Only one product is sold, or the sales mix stays constant

Extra assumptions in the tax appendix

Taxable income equals accounting income, and the tax rate is constant

Example of violating the linearity assumption

A volume discount, or a price cut needed to sell more units

Example of violating the constant sales mix assumption

Customers shift toward the cheaper, lower-margin model

What happens to CVP results outside the relevant range?

The formulas still produce a number, but it can't be trusted

Sales mix

The relative proportion of each product sold, in units or in sales dollars

Bundle (multi-product CVP)

A made-up package of products in the sales mix ratio (e.g. 3 A + 1 B), treated as one unit

Bundle UCM

Sum of (units of each product in the bundle x that product's UCM)

Break-even bundles formula

Fixed costs / bundle UCM

After finding break-even bundles, what is the last step?

Unpack: bundles x units per product in the bundle gives units of each product (bundles are not units)

Unit mix vs. dollar mix: example

A 1:1 unit mix of 40 and 120 dollar products is a 25/75 split in sales dollars

When the mix is given in sales dollars, use which measure?

The weighted-average CM ratio (weights are the dollar mix percentages)

Why use a weighted average rather than a simple average?

Products sold more often count more; the simple average works only for a 1:1 unit mix

Mix shifts toward the lower-margin product: effect on break-even and profit?

Break-even rises and profit at a given volume falls

Mix shifts toward the higher-margin product: effect on break-even and profit?

Break-even falls and profit at a given volume rises

Operating leverage formula

Contribution margin / operating income

What does operating leverage measure?

How sensitive profit is to a change in sales; the profit change per 1 percent change in sales

% change in profit using leverage

Operating leverage x % change in sales

What creates high operating leverage?

A cost structure with high fixed costs and low variable costs

Does operating leverage stay constant as sales change?

No; it is a snapshot at one sales level and falls as sales rise above break-even

Operating leverage near break-even

It becomes very large because operating income is near zero (undefined at exactly break-even)

Is high operating leverage better?

No; it means bigger profit gains when sales rise and bigger losses when sales fall

Operating leverage as the inverse of what ratio?

The margin of safety ratio (leverage = 1 / MOS ratio)

Trap: CM / Sales vs. CM / operating income

CM / Sales is the CM ratio; CM / operating income is operating leverage

After-tax profit formula

Before-tax profit x (1 - tax rate)

Before-tax profit from an after-tax target

After-tax profit / (1 - tax rate)

Steps for an after-tax target profit problem

Convert the after-tax target to before-tax first, then use the target-profit formula with the before-tax figure

Is fixed cost divided by (1 - tax rate)?

No; only the profit target is converted

Effect of the tax rate on break-even

None; at break-even profit is zero so no tax is paid

Effect of a higher tax rate on units needed for an after-tax target

More units are needed (the required before-tax profit rises)

Trap: tax conversion at a 40 percent rate

Divide by 0.60; do not multiply by 1.40