CVP with Profit and Taxes
Basic break-even tells you where profit is zero. Most exam questions go one step further: how many units do you need to sell to earn a target profit after taxes? The trick is to gross up the after-tax target to a pre-tax number first, then use the usual CVP formula.
CVP with a target profit after tax, explained simply
To hit an after-tax profit target, first gross it up to pre-tax (target ÷ (1 − tax rate)), then use units = (fixed costs + pre-tax profit) ÷ contribution margin per unit. In the example, $30,000 after a 25% tax is $40,000 pre-tax, so the company needs (40,000 + 40,000) ÷ $20 = 4,000 units.
What this CVP target profit lesson covers
- How to add a target profit to the break-even formula
- How to convert an after-tax profit target into pre-tax profit
- How to find the units and sales dollars needed for a target net income
- How to check your answer with a quick income statement
CVP target profit formulas, explained
- Target net income
- profit wanted after taxes
- t
- income tax rate
- FC
- total fixed costs
- P
- selling price per unit
- VC
- variable cost per unit
- t
- income tax rate
How to find units for an after-tax target step by step (worked example)
Price is $50, variable cost is $30 per unit, fixed costs are $40,000 and the tax rate is 25%. How many units must the company sell to earn $30,000 after tax?
- Gross up the target: $30,000 ÷ (1 − 0.25) = $40,000 pre-tax profit.
- Contribution margin per unit = $50 − $30 = $20.
- Units = ($40,000 + $40,000) ÷ $20 = 4,000 units.
- Sales dollars = 4,000 × $50 = $200,000.
- Check: $200,000 − $120,000 − $40,000 = $40,000 pre-tax; minus 25% tax = $30,000.
Answer: 4,000 units, or $200,000 in sales.
Break-even vs pre-tax target vs after-tax target
| Goal | Formula | Units in the example |
|---|---|---|
| Break even | FC ÷ CM per unit | 2,000 |
| $40,000 profit before tax | (FC + 40,000) ÷ CM per unit | 4,000 |
| $30,000 profit after 25% tax | [FC + 30,000 ÷ 0.75] ÷ CM per unit | 4,000 |
Harder CVP target profit questions
Do taxes change the break-even point?
No. At break-even, profit is zero, so there's no tax. Break-even stays at 2,000 units; taxes only matter once you aim for a profit.
How many units for $45,000 after tax?
Gross up: 45,000 ÷ 0.75 = $60,000 pre-tax. Units = (40,000 + 60,000) ÷ 20 = 5,000.
Common CVP target profit questions
How do you calculate target profit after tax in CVP?
First convert the after-tax target into pre-tax profit by dividing it by one minus the tax rate. Then add that pre-tax profit to fixed costs and divide by contribution margin per unit to get the units you need to sell.
Why do you divide by (1 − tax rate)?
Taxes take a slice of every dollar of pre-tax profit. If the tax rate is 25%, you keep 75 cents of each dollar, so you need target net income divided by 0.75 in pre-tax profit to end up with the after-tax amount you want.
Do taxes change the break-even point?
No. At break-even, profit is zero, so there is no income tax to pay. Taxes only matter when you are solving for a positive target profit, which is why the after-tax gross-up appears in target profit questions only.
What is the difference between target operating income and target net income?
Target operating income is profit before income taxes. Target net income is profit after taxes. If a question gives net income, convert it to operating income before using the CVP formula.