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Cost-Volume-Profit Analysis: A Simple Model for Evaluating Decision Options A model is always an abstraction. It is a representation, sometimes mathematical, of what are believed to be the relations among the relevant decision options . Sample Questions Raised and Answered by CVP Analysis
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1. How many units must be sold (or how much sales revenue must be generated) in order to break even?
2. How many units must be sold to earn a before-tax profit equal to $60,000? A before-tax profit equal to 15 percent of revenues? An after-tax profit of $48,750?
3. Will total profits increase if the unit price is increased by $2 and units sold decrease 15 percent?
4. What is the effect on total profit if advertising expenditures increase by $8,000 and sales increase from 1,600 to 1,750 units?
5. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit and sales increase from 1,600 units to 1,900 units?
6. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit, advertising expenditures are increased by $8,000, and sales increased from 1,600 units to 2,300 units?
7. What is the effect on total profit if the sales mix is changed?
The breakeven point is the point where profit is zero,
so = 0 = Revenue - Cost
= SP*units sold - FC - VC*units sold
= (SP - VC)*units sold - FC
units sold = FC/(SP - VC)
We will call units sold at = 0: BEunits
Breakeven units (BEunits) * SP, or
SP * BEunits = SP*(FC/CM)
Breakeven revenue = FC/(CM/SP)
X = Break-even point in units
Y = Break-even point in revenue
I = (P - V)X - F
Slope = P - V
Data: The Doral Company manufactures and sells pens. Present sales output is 5,000,000 per year at a selling price of $.50 per unit. Fixed costs are $900,000 per year. Variable costs are $.30 per unit.
Compute the new operating income if . . .
1. A $.04 per-unit increase in variable costs.
2. A 20% decrease in fixed costs, a 20% decrease in selling price, a 10% decrease in variable costs, and a 40% increase in units sold.
Compute the new breakeven point in units for
each of the following changes.
The Rapid Meal has two restaurants that are open 24 hours per day. Fixed costs for the two restaurants together total $450,000 per year. Service varies from a cup of coffee to full meals. The average sales check for each customer is $8.00. The average cost of food and other variable costs for each customer is $3.20. The income tax rate is 30%. Target net income is $105,000.
Compute the total dollar sales needed to obtain the
target net income.
How many sales checks are needed to break even?
Compute net income if the number of sales checks
Assume the following:
Regular Deluxe Total Percent
Units sold 400 200 600 ----
Sales price per unit $ 500 $750 ---- ----
Sales $200,000 $150,000 $350,000 100.0%
Less: Variable expenses 120,000 60,000 180,000 51.4
Contribution margin $ 80,000 $ 90,000 $170,000 48.6%
Less: Fixed expenses 130,000
Net income $ 40,000
1. What is the break even point?
2. How much sales revenue of each product must be generated to earn
a before tax profit $50,000?