Cost Volume Profit Analysis Flashcards
CVP analysis (break-even analysis)
What is it?
What is it useful for?
What does it help management answer?
What does it look at?
What impacts does it show (2)?
What is the analysis determined by
Short answers
- Simple but powerful financial model concerning the relationship between profit and the level of activity.
- Very useful for business planning and marketing decisions
- Helps management answer various questions in relation to the desired sales levels
- Looks at relationship between volume and sales revenue, costs and profit in the short run
- The impact on profits of increasing or decreasing sales levels
- Impact on profits if expenditures on marketing are increased
- The analysis determined by the product’s cost structure
Cost structure of product or service
What are variable, fixed and semi-variable costs?
VARIABLE COSTS:
- costs which vary proportionately with output (e.g. raw materials).
FIXED COSTS:
- costs which do not change when output changes (e.g. business rates).
SEMI-VARIABLE COSTS:
- costs which are partly fixed and partly variable (e.g. land-line telephone).
Contribution
What is contribution and its formula?
What is the Breakeven point>
Contribution
Selling price – variable costs
i.e. contributes towards covering the fixed costs. Anything in excess is profit
Breakeven point
Point at which there is no profit, no loss, i.e. sales are equal to costs
Break even chart
Picture
- The margin of safety indicates how much actual sales exceed the break-even sales.
- The break-even point marks where sales equal total costs—no profit, no loss.
Contribution Relationships
Picture
Economists vs accountant’s view
What do economists assume?
3 stages?
- Economists assume that revenue volumes can only be increased by reducing selling price per unit, therefore the revenue will not increase proportionately with output (i.e. non linear)
- Costs are assumed to be high at low levels of volume output as the plant is not operating efficiently at this range but unit costs decrease as production increases (increasing returns to scale)
- However, as output increases the plant begins to operate efficiently and costs do not rise as quickly
- However, as production increases beyond a certain point labour become inefficient and costs increase again rapidly (decreasing returns to scale as economies of scale cannot be achieved due to bottlenecks, breakdowns etc)
Economists cost-volume graph (3 things about it and a picture)
- Curvilinear graph results in two break-even points.
- Note the shape of the total cost function:
- initial steep rise, levels off, followed by a further steep rise.
- The total revenue line initially rises steeply,then levels off and declines.
Economists vs accountant’s view
Picture of graph (5 lines)
Accountants model
Assumes (2)?
Therefore?
Results in (2)
Assumes:
- a constant selling price per unit
- a constant variable cost per unit
- therefore a linear relationship for total revenue and total costs
- Results in use of straight lines on CVP diagrams
- Results in only one break-even point
Fixed costs
What do economists assume and why?
What do accountants assume?
.
- Economists assume that fixed costs vary depending on the level of output.
- Lower levels of output would have lower fixed costs due to closed facilities, less staffing etc
- Accountant’s assume unchanged fixed costs within the relevant range
Accountant’s fixed cost function (2 points and a picture)
- Within the short term the firm anticipates that it will operate between output levels Q2 and Q3 and commits itself to fixed costs of 0A.
- Costs are fixed in the short term, but can be changed in the longer term.
Accountants model
What is it not meant to provide?
What does it only consider?
And what does that terms mean?
- Not meant to provide an accurate representation of all possible outputs
- Only considers a ‘relevant range’ for short term planning
- ‘relevant range’ is the output range at which a firm expects to be operating within a short-term planning horizon
Graphical and non graphical methods to determine break-even point
Mathematical formulas
- Net Profit
- Break-even point
Net profit
= (units sold x unit selling price) – (units sold x unit variable cost + total fixed overheads)
OR
NP = net profit
X = units sold
P = selling price
b= unit variable cost
a = total fixed costs
NP = PX - bX+a
Breakeven point
Break-even point is when the total costs are equal to total revenue
Therefore:
£0= Px - (a+bx)
The break-even point is at the level of output where:
a + bx = Px
Fixed costs + variable costs = sales + net profit of £0
Example 1
Assume a company manufactures a toy. The following information is available:
Selling price per toy £20
Variable costs per toy = £12
Total fixed costs £8000
What is the breakeven point in units (i.e. what is x)?
£8,000 + 12x= £20x - £0
£8,000 = £20x- £12x (note that this is the contribution) OR Fixed costs /contribution per unit
£8000/£8x = 1000 units
Proof
To prove the figure is accurate:
Total revenue £20,000 (1000 x £20)
Less variable costs £12,000
Less fixed costs £8,000
Profit and loss £0 (i.e. break-even)
Example 2
Assume a company manufactures a toy. The following information is available:
Selling price per toy £20
Variable costs per toy = £12
Total fixed costs £8000
- Assume the company targets a profit of £16,000.
How many units must it sell to achieve this profit?
i.e. Fixed costs + target profit/contribution per unit
(£8,000 + £16,000) /£8 = 3000 units
1000 + £16,000/£8 = 3000 units
Example 3
Assume a company manufactures a toy. The following information is available:
Selling price per toy £20
Variable costs per toy = £12
Total fixed costs £8000
Assume the company manages to sell an additional 1000 units above break-even, what is the impact on profit (i.e. 2000 units)
NP = £20 x 2000 – (£8000 + £12 x 2000)
NP = £40,000 - £32,000
NP = £8,000 additional
1000 x £8 = £8,000 additional
Example 4
Assume a company manufactures a toy. The following information is available:
Selling price per toy £20
Variable costs per toy = £12
Total fixed costs £8000
Assume fixed costs will increase to £16,000. Determine how many units must be sold to cover these costs
Contribution per unit is £8 (i.e. £20- £12).
£16,000/ £8 = 2000 units
Profit – volume ratio
What is it aka?
What is it?
What assumption does it have?
Assume a company manufactures a toy. The following information is available:
Selling price per toy £20
Variable costs per toy = £12
Total fixed costs £8000
What is the PV ratio?
What can it be used to determine?
Wha can it also be used to calculate and how?
- Also known as the contribution margin ratio
- PV ratio is the contribution divided by the sales
- Assumption that selling price and variable costs per unit stay constant
Contribution/sales = £8/ £20 = 0.40
i.e. for every £1 sale a contribution of £0.40 contribution is earned.
- PV ratio can be used to determine contribution for varying levels of sales
E.g. for a sales level of £500,000 the contribution would be £200,000 (sales x PV ratio)
- Break-even sales can also be calculated using the PV ratio
Fixed costs/PV ratio = BE sales (£)
Using the same information £8000/0.4 = £20,000
£20,000 sales = 1000 units (break-even point)
Margin of safety
What does it indicate? (2)
If the sales are expected to be 4000 units for sales revenue of £80,000 with a BEP of 1000 units, the margin of safety will be?
What can it also be expressed as and what is the formula for that?
- Indicates how much sales may decrease before a loss occurs
- How many units above break-even point
Example:
- If the sales are expected to be 4000 units for sales revenue of £80,000 the margin of safety will be 3000 units (i.e. 4000 – 1000 units) or £60,000
Alternatively express as a ratio
Percentage margin of safety = [expected sales (or actual) – breakeven sales]/expected sales (or actual) (£)
Margin of Safety graph (picture)
Margin of Safety example
On one of its production lines, a motor vehicle manufacturer produces 500 all-terrain vehicles a year and sells them for £30,000 each. If the variable cost of each vehicle is £20,000 and the total fixed costs of the line are £2 million, calculate the margin of safety for the production line (a) in number of vehicles, and (b) as a percentage of sales (£).
Break even in vehicles = 200
Margin of safety is 500 – 200 = 300 units
Margin of safety in sales =
300 units x £30,000 = £9 m/£15 m = 60%
Constructing graphs
What are they useful for (2)?
3 types of graph?
- Graphs are usually easier for managers to understand
- Can see the loss or profit for different levels of output
3 types of graph:
a) break – even chart
b) profit volume graph
c) contribution chart
Traditional Breakeven Chart (picture)
Contribution Breakeven Chart (picture)
Profit–volume Chart (picture)
Multi-product CVP analysis
Why is it needed?
When can the same approach be used?
Generally…?
- In practice firms often have more than one product/service
- Same approach can be used if fixed costs are directly attributable to products
- Generally, most fixed costs are common and cannot be directly traced
Multi-product CVP analysis
3 steps
- Convert sales volume measure of the individual products into standard batches of products based on the sales mix
E.g. if planned sales are 1000 of A and 2000 of B then sales mix is 1:2
- A contribution based on the standard batch can be determined.
Assume A’s contribution is £30 and B’s £50 then the contribution would be £30 + £100 (1 A and 2 B), that is £130/3 = £43.33
- The breakeven is then determined by using this contribution as if it were for a single product
Multi-product CVP example
H Ltd manufactures and sells two products, J and K. Annual sales are expected to be in the ratio of J:1 and K:3. Total annual sales are planned to be £420,000. Product J has a contribution to sales ratio of 40% (0.40) and product K is 50% (0.50). Annual fixed costs are estimated to be £120,000
Calculate the break-even point in sales value using the CVP ratio
CVP ratio = contribution/sales
= (0.40 x1 + 0.5 x3)/4
= 0.475 or 47.5%
Break-even sales = fixed costs/CVP ratio
= £120,000 /0.475
= £252,632
Another multi-product example
A company manufactures and sells two products X and Y
Annual fixed costs are £273,000
What is the break-even point in sales revenue?
Current sales mix is 4:1
Weighted average contribution = (4x £4 + 1 x £5)/5 = 4.2
Fixed costs/weighted average contribution=
£273,000/4.2 = 65000 units
Split between X and Y in 4:1 mix
X = 52000 units and Y = 13,000 units
X = 52,000 x £12 = £624,000 and Y = 13,000 x £8 = £104,000 Total break-even revenue = £728,000
Limitations of CVP analysis
- All other variables remain constant
e.g. sales mix, production efficiency, price levels, production methods. - Assumed that the costs/selling price are linear
- Complexity-related fixed costs do not change. If the range of items produced increases but volume remains unchanged, then it is assumed fixed costs will not alter.
- Profits are calculated on a variable costing basis.
- Unit variable cost and selling price are constant per unit of output.
- Cannot use the analysis outside the relevant range.
- Costs can be accurately divided into their fixed and variable elements.
- Single product or constant sales mix.
- It is assumed that costs are matched to income, i.e. there is no increase or decrease in stock levels over the period.
- It is not very useful for multi-product businesses as different breakeven points are produced for different sales mixes.
- It is difficult to measure activity for ‘jobbing’ businesses where every item produced is different (e.g. a large construction firm).
Recap - Another Way to Remember the Marginal Cost Equation
TP = N(SP - VC) - TFC
key:
TP = total profit
N = number of units
SP = unit selling price
VC = unit variable cost
TFC = total fixed costs
SP - VC = unit contribution
