Week 4 - Cost behaviour and cost- volume-profit (CVP) analysis

What are the key steps in the high-low method?

1. Calculate increase in costs (Y axis) from lowest to highest level 2. Calculate increase in output (X axis) from lowest to highest level 3. Divide increase in costs (Y₂ - Y₁) by increase in output (X₂ - X₁) to get variable cost per unit 4. y intercept or (a) in the function is the total fixed costs

Answer

1. Increase in costs (highest - lowest) 3300 - 2900 = 400 2. Increase in outputs (highest - lowest) 2600 - 1800 = 800 3. Variable cost per unit 400/800 = £0.5 4. Fixed cost 3300 - (0.5 x 2600) = £2000

Define semi variable costs

A cost containing both fixed and variable components and which is thus partly affected by a change in the level of activity Note the assumptions we mentioned before only hold for a particular range (where it is linear)

Define scarse resource

A resource where we do not have enough supply to undertake every opportunity to make additional contribution

What is the cost-volume-profit analysis (aka breakeven analysis)?

A study of the effects of changes in fixed cost, variable cost, sales price/quantity mix on future profit.

Outline the steps for finding the break even point algebraically

Equate total revenue and total cost functions and solve for Q 1) Total Revenue TR = P x Q 2) Total cost (total fixed + total variable) TC = FC + (VC x Q) 3) Equate TR and TC TR = TC 4) Sub in TR and TC expressions P x Q = FC + (VC x Q) 5) Put Q on one side (P x Q) - (VC x Q) = FC 6) Simplify Q (P - VC) = FC ; Note: Q (P - VC) would be total contribution 7) Solve for Q to give us the units of sales at the BE point Q = FC/(P - VC) Note: (P - VC) would be contribution per unit Notice we have the BE quantity is fixed cost/contribution per unit which is what we saw before

Define the breakeven point (in units)

Fixed costs/contribution per unit

If we have a higher leverage operation what does this mean?

High fixed cost compared to variable costs It means that small changes in sales volume results in large changes in operating income It is more risky because it means operating profit is highly variable

If you have a higher operating leverage what can you deduce about the break even point?

Higher operating leverage means higher break even point.

Define stepped fixed costs

If activity is expanded to the point where further investment in fixed costs is needed, e.g. a new factory premises is to be rented then the rent cost will increase to a new, higher level

Once you found the break even point is units - how do you find the break even in sales?

Just muliply your break even units by price So: Q x P = (F x P)/(P - VC) An equivalent formula is Q x P = F/((P - VC)/P) Which if you notice is fixed cost/ (contribution per unit/selling price) i.e fixed cost / C/S ratio

What does the high-low method achieve?

Method used to separate fixed costs from variable costs when we have mixed costs shown in a scatter graph plot.

Which method is more feasible and for what amount of trees? • Bowsaw - Fixed cost is £5.00 - Variable cost is £4 per tree • Chainsaw - Fixed cost is £305 - Variable cost is £1 per tree Suggest whether Lumberjacks Ltd must invest in Chainsaw?

Use the above formula to find Q (FC₂ - FC₁)/(VC₁ - VC₂) (305 - 5)/3 = 100 So if Q > 100 then they should invest in the Chainsaw with the higher fixed cost

What is marginal cost the same as?

Variable cost

Outline the high-low-method

We have data pairs of activity levels and their corresponding total cost figures High-low method only takes two extreme data points as the inputs We then find the gradient of this function which gives us the average variable cost per unit We find the y intercept of the function to give us the total fixed cost We have our linear cost volume function: y = a + bx

What can you deduce about the relevent range from this graph?

We see there are two points where TC = TR so two break even points. That means the relevent range cannot contain both Q₁ and Q₂.

Where exactly is the break-even point?

When total revenue = total cost Alternatively when the fixed cost is equal to the total contribution

Define the sales in £ required for desired profit

Where C/S ration (aka contribution margin) = (contribution/unit)/(selling price/unit)

Consider the following: The same known task can be undertaken using two methods: 1) High fixed costs 2) or high variable costs Which is the better method?

Write out expressions for total cost using both methods Make them equal to each other as this is when they will cost the same Rearrange for Q - at this value of Q both methods will cost the same, any further production would mean the method with the higher fixed cost would be a better option and more feasible.

Do following question and read filed answer on week 4 example 3

pick c only

Answer

sales units required for desired profit = Fixed cost + desired profit / (contribution per unit) Contribution per unit = sale of one unit - total variable of one unit Sales = 35 Total variable = 11 + 7 + 2 Contribution per unit = 35 - 20 = 15 Fixed cost = 45,000 Desired profit = 30,000 30,000 + 45,000 / 15 = 5000 units So the sales in £ is 5000 unitsx £35 per unit = £175000

What is sensitivity analysis?

- Used to answer what if questions -used to make short term decisions (short term prices, allocation of limited resources etc)

Define Operating Leverage

-Used in CVP analysis -Measures the relative mix of variable and fixed costs

What is the limitations of CVP?

-only assume linear cost behaviour -assumes we can separate fixed from variable costs -assumes unchanged levels of operating efficiency so does not consider economies/diseconomies of scale -assume selling price is the same for all customers in practise -for more than one product this would be problematic -no inflation factors are considered

How does one interpret the operating leverage

1% increase/decrease in sales leads to (operating leverage)% increase/decrease in operating profit respectively. So a lower operating leverage means there is more stability

State three major assumptions we will consider

1) Total costs are linears (both variable and fixed) 2) Only one cost driver (e.g labour hours or no. of units) 3) Costs can always be defined as either fixed or variable with respect to: - a specific cost object - a defined time span - a particular 'relevant range' in the level of the cost driver (activity level)

Outline the steps for finding the break even point graphically

1) We want to draw the TC and TR curves and then where they intercept is where the break even point is 2) Drawing the TC Draw a line that intersects vertical axis at level of fixed cost and has a slope of MC 3) Drawing the TR Draw a line through origin with a slope of product price, P 4) Finding break-even point The quantity where TR = TC is the break even point

How do you calculate operating leverage?

Contribution / operating profit Contribution = sales - variable costs Operating profit = sales - variable cost - fixed cost

Define variable costs and illustrate in a graph

Costs that change in direct proportion to changes in activity (e.g. output volume, time).

Define fixed costs and illustrate in a graph

Costs that remain unchanged for a given time period regardless of changes in activity levels.

What is marginal revenue the same as?

Price per unit

Define limiting factor

Some input we do not have enough of i.e labour supply

When you have scarce resources which product should you choose to produce?

The product which makes the highest contribution per limiting factor. Note this would be the ideal situation but in real life there will be demand for the other products too.

Recall what contribution is

Total revenue - total variable cost Sales - marginal COS - non-manufacturing variable costs