<5.5 BREAK-EVEN ANALYSIS>

--CONTRIBUTION--

--INTRODUCTION--

Q. Have you ever wondered why shops or hotels with barely any customers still remain open? Surely they are making losses as they sell very little but still have to pay their fixed costs such as rent right!
So why does a loss-making business stay open?
The answer lies in whether or not by staying open, the little business they do conduct generates enough revenue to cover the daily variable costs of staying open (E.g- staff wages, raw materials etc...). As long as they cover them the money left over can 'CONTRIBUTE' towards the fixed costs, making the loss smaller.
In other words the revenue left after deducting variable costs is called the contribution, which is used to pay for the remaining fixed costs, and of course any surplus is profit.

--PER UNIT--

CONTRIBUTION PER UNIT refers to the $-amount that is 'LEFT OVER' after paying the variable costs for each item sold.
In other words PRICE - AVERAGE VARIABALE COST.
If a business sells an item for more than the variable cost, it is making a 'CONTRIBUTION' towards covering the fixed costs. But this doesn’t mean the business is making a profit yet!..
NOTE: Any changes in fixed costs have NO IMPACT on conTribution per unit, only on profit and losses.

--TOTAL--

TOTAL CONTRIBUTION is the contribution from all items sold.
If the total contribution is higher than the fixed costs, then the business starts making a PROFIT. But if it’s lower, the business is making a LOSS.

--PAST PAPER TASK--

Using information from Table 1, calculate the total contribution per month for the production of 20,000 chocolate-filled donuts and then work out the monthly profit if Roscas sells 20,000 sugar donuts and 20,000 chocolate-filled.
20,000 * $5 = $100,000 Total revenue
20,000 * $2 = $40,000 Total Variable Costs
$60,000 left to contribute to fixed costs
Profit = TR - TC
20,000 Sugar donuts

--BREAK-EVEN ANALYSIS--

--DEFINITION--

The verb 'TO BREAK-EVEN' generally means you are 'NO LONGER LOSING', and in business, it refers to THE LEVEL OF OUTPUT at which a firm is 'NO LONGER MAKING LOSSES' in other words when their TOTAL COSTS are COVERED BY THE TOTAL REVENUE they earn. (TC = TR, when PROFIT = $0).
BREAK EVEN ANALYSIS as the name suggest helps firm's visualise targets and helps with various decisions.

--USING THE CHART METHOD--

--COST & REVENUE CURVES--

--BREAKEVEN QUANTITY/PRICE--

--PROFIT/LOSS--

--SAFETY MARGIN--

--CONTRIBUTION & BREAKEVEN--

--DEFINITION--

As we know contribution per unit refers to the amount of revenue 'LEFT OVER' after paying the variable costs for each item sold.
If a business sells an item for more than the variable cost, it is making a 'CONTRIBUTION' towards covering the fixed costs.
Atthe level of output where TOTAL CONTRIBUTION = TOTAL FIXED COST the firm will BREAKEVEN.
We can see below that as output increases total revenue climbs at a faster rate than variable costs (For example you sell 5 units at $10 to earn $50 revenue, yet the variable cost per unit costs only $2, meaning 5 units costs $10 in variable costs, leaving $40 contribution at 5 units) meaning the GAP BETWEEN TR and VC is the CONTRIBUTION.

--USING THE TABLE METHOD--

When presented with a table of data like below we can find the breakeven level of output by identifying the quantity at which the Profit/Loss = 0, which is 500 units
If this is the format of the question you are given you will likely need to work out the last 3 oluns yourself.

--USING THE FORMULA METHOD--

--USING CONTRIBUTION PER UNIT--

THE BREAK-EVEN FORMULA:
BREAK-EVEN Q = FIXED COSTS / CONTRIBUTION PER UNIT
In other words,
"How many units must be sold before the total contribution matches the fixed costs?"

--WORKED EXAMPLE--

Selling price = $5
Variable cost per unit = $2
contribution per unit = $3
Total fixed cost =$3000 per/year
To cover all costs need to sell $3000/$3 = 1000 units

--PRICE/COST CHANGES--

--CHANGE IN PRICE--

--CHART METHOD--

--FORMULA METHOD--

If the PRICE INCREASED then AR would rise and assuming variable costs remain unchanged then the CONTRIBUTION PER UNIT WILL INCREASE and the firm BREAKING-EVEN AT A LOWER LEVEL OF OUTPUT. (...and vice versa).
BREAK-EVEN Q = FIXED COSTS / CONTRIBUTION PER UNIT

--WORKED EXAMPLE--

Selling price = $5 -> $6
Variable cost per unit = $2
contribution per unit = $3 -> $4
Total fixed cost =$3000 per/year
To cover all costs need to sell $3000/$3 $4 = 1000 units 750 units

--CHANGE IN VARIABLE COST--

--CHART METHOD--

--FORMULA METHOD--

If the VARIABLE COST INCREASED (assuming all othe things remain constant) then the CONTRIBUTION PER UNIT WILL DECREASE which will result in the firm BREAKING-EVEN AT A HIGHER LEVEL OF OUTPUT. (...and vice versa).
BREAK-EVEN Q = FIXED COSTS / CONTRIBUTION PER UNIT

--WORKED EXAMPLE--

Selling price = $5
Variable cost per unit = $2 -> $3
contribution per unit = $3 -> $2
Total fixed cost =$3000 per/year
To cover all costs need to sell $3000/$3 $2 = 1000 units 1500 units

--CHANGE IN FIXED COST--

--CHART METHOD--

--FORMULA METHOD--

If the FIXED COST INCREASED (assuming all other things remain constant) and the CONTRIBUTION PER UNIT REMAINS UNCHANGED the firm willl BREAK-EVEN AT A HIGHER LEVEL OF OUTPUT. (...and vice versa).
BREAK-EVEN Q = FIXED COSTS / CONTRIBUTION PER UNIT

--WORKED EXAMPLE--

Selling price = $5
Variable cost per unit = $2
contribution per unit = $3
Total fixed cost =$3000 per/year -> $4000
To cover all costs need to sell $3000 4000/$3 = $1000 1333.3 units

--IMPORTANT CALCULATIONS--

--CALCULATING TARGET PROFIT OUTPUT--

"How many units must be sold before the total contribution matches the the target profit?"
So far we have just looked at identifying breakeven which as we know is a state of ZERO PROFITS, but of course companies often like to SET PROFIT TARGETS, so given that we already know that....
BREAK-EVEN Q = FIXED COSTS / CONTRIBUTION PER UNIT
...therefore to work out the profit target output...
TARGET OUTPUT Q = FIXED COSTS + PROFIT TARGET / CONTRIBUTION PER UNIT

--WORKED EXAMPLE--

Selling price = $5
Variable cost per unit = $2
contribution per unit = $3
Total fixed cost =$3000 per/year
Target profit = $6000
To cover all costs and earn the profit target need to sell $3000+$6000/$3 = 3000 units

--CALCULATING B/E REVENUE--

"How much revenue must be earned before the total contribution matches the fixed costs?"
So far we have just looked at identifying breakeven in terms of units sold but how can we work out how much revenue must be earned in order to breakeven?....
BREAK-EVEN REVENUE = FIXED COSTS / 1 - (VARIABLE COST/PRICE)
...this looks a bit strange but it's actually quite simple as Firstly, by dividing VARIABLE UNIT COSt by the UNIT PRICE we get the % of each dollar earned that goes to pay for variable costs, thus 1 - this value will be the % of each dollar earned that is left to contribute towards fixed costs....so we are left with the question of how many dollars need to be made for this contribution to equal the fixed costs?
Simples, FIXED COSTS / 1 - (VARIABLE COST/PRICE)

--WORKED EXAMPLE--

Selling price = $5
Variable cost per unit = $2
Fixed costs = $3000
So, $2/$5 = 0.4 means that for every dollar earned in revenue, 40% goes to paying variable costs, meaning 1 - 0.4 = 0.6 60% of each dollar earned contributed to the fixed costs
This means that contribution per $ = $0.6, therefore how many dollars are needed to be earned so that 60% of them = $3000?
$3000/0.6 = $5000

--CALCULATING B/E TARGET PRICE--

"What price should I set so we can breakeven at X amount?"
It could be the case that a firm wishes to breakeven as soon as it can, and it has some flexibility with its prices, so wants to know what price it should set in order to breakeven (Make no losses) at a specific production level.
BREAK-EVEN PRICE = (FIXED COSTS / PRODUCTION LEVEL) + VARIABLE COST
...this also looks a bit strange but it's actually quite intuative as firstly, fixed Costs / production level spreads the fixed costs over all the products to work out the contribution per unit needed, which when added to the variable cost gives the selling price needed to cover both and achive B/E at the chosen production level.

--WORKED EXAMPLE--

Selling price = $?
Variable cost per unit = $2
Fixed costs = $3000
Desire to B/E at 1000 units
So, the selling price must cover the fixed cost per unit $3000/1000 = $3
...and we know that the variable cost per unit is $2...
Therefore to breakeven at 1000 units they should charge $3 + $2 = $5

--LIMITATIONS--

--LIMITATIONS OF BREAK-EVEN ANALYSIS--

This chart relies on some rather UNREALISTIC ASSUMPTIONS:

1) Firstly, It assumes the FIRM IS ABLE TO SELL ALL THE GOODS THEY PRODUCE UP TO THEIR CAPACITY, which is very optimistic given the variables that impact demand such as tastes and preferences, the price of substitutes etc...

2) Secondly it assumes that ALL THE PRODUCE WIL BE SOLD BY CHARGING EXACTLY THE SAME PRICE PER UNIT, ignoring the fact that firm's may need to lower prices in order to sell more and remain competitive with rivals.

3) Thirdly, it assumes that the FIXED COSTS REMAIN THE SAME, however often external factors cause them to increase, e.g. growing demand for factory space means the owner of the factory increases the rent.

4) Fourthly, it assumes that VARIABLE COSTS PER UNIT ARE FIXED such as wages, which presupposes workers will simply work more if they are asked, however in reality workers may seek overtime or extra pay, especially if workers are already employed

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