❏ BEP Analysis n = number of units/volume B = Breakeven volume
TC = Total cost P = Unit (selling) price
FC = Fixed cost VC = Variable cost;
TFC = Total Fixed Cost TVC = Variable Cost/Unit
Revenue/period = n P
TC/period = n VC + FC
Profit/Loss = Revenue - TC = n P - (n VC + FC) = n (P - VC) - FC
At BEP, Profit = 0 ==> 0 = n (P - VC) - FC or n =
FC
P - VCChapter 5: Revenue and Cost Analysis
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❍ P - VC is called contribution margin (CM),
❖ The difference between selling price and variable costs. It is the portion of the selling price that contributes to paying off the fixed cost (after covering VC).
❖ When the total contribution margin is exactly equal to total fixed costs, sales are at the
Break-Even Point. The contribution of each unit sold beyond BEP is the increment of profit. ❍ At n = B the sum of contributions from units equals the total fixed cost. The contribution of each unit sld beyond n = B is an increment of profit.
❍ Example 5-1: If VC is 60% of sales; with unit price at $10/each and FC = $40,000. What is the total sales?
Sales @ BEP = a (Sales @ the BEP) + TFC
X = .60(X) + $40,000
X = $100,000
To find break-even in units:
$100,000/$10.00 = 10,000 or BEP in units = TFC/(Price-VC per unit)
$40,000/($10.00-$6.00) = 10,000
❍ Example 5-2: A small coal mine can produce a max of 100,000 tons per month. The coal sells for $30.00 per ton and the contribution contribution is around 75%. TFC per month is $1,850,000. How many tons of coal the mine has to produce in order to break even? Total revenue = n P = 100,000 x $30.00 = $3,000,000.
Total contribution = 0.75 x 3,000,000 = $2,250,000
B (% capacity) = FC Contribution =
1850000
2250000 = 82.22%
It requires 100,000 tons x 82.22% = 82,222 tons to break even.
Assuming a tax rate of 40%;
Net profit = Profit (1 - tax rate)
= (Revenue – TC)(1 – tax rate)
= [n(P –