Break-even point is the volume of sales where there is neither profit nor loss. At this point revenues and total costs are equal. For every unit sold in excess of the break-even point, profit will increase by the amount of the contribution per unit. All the variable costs and fixed costs are covered by the sales revenue.

At Break-even point, BEP,

Total revenue = Total costs

Profit P = 0

Contribution – Fixed costs = 0

Contribution = Fixed cost

**Break-even analysis**

**Mathematical determination of Break-even point**

From the definition of break-even point, one can say that:

Note that this formula is identical to the CVP one except for the profit, which in this case is zero. This brings out clearly the idea that break-even analysis and cost volume profit analysis are one and the same thing. In fact, the terms are at times used interchangeably.

To obtain break-even sales in shillings where one is dealing with a single item, multiply the break- even sales volume by the sales price. Alternatively, use the contribution margin ratio to compute the same.

Using the equation below, one can calculate break-even sales in Shillings as follows:

**Using the graphical approach**

Break-even charts graphically display the relationship of cost to volume and profits and show profit or loss at any sales volume within a relevant range. This is shown in the graph below. (Assumption; fixed costs do not change)

**>>> Illustration (Break-even and CVP analysis)**

ABC produces and sells Product X at Shs.500. The Unit manufacturing cost of X is Shs.200 and total fixed manufacturing costs equal to Shs.300,000. The company incurs selling and administration costs equal to 2% of sales revenue and fixed selling cost of Shs.100,000 per annum.

**Required:**

a) Determine the break-even sales in units and in shillings

b) Determine the units that should be sold to earn a net income of Shs.200,000

c) If the company was in the 30% tax bracket, how many units will have to be produced to earn the Shs.200,000

d) Management is considering a policy which would increase fixed manufacturing costs by shs.200,000 but cut down on the variable manufacturing cost by 20%

(i). What is the break-even point in units and in revenue under this policy?

(ii). Assuming the 30% tax bracket, how many units will have to be produced to earn the target profit of Shs.200,000 under this new policy?

e) At what level of sales level will management be indifferent between the two policies?

f) Assuming that the maximum possible demand is 6,000 units, determine the range of

sales which will be financially beneficial in each policy.

**Solution**

Let the number of units produced be x

Policy II is more profitable than Policy I between 2,630 units and 4,902 units while Policy I is more profitable between 4,902 units and 6,000 units of output.

**CVP and computer applications**

The wide availability of personal computers encourages more managers to apply cost volume profit analysis. Computers can quickly make the computations for changes in the assumptions identifying proposed projects e.g. computer spreadsheets allow managers to determine the most profitable combination of selling process, variable and fixed cost volume. A manager enters into the computer various numbers for price and cost in an equation based on CVP relationships to yield target income for each combination. Because of a computer’s speed and accuracy in providing this information, the manager can select the most profitable actions.