Marginal Cost Equations and Breakeven Analysis

From the marginal cost statements, one might have observed the following:

Sales – Marginal cost = Contribution ......(1)

Fixed cost + Profit = Contribution ......(2)

By combining these two equations, we get the fundamental marginal cost equation as follows:

Sales – Marginal cost = Fixed cost + Profit ......(3)

This fundamental marginal cost equation plays a vital role in profit projection and has a wider application in managerial decision-making problems.

The sales and marginal costs vary directly with the number of units sold or produced. So, the difference between sales and marginal cost, i.e. contribution, will bear a relation to sales and the ratio of contribution to sales remains constant at all levels. This is profit volume or P/V ratio. Thus,

P/V Ratio (or C/S Ratio) = Contribution (c) ......(4)

Sales (s)

It is expressed in terms of percentage, i.e. P/V ratio is equal to (C/S) x 100.

Or, Contribution = Sales x P/V ratio ......(5)

Or, Sales = Contribution ......(6)

P/V ratio

The above-mentioned marginal cost equations can be applied to the following heads:

1. Contribution

Contribution is the difference between sales and marginal or variable costs. It contributes toward fixed cost and profit. The concept of contribution helps in deciding breakeven point, profitability of products, departments etc. to perform the following activities:

• Selecting product mix or sales mix for profit maximization

• Fixing selling prices under different circumstances such as trade depression, export sales, price discrimination etc.

2. Profit Volume Ratio (P/V Ratio), its Improvement and Application

The ratio of contribution to sales is P/V ratio or C/S ratio. It is the contribution per rupee of sales and since the fixed cost remains constant in short term period, P/V ratio will also measure the rate of change of profit due to change in volume of sales. The P/V ratio may be expressed as follows:

P/V ratio = Sales – Marginal cost of sales = Contribution = Changes in contribution = Change in profit

Sales Sales Changes in sales Change in sales

A fundamental property of marginal costing system is that P/V ratio remains constant at different levels of activity.

A change in fixed cost does not affect P/V ratio. The concept of P/V ratio helps in determining the following:

• Breakeven point

• Profit at any volume of sales

• Sales volume required to earn a desired quantum of profit

• Profitability of products

• Processes or departments

The contribution can be increased by increasing the sales price or by reduction of variable costs. Thus, P/V ratio can be improved by the following:

• Increasing selling price

• Reducing marginal costs by effectively utilizing men, machines, materials and other services

• Selling more profitable products, thereby increasing the overall P/V ratio

3. Breakeven Point

Breakeven point is the volume of sales or production where there is neither profit nor loss. Thus, we can say that:

Contribution = Fixed cost

Now, breakeven point can be easily calculated with the help of fundamental marginal cost equation, P/V ratio or contribution per unit.

a. Using Marginal Costing Equation

S (sales) – V (variable cost) = F (fixed cost) + P (profit) At BEP P = 0, BEP S – V = F

By multiplying both the sides by S and rearranging them, one gets the following equation:

S BEP = F.S/S-V

b. Using P/V Ratio

Sales S BEP = Contribution at BEP = Fixed cost

P/ V ratio P/ V ratio

Thus, if sales is $. 2,000, marginal cost $. 1,200 and fixed cost $. 400, then:

Breakeven point = 400 x 2000 = $. 1000

2000 - 1200

Similarly, P/V ratio = 2000 – 1200 = 0.4 or 40%

800

So, breakeven sales = $. 400 / .4 = $. 1000

c. Using Contribution per unit

Breakeven point = Fixed cost = 100 units or $. 1000

Contribution per unit

4. Margin of Safety (MOS)

Every enterprise tries to know how much above they are from the breakeven point. This is technically called margin of safety. It is calculated as the difference between sales or production units at the selected activity and the breakeven sales or production.

Margin of safety is the difference between the total sales (actual or projected) and the breakeven sales. It may be expressed in monetary terms (value) or as a number of units (volume). It can be expressed as profit / P/V ratio. A large margin of safety indicates the soundness and financial strength of business.

Margin of safety can be improved by lowering fixed and variable costs, increasing volume of sales or selling price and changing product mix, so as to improve contribution and overall P/V ratio.

Margin of safety = Sales at selected activity – Sales at BEP = Profit at selected activity

P/V ratio

Margin of safety is also presented in ratio or percentage as follows: Margin of safety (sales) x 100 %

Sales at selected activity

The size of margin of safety is an extremely valuable guide to the strength of a business. If it is large, there can be substantial falling of sales and yet a profit can be made. On the other hand, if margin is small, any loss of sales may be a serious matter. If margin of safety is unsatisfactory, possible steps to rectify the causes of mismanagement of commercial activities as listed below can be undertaken.

a. Increasing the selling price-- It may be possible for a company to have higher margin of safety in order to strengthen the financial health of the business. It should be able to influence price, provided the demand is elastic. Otherwise, the same quantity will not be sold.

b. Reducing fixed costs

c. Reducing variable costs

d. Substitution of existing product(s) by more profitable lines e. Increase in the volume of output

e. Modernization of production facilities and the introduction of the most cost effective technology