The production rate for product P is 5 units per hour and for component Q is 10.

The effective cost of making a unit of component Q is:

Marginal cost of production £7

Plus Opportunity cost of £2

-----

The effective cost is £9

-----

By switching capacity from product P to component Q there is £2 contribution lost. This is an opportunity cost ie. it is the benefit foregone by choosing one course of action over the other.

Limiting factor decisions

Often a company finds that there is a limiting factor or constraint which inhibits its capacity to meet the desired production level. The limiting factor may be any resource eg. materials, labour or machine hours. Management has to decide what is the best way to allocate the scarce resource among the product range in the most effective way so that profits are maximised.

Example:

Product	X	Y	Z
Desired production (units)	1,000	2,000
	£	£	£
Selling price per unit
Variable cost per unit
	-----	-----	-----
Contribution per unit

A special machine is used to manufacture the three products and there are only 15,000 machine hours available.

Product X uses 20 machine hours per unit.

Product Y uses 5 machine hours per unit.

Product Z uses 2 machine hours per unit.

	X	Y	Z
Contribution per unit
No. of machine hrs.
Contribution per machine hr.
Ranking	(3)	(2)	(1)

Desired production level

Product Z	500 units x 2 hrs.	1,000 hrs
Product Y	2,000 x 5 hrs	10,000 hrs
Product X	200 x 20	4,000 hrs

Product Z earns 500 units x £10 = £5,000 contribution

Product Y earns 2,000 units x £15 = £30,000 contribution

Product X earns 200 units x£20 = £4,000 contribution

---------

£39,000 contribution

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Profit Planning or cost profit volume analysis

Management feels it helpful to ascertain the level of profits earned at certain levels of output and sales.

Example:

A company makes product X which has a selling price of £10 per unit and variable costs of £5 per unit with fixed costs of £20,000.

Sales (units)	2,000	4,000	6,000	8,000	10,000
	-------	------	-------	-------	--------
	£	£		£	£
Sales revenue	20,000	40,000	60,000	80,000	100,000
Variable costs	10,000	20,000	30,000	40,000	50,000
	--------	--------	--------	--------	--------
Contribution	10,000	20,000	30,000	40,000	50,000
Fixed costs	20,000	20,000	20,000	20,000	20,000
	--------	--------	--------	--------	--------
Net profit (loss)	(10,000)	---	10,000	20,000	30,000
	--------	--------	-------	-------	--------

At sales of 4000 units the company is at break-even point ie. contribution is equal to the fixed costs.

COST VOLUME PROFIT

ANALYSIS

Lesson 3

Cost Volume Profit Analysis

The CVP model makes the assumptions that costs can be simply divided into fixed and variable costs. It assumes that over a range of output levels - the relevant range - fixed costs remain constant and variable costs increase directly with output. The variable costs behave in a linear fashion. The fixed costs are periodic costs so that cost items such as rent, rates, insurance, depreciation etc. are constant at all levels of output. There is also an assumption that the sales revenue behave in a linear fashion ie. the selling price is constant per unit of output.

Economists take a more realistic view of cost behaviour. They contend that variable costs do not behave in a linear fashion but are effected by economies of scale. Companies can benefit from discounts for bulk purchases of materials and

The economies from the division of labour. The economists’ model represented in a curvilinear graph shows the total cost line rises steeply at low output levels, levels off within a range of output and finally rises steeply again as the benefits of economies of scale decline. The total revenue line rises steeply, levels off and then declines. This curvilinear total revenue line reflects the fact that to achieve more sales the company may have to reduce the selling price and does not increase proportionally with output.

As a compromise it is possible to accept the assumptions that the CVP model is based on within a certain range of output - the relevant range. Therefore, the CVP model can be used as a planning technique to:

(a) find the break-even point

(b) determine the margin of safety

(c) determine a target volume

(d) establish the profit volume ratio or contribution volume ratio

(e) determine the operating gearing