### P/V Ratio

*P/V Ratio*When the contribution from sales is expressed as a sales value percentage, then it is known as profit/volume ratio (or P/V ratio). The relationship between the contribution & sales is expressed by it. Sound ‘financial health’ of a company’s product is indicated by better P/V ratio. The change in profit due to change in volume is reflected by this is reflected by this ratio. If expressed on equal footing with sales, it will show how large the contribution will appear. If size of sales is $ 100, then P/V ratio of 60% will mean that contribution is $ 60.

One important characteristic of P/V ratio is that at all levels of output it will remain constant because at various levels, variable cost as a proportion of sales remains constant.. When P/V ratio is considered in conjunction with margin of safety, it becomes particularly useful. P/V ratio can be referred by other terms like: (a) marginal income ratio, (b) contribution to sales ratio, & (c) variable profit ratio.

P/V ratio may be expressed as:

*P/V ratio= Contribution / Sales*

*=*

__Sales – Variable cost__*Sales*

*= 1-*

__Variable cost__*Sales*

*Or, P/V ratio =*

__Fixed Cost + Profit__*Sales*

It is also possible to express the ratio in terms of percentage by multiplying by 100. Thus a relationship between the contribution & sales is established by the profit/volume ratio. Hence it might be better to call it as a

*Contribution/Sales ratio (or C/S ratio)*, though the term Profit/Volume ratio (P/V ratio) is now widely called.

Also, by comparing the change in contribution to change in sales or by change in profit to change in sales, it is possible to compute the ratio. Because it is assumed that the fixedcost will remain the same at different levels of output, an increase in contribution will mean increase in profit.

Thereby,

*P/V ratio =*

__Change in contribution__*Change in sales*

*Or,*

__Change in profit__*Change in Sales*

Improvement in P/V ratio should always be tried to be bought in by the management. The higher the rate, the greater will be the contribution towards fixed costs & profit.

__Improvement of P/V Ratio:__By the following ways, an improvement in this ratio can be achieved by:

- The selling price increase; but the risk that the volume of sales might be affected
in involved in it.

- By purchasing the latest machinery, a reduction
in the variable cost per unit can be achieved,
thereby cutting the hours which may be required
to complete each operation. However, higher fixed
costs such as depreciation & insurance
might offset this reduction.

- By concentrating on those products by which highest
contribution can be achieved.

- For doing business analysis, in the hands of management, the P/V ratio is an invaluable tool.

__Advantages of P/V Ratio:__Some of its uses are under mentioned:

- This ratio determines profitability of a line of
product & also
overall profitability of a number of products;

- This ratio compares the profitability of different
lines of products, sales, companies, factories
etc.

- This ratio calculates break-even sales, profit at different levels of output, turnover which may be required for a desired profit or to offset reduction in price or to meet increased expenditure.

__Limitations of P/V Ratio:__Using of P/V ratio for deciding the product-worthy additional sales efforts & productive capacity & host of other managerial exercises; is a growing trend among managers.

Following are the limitations of the use of P/V ratio:

- On excess of revenues over variable cost, the P/V ratio heavily leans on.

- The capital outlays that are required by the additional
productive capacity & the
additional fixed costs, that are added, are not
taken into consideration by the P/V ratio.

- The profitable products lines which might be emphasized & unprofitable
product lines which might be re-evaluated for elimination,
can be suggested by the inspection of P/V ratio
of the products. Final decision cannot be taken
by mere inspection of P/V ratio. For this purpose,
for taking into consideration differential cost
of the decision & opportunity costs etc, analysis
has to be broadened. Thereby, only the area that
needs to be probed is indicated.

- Because only an indication regarding the relative profitability of the products or product lines is given by the P/V ratio, for the purpose of decision making, it has been referred to as the questionable device. P/V ratio are good for forming impression & not for making decision provided other things are equal.

__Problem 1:__A company produces a single article. About its product, the following cost data has been given:

Selling price per unit $ 40

Marginal cost per unit $ 24

Fixed cost per annum $ 1600

Calculate: (a) P/V ratio, (b) Break-even sales,

(c) Sales to earn a profit of $ 2000, (d) Profit at sales of $ 12000,

(e) If sales price is reduced by 10%, then a new break-even sales.

**We know that**

__Solution:__*Sales – Variable cost = Fixed cost + Profit*

By multiplying & dividing left hand side by Sales

Or,

*Sales (Sales –Variable Cost)/Sales = Fixed cost + Profit*

*Or, Sales * P/V ratio = Contribution*

(a)

*P/V ratio = Contribution / Sales * 100*

= [(40-24)/40] * 100

= 16/40 * 100

= 40%

(b)

*Break-even Sales*=

*Sales * P/V ratio= Fixed cost*

Or, Sales * 40% = 1600

Or, Sales = 1600/40

Or, Sales = $ 4000 (or 200 units)

(c) Sales to earn a profit of $ 2000

*Sales * P/V ratio = Fixed cost + Profit*

Or, Sales * 40% = 1600 + 2000

Or, Sales = 1800/40%

Or, Sales = $ 4500 (or 112.5 units)

(d) Profit at sales of $ 12000

*Sales * P/V ratio = Fixed cost + Profit*

Or, 12000 * 40% = 1600 + Profit

Or, Profit = $ 3200

(e) New Break-even sales, if sales price is reduced by 10%

New Sales price = $40 - $4 = $36

Marginal cost = $24

Contribution = $36 - $24 = $12

*P/V ratio = Contribution / Sales*

= (12/36) *100 = 33.33%

*B.E.S * P/V ratio = Fixed Cost (at B.E.P, contribution is equal to fixed cost)*

Or, B.E.S = 1600/33.33%

Or, B.E.S = $ 4800

*Break-even point*__Problem 2:__A company, which currently utilizing 80% capacity with a turnover of $ 1600000 at $ 50 per unit, manufactures a product. The cost data are as under:

Material cost $ 15 per unit, Labour cost $ 12.50 per unit.

Semi-variable cost (including variable cost of $ 7.50 per unit) - $ 360000

Fixed cost $ 180000 up to 80%

**level of output, beyond this an additional $ 40000 will be incurred.**

Calculate: (a) Activity level at Break-even point;

(b) Number of units which need to be sold so that net income of 8% can be earned.

(c) Activity level needed for earning a profit of $ 190000; &

(d) If break-even point is to be brought down to 40% activity level, what will be the selling price per unit?

__Solution:____(a) Activity level of break-even point__

*Sales at BEP * P/V ratio = Fixed Cost*

*Or, Sales at BEP= Fixed cost/ P/V ratio*

*Or, Activity level of break-even point = (Fixed cost/ P/V ratio) / Selling Price*

= {$ 300000/ (15/50)} / 50

= 2 0000 units

= (20000 / 40000) * 100 = 50%

(b) Let us assume that for earning net income of 8% of sales, the number of units sold be x:

Or, $ 50x – 35x = $ 300000 + 8% of ($ 50x)

Or, $ 50x – 35x = $ 300000 + 4x

Or, x = 27273 units.

(c)

__Activity level needed to earn a profit of $ 190000:__

Sales required to earn a profit of $ 190000 = (Fixed cost + Desired profit) / contribution per unit.

Required sales = $ (300000 + 40000 + 190000) / 15

= 35333 units

Thus, activity level needed to earn a profit of $ 190000 = (353330/40000) * 100 = 88.33%.

__(d) Selling price per unit if break-even point is to be brought down to 40% (or 16000 units):__

Let us assume that selling price = X

Activity level at BEP = 16000

16000 units = (Fixed cost / P/V ratio) / Selling price

16000 units = $300000 *

__X___*

__1__

X-35 X

Or, 16000X -560000 = 300000

Or, X = (560000+300000) / 16000 = $ 53.75

**$**

__Working Notes:__(1) Selling price 50

Variable cost (15+12.50+7.50)

__35__

Contribution per unit

__15__

(2) Number of units sold at 80% capacity = $1600000/50 = 32000 units

Maximum capacity = 32000/80% = 40000 units

(3) Fixed cost element in semi-variable cost: $

Semi-variable cost 360000

Less: Variable cost 32000 units @ $ 7.50

__240000__

Fixed cost element

__120000__

(4) Total fixed cost of 80% capacity = $ 180000+ $ 120000 = $300000

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