Friday, 12 July 2013

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

  2. 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.

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

  4. 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:
  1. This ratio determines profitability of a line of product & also overall profitability of a number of products;

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

  3. 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:
  1. On excess of revenues over variable cost, the P/V ratio heavily leans on.

  2. 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.

  3. 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.

  4. 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.
Solution: We know that 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    
Problem 2: Break-even point
         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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