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# Me Break Even Analysis & Profit Function

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• 1. Break-even Analysis: BEP in terms of physical units = TFC Break even point means : Total Cost = Total Revenue P-AVC (Contribution margin) BEP in terms of Sales Value : Break-even Point = Total Fixed Cost/ Contribution Ratio TFC/CR Contribution Ratio = Total Revenue – Total Variable Cost CR= TR – TVC = TFC x TR Total Revenue TR TR - TVC Q.17 Given the following total cost and total revenue functions, determine the break-even point: TC = 480 + 10Q (TFC + TVC (AVC x Quantity) TR = 50Q Total Fixed Cost is 480. (TFC) Average Variable Cost = Rs.10 (AVC) Total Revenue = 50Q (Given) = Price x Quantity. TR = TC 50Q = 480 + 10Q 40Q = 480 Q = 12. Break even quantity is 12 units. TR = 50Q = 50 x 12 = 600, TC = 480 + 10Q = 480 + 120 = 600 Therefore TR = TC = Breakeven point. Breakeven price : 50Q = 600 Price x Quantity = 600, Price = Rs.50 Q.18 A firm incurs fixed cost of Rs.4000 and variable cost of Rs.10000 and its total sales receipts are Rs.15000. Determine the breakeven point. CR = TR – TVC =( 15000 – 10000) / 15000 = ⅓
• 2. BEP = (TFC x TR) / (TR-TFC) = 4000 x 15000 / 15000 – 10000 = 60000000 divided by 5000 = 12000 BEP = TFC/CR = 4000 divided by ⅓ = 4000 x 3 = 12000. BEP means TC = TR TC = TFC + TVC 12000 = 4000 + TVC TVC = 8000 Assumptions of Break-even analysis: 1. Cost function and Revenue Function are linear. 2. Total Cost is divided into Fixed and Variable Costs. 3. Selling price is constant. 4. The volume of sales and volume of production are identical. 5. Average and Marginal Productivity of factors are constant. 6. The product-mix is stable in the case of a multi-product firm. 7. Factor price is constant. In practice, these assumptions are unlikely to be fulfilled. Limitations of BEA: It is static : Everything is assumed to be constant, implying a static condition, which is unrealistic and unsuitable for dynamic situation. It is unrealistic: It is based on many assumptions which do not hold good in practice. Linearity of cost and revenue functions are true only for a limited range of output. It has many shortcomings: BEA regards profit as a function of output only. Impact of technical change, better management, division of labour, improved productivity and other factors influencing profit are ignored. Its scope is limited to short run only: BEA is not an effective tool for long run analysis as it is static. It assumes horizontal demand curve with the given price of the product: This is not so in the case of a monopoly firm.
• 3. It is difficult to handle selling costs in the BEA: Selling costs do not vary with output. They manipulate sales and affect the volume of output. The traditional BEA is very simple: It makes no provision for Corporate Income tax etc. Usefulness of BEA: Despite these limitations BEA is a useful tool of analysis. BEA provides a rough guideline for the alternative possibilities and arriving at a better decision. Of course, BEA is not a perfect substitute for judgment of commonsense and intuition possessed by the businessman. But it can be a good supplement to the value judgment and logical deductions made with commonsense. BEA is particularly useful for decision making in regard to pricing, cost control, product-mix, channels of distribution etc. • BEA provides microscopic view of the profit structure of the firm. • Empirical cost functions required in BEA can be of great help for cost control in business. • BEA when it provides a flexible set of projections of costs and revenue under expected future conditions can serve the purpose of profit prediction and becomes a tool for profit making. • BEA can be used for determining the ‘safety margin’ regarding the extent to which the firm can permit a decline in sales without causing losses. • Safety Margin = Sales – BEP x 100 Sales BEA can be useful in determining the target profit sales volume. TFC – Target Profit Target Sales Volume = ------------------------- Contribution margin It is useful in arriving at make or buy decision.
• 4. In short, BEA is highly significant in business decision making pertaining to pricing policy, sales projection, capital budgeting, etc. However, the technique is to be used cautiously. Q.19 A firm incurs fixed expenses amounting to Rs.12000. Its variable cost of product X is Rs.5 per unit. It selling price is Rs.8. Determine its break- even quantity (BEQ) and safety margin for the sales of 5000 units. Interpret the result. (i) BEQ = TFC = 12000/ (8-5) = 4000 P-AVC ii) Safety Margin = Sales – BEQ x 100 = 5000 – 4000 x 100 = 20% Sales 5000 BEQ or BEP 4000 units of product X in this case implies that the firm would not have any loss or profit of selling this level of output at Rs.8. In other words, this is zero profit-output level because: ∏ = TR – TC In this case, TR = P.Q = 8 x 4000 = 32000 TC = TFC + TVC = 12000 +5 x 4000 = 32000 ∏ = 32000 – 32000 = 0. The safety margin 20% in this case suggests that the firm can afford to reduce its price by 20% increasing the volume of sales by 20% to 5000 units before incurring a loss. Q.21.A firm starts its business with fixed expenses of Rs. 60,000 to produce commodity X. Its variable cost is Rs2 per unit. Prevailing market price of the product is Rs.6. How much the firm should produce to earn a profit of Rs.20,000 at this price. In this case, we have to determine target profit sales volume (TPS) by using the formula TPS = TFC – Target Profit Contribution Margin = Price – AVC = 6 – 2 = Rs.4 Contribution margin
• 5. TPS = 60,000 – 20,000 = 40000/4 = 10,000 4 The firm should produce 10000 units of X to earn targeted profit of Rs.20,000 per unit of time. Q.22 A manufacturer buys certain components for producing X at Rs.20 per unit. If he has to make these components, it would require a fixed cost of Rs.15000/- and average variable cost of Rs.5 per unit. His present requirement is 1000 units of these components. Advise him whether he should make or buy them, if he intends to double the output. In this case we need to measure the BEP of the components. BEP = TFC Here for P we have to take the purchase price. P – AVC BEP = 15000 = 15000 = 1000 20 – 5 15 At 1000 units requirement, it makes no difference whether the firm buys or makes the components. But when the requirement increases, it is profitable to make the components. Q.23 Calculate the break even point from the following data. Sales = 550 units Sales Receipts = Rs.28,875 Total Fixed Costs = Rs.10,000 Total Variable Costs = Rs.11,000 BEP = Total Fixed Cost Contribution Ratio CR = TR – TVC = 28,875 – 11000 = 17875/28875 TR 28875 Contribution Ratio Sales Receipts = 28875 Sales = 550 units Sale Price : 28875/550 = Rs. 52.50 Total Veriable Cost = 11000 AVC = 11000/550 = 20 Total Fixed Cost = 10,000
• 6. BEP = TFC = 10000/ 52.50 - 20 (Cont. margin = 52.50 – 20 = Rs.32.50) P – AVC 307.69 units. Q. 24 Given the following functions, find break-even point. Total cost = 100 + 5X Total Revenue = 10Y, where X is the quantity sold. Sale Price = 10Y / X TFC = 100 Cost price per unit = Rs.5 Quantity sold = X. BEP = Total Fixed Cost / Cont.Margin 100 – (10Y/X – 5) = 105 – 10Y/X Q.25 A firm purchases ball bearings at Rs.12. Its monthly requirement is 1000 units. If it decides to make its fixed cost would be Rs.18, 000 and variable cost Rs.5 per unit. What is your advice? P = Purchase price = Rs.12 AVC = Rs.5 TFC = Rs.18000 BEP = TFC/P-AVC = 18000/(12-5) 18000/7 = 2571.43 units. It is not advisable to make the ball bearings, as the requirement is only 1000 units, which is well below the breakeven level. Q.26 For a new product, a manufacturer set up an infrastructure which costs him Rs.1, 40,000 and variable cost is estimated as Rs.125 for each unit of the product. The sale price per unit is fixed at Rs.160. Write down the cost function Cx, Revenue function Rx and Profit function Px for X units of the product. How many number of units are to be produced in the first year of production so that there may be no loss or gain during that year. TFC = 1,40,000 AVC = 125 Sale Price = P = 160 Contribnution margin = P – AVC = 160 – 125 = 35 BEP = TFC/Cont.margin = 140000 / 35 = 4000 units.
• 7. Total Cost = Cost function Cx = 140000 + 125X TR = Revenue function Rx = 160X At breakeven point Px = Rx – Cx ( Profit) = 0 TR or Rx = TC or Cx 160x = 140000 + 125x 160x – 125x = 140000 35x = 140000 X = 4000 Therefore minimum number of units that should be produced in the first year is 4000 so that there will be no profit/loss. Q.27 A company produced a commodity with Rs.10000 fixed costs. The variable costs are estimated to be 25% of the total revenue received on selling the product at the rate of Rs.6 per unit. Find the total revenue, total cost and profit functions.and BEP. If X is the number of units produced, then toal revenue Rx (TR) = 6X And Variable cost 25% of 6X = 3/2 X Total Fixed cost TFC = 10,000 TC (Cx) = TFC + TVC = 10000 + 3/2 X At BEP Px = 0 Therefore TR (Rx) = TC (Cx) 6X = 10000 + 3/2 X 6X – 3/2 X = 10000 9/2 X = 10000 X = 10000 x 2/9 = 20000/9 = 2222.22 units. Profit function Px = Rx – Cx = 6X – 10000 – 3/2X = 9/2X – 10000 Q.28. A profit making company wants to launch a new product. It observes that the fixed cost of the new product is Rs.35000 and the variable cost per unit is Rs.500. The revenue received on the sale of X units is given by 5000X – 100 X2 . Find (i) profit function (ii) break even point. Px (Profit) Rx (TR) Revenue function, Cx (TC) total cost function, then, Rx (TR) = 5000 X – 100 X2 (Given) Cx = TFC + TVC = 35000 + 500X Profit = Px = Rx - Cx = 5000X – 100 X2 – 35000 – 500 X = 4500X – 100 X2 – 35000 BEP = Px = 0 Rx = Cx 5000X – 100X2 = 35000 + 500 X 5000X – 500 X – 100X2 = 35000 4500X - 100 X2 - 35000 = 0 (Divide by -100)
• 8. X2 – 45X + 350 = 0 (X-10)(X-35) =0 Therefore, X= 10 or X = 35. Breakeven values are 10 and 35. Q.29 A company has fixed cost of Rs.10000 and cost of producing one unit of its product is Rs.50. If each unit sells for Rs.75, find the break even value. Also find the values of x for which the company always results in profit. Cx = 10000 + 50X (TFC + TVC) Rx = Sale Price x X = 75X Profit Px = Rx – Cx = 75X – 50X – 10000 At BEP Px = 0 75X – 50X -10000 = 0 25X = 10000 X = 400 On producing and selling 400 units, the company is neither making a loss/profit. The company will aways remain on profit if Px > 0 25X – 10000 > 0 giving X > 400.