Give an example from your own experience where you used a break-even point analy

Question

Give an example from your own experience where you used a break-even point analysis. What parameters were necessary to find the break-even point? Please include your break-even calculations based on the equation from page 8 in the textbook.

8 CHAPTER 1 • InTRoDUCTIon To QUAnTITATIvE AnAlysIs The BEP results in $0 profits. The parameters in this model are f, n, and s, as these are inputs that are inherent in the model. The number of units sold (X) is the decision variable of interest. EXAMPLE: PRITCHETT’S PRECIOUS TIME PIECES We will use the Bill Pritchett clock repair shop ex- ample to demonstrate the use of mathematical models. Bill’s company, Pritchett’s Precious Time Pieces, buys, sells, and repairs old clocks and clock parts. Bill sells rebuilt springs for a price per unit of $8. The fixed cost of the equipment to build the springs is $1,000. The variable cost per unit is $3 for spring material. In this example, s=8 f = 1,000 n=3 The number of springs sold is X, and our profit model becomes Profit = +8X - +1,000 - +3X If sales are 0, Bill will realize a $1,000 loss. If sales are 1,000 units, he will realize a profit of +4,000 [+4,000 = 1+8211,0002 - +1,000 - 1+3211,0002]. See if you can determine the profit for other values of units sold. In addition to the profit model shown here, decision makers are often interested in the break-even point (BEP). The BEP is the number of units sold that will result in $0 profits. We set profits equal to $0 and solve for X, the number of units at the BEP: Variable cost is often expressed as the variable cost per unit multiplied times the number of units. Thus, we can also express profit in the following mathematical model: where Profit = Revenue - 1Fixed cost + Variable cost2 Profit = 1Selling price per unit21Number of units sold2 - 3Fixed cost + 1Variable cost per unit21Number of units sold24 Profit = sX - 3f + nX4 Profit = sX - f - nX (1-1) s = selling price per unit f = fixed cost n = variable cost per unit X = number of units sold 0 = sX - f - nX 0 = 1s - n2X - f f = 1s - n2X X=f This can be written as Solving for X, we have This quantity (X) that results in a profit of zero is the BEP, and we now have this model for the BEP: BEP = Fixed cost 1Selling price per unit2 - 1Variable cost per unit2 s-n BEP = f (1-2) s-n

Explanation / Answer

An example from my own experience where I used a breakeven point analysis was when my company was contemplating manufacturing and selling a new product. We are a company that makes paints for home. Recently we decided to diversify into other categories like paints for automobiles and for industrial use. As a financial analyst working in the finance and accounting department of the company I was assigned the task of determining the breakeven point for the new paint products that the management was contemplating to launch in the market.

The parameters that were necessary to find the breakeven point were fixed costs, selling price per unit and variable costs per unit. Manufacturing of new types of paints entailed fixed costs like salary of the supervisor, opportunity costs of using the factory space (similar to rent), cost of utilities and interest expenses on loan taken for financing this new project. Variable costs consisted of cost of materials, piece rate labor, and commissions paid to salesmen. All the figures were provided by the cost department.

The fixed costs were $10,010 per year. Selling price per unit was $100 and variable cost per unit was $65. Thus break even = fixed costs/(selling price per unit – variable costs per unit)

= 10,010/(100-65)

= 286 units.

Thus the new paint for automobiles and industrial use will have to sell 286 units for break even. It is only after 286 units are sold that profits will start coming in.

Total revenue at 286 units = 286*100 = $28,600

Total costs = fixed costs + variable costs = 10,010 + ($65*286) = 10010+18590 = $28,600

Thus profit = revenue – costs = 28600-28600 = $0

From the 287th unit onwards profits will start occurring.

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