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A new break-even analysis uses production time vs. quantity.

Using a variable foundrymen can control, a new approach to break-even analysis has been developed.

Break-even analysis has traditionally been based upon production quantity, a,variable most foundry managers have no control over. A new break-even analysis approach has been developed based on production time, a variable that foundry production personnel can control. This approach assists in the evaluation of the feasibility of foundry products.

Break-even Options

There are four break-even points that have been used in evaluating the profitability of operations.

Shut-Down Point--This is the time at which the revenues are equal to the sum of the production costs, such as material, labor and maintenance. For production times greater than the shutdown point, it is more profitable to shutdown than to operate.

Break-even at Cost--This point is the production time at which revenues are equal to the sum of the production and overhead costs or the total costs. At production times between the shutdown and break-even points, the product will lose money but recover some of the overhead costs. This may occur when business is poor and the foundry operates at a loss with the expectation that business will get better.

Break even at Required Return--This is the production time at which not only are the total costs (production and overhead) recovered, but also a desired level of return is recovered.

Break even at Required Return after Taxes--This is the production time at which the total costs, taxes and required level of return are recovered.

The shutdown point has been used in continuous manufacturing, but has rarely been used in discrete manufacturing like foundry production. The break-even at cost point is the most commonly used break-even point, but break-even points at required return and required return after taxes are now receiving more consideration in profit evaluations.

Cost Reassignment

Costs are generally classified as fixed semi-variable and variable with respect to production quantity. However, with the use of a time base, costs must now be reclassified as production and overhead with respect to production time. Items such as property taxes, insurance and administrative salaries that were classified as fixed on the production quantity basis, would be classified as overhead on the production time basis.

On the production time basis, the direct material costs would be fixed as the order size is fixed, whereas on the production quantity basis the material costs would still be a variable cost and maintenance costs would tend to be a semi-variable cost on the time based system. In addition, since the order size is fixed, the revenues would be fixed on a time-based system.

Foundry Example

To illustrate how break-even analysis is used, consider a foundry that receives an order for 1000 castings at a purchase price of $13 per unit or $13,000. The foundry estimates its metal cost for the castings to be $2 per unit or a total of $2000. The administrative overhead costs are estimated to be $20 per hr, the variable (labor) costs are estimated to be $18 per hr, and the semi-variable (maintenance) costs are estimated to be $2 per hr plus $1000. The required return can either be a fixed amount or be a fixed amount per hr; for this problem it will be $10 per hr.

The data is summarized in Table 1 and the calculations for the various break-even points are presented. Note that in the break-even at required return after taxes the sum of the required return and the taxes on the required return is obtained by dividing the required return by 1 minus the decimal tax rate.

Table 1. Cost/Revenue Data for Break-even Analysis for Variable Production Time Model
Item $/hr $ Decimal
Revenue (Overhead) Costs 13,000
Variable Costs (Labor) 20
Semi-variable Costs 18
 (Maintenance) 1000
Fixed Costs (Material) 2 2000
Required Return 10
Tax Rate (33.3%) .333
Note: x=hr (production time)

Shut-down Point
 Revenue = Production Cost
 13,000 = 18x + 2x + 1000 + 2000
 13,000 = 20x + 3000 = Production Costs
 20x = 10,000
 x = 500hr

Break-even at Cost
 Revenue = Production Costs + Overhead Costs
 13,000 = 20x + 3000 + 20x
 13,000 = 40x + 3000 = Total Costs
 40x = 10,000
 x = 250hr

Break-even at Required Return
 Revenue = Total Costs + Required Return
 13,000 = 40x + 3000 + 10x
 13,000 = 50x + 3000
 50x = 10,000
 x = 200hr

Break-even at Required Return After Taxes
 Revenue = Total Costs + Required Return + Taxes
 13,000 = 40x + 3000 + 10x/(1--tax rate)
 13,000 = 40x + 3000 + 10x/(1-0.333)
 13,000 = 40x + 3000 + 15x
 55x = 10,000
 x = 181.1 or 182hr

The four break-even points are illustrated in Fig. 1 as a function of production time. If the scheduled production time is more than 500 hr (shutdown point), the product should not be produced. It is more economical to close the foundry because all of the production costs and none of the over, head costs will be recovered.


If the production time is between 250-500 hr (break-even at cost and shutdown point, respectively), the production costs will be recovered and only some of the overhead costs will be recovered. Therefore, the product will be losing money.

All costs will be recovered and some profit will be made if the production time is fewer than 250 hr (break-even at cost). If the production time is 200 hr (break-even at required return), all costs plus the desired required return (before taxes) will be obtained. Finally, at a production time of 182 hr (break-even at required return after taxes), the required return and taxes on the required return will be obtained.

Profitability as a Function of Production Time

A new alternative presentation of the break-even analysis is presented in Fig. 2, which illustrates the profitability as a function of the production time. In Fig. 2, the relationship between profits, taxes and costs and the break-even points can be observed. The chart indicates an increase in profits as production time is decreased. The equations for the various lines A, B, C and D for the example are:

Line A = Revenue-Production Costs

= 13,000-(3000 + 20x)

= 10,000-20x Line B = Revenue-Total Costs

= 13,000-(3000 + 20x + 20x)

= 10,000 - 50x Line C = Revenue-Total Costs--Required


= 13,000-(3000 + 40x)-10x

= 10,000-50x Line D = Taxes = 0.333 * Line B

= .333 (10,000-40x)

= 3333-13.33x


The break-even points can be found at the intersections of the four lines and the zero profit line. The shutdown point is obtained by the intersection of the zero profit line and Line A. The cost break-even point is obtained by the intersection of the zero profit line and Line B. The break-even point at required return is found by the intersection of Line C with the zero profit line. The break-even point at required return after taxes is found at the intersection of Line C and Line D.

Figure 2 also indicates a foundry's production costs, overhead costs, required return, net profits less required return, and taxes when the production time is below the cost break-even point. If the production time is greater than the cost break-even production time, the product costs exceed the revenues and a loss is incurred . Thus, there are no required returns, profits or taxes (on profits).

One advantage of a profitability plot is that it indicates how profits are increased by reducing production times. This approach gives an indirect insight to the success of the just-in-time approach of manufacturing, which reduces production time and increases profits. An additional advantage of the profitability plot is that it indicates the effect of overhead costs upon profitability, whereas ;n the traditional variable quantity approach the overhead costs were hidden in the fixed costs.

This new approach to break-even analysis indicates the importance of production time upon profits for production managers. It also can be used by management to recognize the effect of overhead costs upon the cost break-even point and profits for various products.
COPYRIGHT 1996 American Foundry Society, Inc.
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1996, Gale Group. All rights reserved. Gale Group is a Thomson Corporation Company.

Article Details
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Author:Creese, Robert C.
Publication:Modern Casting
Date:Mar 1, 1996
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