Financial Management: Risk and Leverage, Break-Even Analysis PDF

VE Basic Principles of Financial Management LM Brümmer JH Hall E du Toit  Risk and leverage, and break-even analysis LEARNING OUTCOMES After studying this cha...

VE Basic Principles of Financial Management LM Brümmer JH Hall E du Toit  Risk and leverage, and break-even analysis LEARNING OUTCOMES After studying this chapter, you should: nderstand the significance of the degrees of operating and financial leverage know what operating risk is.also know the difference between operating risk and financial.understand operating leverage and its implications risk.know what constitutesoperating costs.know under what conditionsthe operating lever will operate either negatively or positively.beableto plot the appropriate graphs defining the various break-even points grasp themeaning of break-even analysis and be able to make the relevant calculations be able to measure risk. INTRODUCTION In Chapter 12 we learned that, to acertain extent, an organisation can accommo date total risk, and hence influence the degree of financial leverage by altering the composition of its capital structure. In this chapter, we continuc the discussion on risk and leverage. However, having discussed financial leverage, we shall now devote time to operating leverage and study the relationship between operating leverage and and return. risk Risk was defined and discussed in somedetail in Chapter 2,but weshall repcat the basic definition here. Quite simply,risk may be defincd as the chance of loss. When we refer to risk, we generally mean total risk. Total risk consists of two clements, namely operating risk and financial risk. In addition, cach of thesehas its own definition. Aswe discovered in Chapter 12, 219 financial risk is related to financial leverage. Likewise, in this chapter we shall dis- Van Schaik Publishers cover that operating risk is relatecdto operating leverage.  and break-even analysS Chapter 13 Risk and leverage, to assess the presence and extenttof risk, Note that in attempting one may analysis of financial statements techniques discussed in the in begin by using the that the of that chapter liquidity, debt Chapter 6. We noted at the beginning refer to the and to measure risk. The debt ratios actmity ratios can be uscd composition and financial structures. Siinmilarly, organisations organisation's capital with ratios that are too low would be more vulnerable to riel lquudity and activity discuss operating risk and In this chapter, we shall first bricfly financal risk some attention to operating Thereafter, we shall devote leverage and also we shall study shew how it is related to financialleverage. Finally, break-even analysis which is related to operating leverage. OPERATING RISK AND FINANCIAL RISK Introduction Before we define these two forms risk, please refer to tthe Statement of of Compre hensive Income of LJE Ltd in Chapter 4,and note how has been it divided into two parts. One of the purposesof this division is to help us remember the detn. tions of operating risk and inancial risk, and to enable us to trace the sources o operating leverage and financial leverage. As we shall see in this chapter, operating and opcrating leverage are con risk cerned with the upper part of the Statement of Comprehensive Income, while financial risk and financial leverage are concerned with the lower part. In addi tion, please studythe remarks concerningthe operational and financial parts of the Statement of ComprehensiveIncome in Chapter 4, since the relevant remarks wil not be repcated here. Degrees of leverage and associated risks In the introduction to this chapter, we encountered the term "degree of financial leverage", which may be altered by changing the compositionof the capital sruk ture. Degrees of leverage apply to both operating and financial leverage. Itis not the intention in this book todiscuss thedegrees of leverage at an length, but we need to explain briefly thetwo concepts and then quote the r the more clearly mulas of operating leverage and financial leverage to highlight under may better relationship between them. When you see the twoformulas, you of Chup stand how the degrees of leverage may be changed, based on ycour study ter 12 and the rest of this chapter. The degrees of leverage are discussed below Degree of operating leverage ofloperatng The degree of operating leverage (DOL)isthe numerical measure inal change leverage and may be defined as follows: when a given percentage tax(EBII 220 results in a greaterchangein carnings beforeinterest and percentage Van Schaik the operating lever is in action and we have operating leverage. The great Publishers The DOL is also affected by the amount of fixed operating coSts.  Risk andleverage, and break even analysis 13 of fixcd opcrating costs relative to variable opcrating costs in an the proportion 's operations, the grcater the degrec of operating leverage. (This point organisation laterin this chapter.) The higher the level of be cxplaincd fixed operating costs capitalised the organisation is,for example being more will the more (e labourintensive), the greaterthe operating lcverage mechaniscd and the opcrating risk than be. will is zero, then operating leverage is neutral. Ifthe DOL When the has a DOL the lever is operating positively and we then have positive operating Valuc, NOsitive Similarly, when the DOL has a negative valuc, the operating lever isopcr- leverage. and we have negative operating leveragc. ncgatively ating as the DOL increases in value, so the leverage effect will escalate, either Finally, or negatively, depending on whether the DOL has a positive or negative positivcly The formula for DOL is as follows: value. change in EBIT percentage change in sales percentage leverage Degree of financial The degree of financialleverage (DFL) is the numerical measure of inancial leverage and may be defined as follows: when a given percentage change in EBIT results in a greater percentage change in carnings per share (EPS),the financial lever is in action and we have financial leverage. The DFL is also affected by the amount of fixed financial costs. If they are relatively high (and here we are referring especially to interest payments),then it high level of debt cap means that the capital structure will have a correspondingly in Chapter 12, the higher the level of debt capital in the capital ital. As explaincd and the higher the financial risk. structure, the greater the financial leverage If the DFL is zero, then financial leverage is neutral. When the DFL has a posi then the financial lever is operating positively and we have positive finan tive value, the financial lever cial leverage. Similarly, when the DFL has a negative value, then is operating negatively and we have negative financial leverage. so the leverage effect will escalate, cither Finally, as the DFL increases in value, the DFL has a positive or negative positively or negatively, depending on whether value. The formula is as follows: in EPS percentagechange in EBIT percentage change Total leverage and total risk the higher the total leverage losum the higherthe levels of total fixed costs, up, in mind also that the degree Will be and, as a result, the higher the total risk. Bear 221 is not the sum of the DOL and the DFL, but instead Of total leverage (DTL) concept is beyond the scope of this OVan Schaik DIL = DOL DELx (an explanation of this Publishers book).  Chapter 13 Risk n and leverage. and He break-even analysts Operating risk To formulate this definition, we refer to the upper part of the Statement of whic prehensive Income, Com- taking special account of sales and operating profit. artsWhc ing risk may be Operat- defined as the income from sales enough to cover production and possibility operating that costs. In other words, operating riskis will not behigh hors ow the chance his that the organisation will suffer an operating loss, which means EBIT is a negative amount, giving rise to the possibility that that suppliers or short- L term trade and other payables will cither not be paid in full, or not be paid at all ATNG Such cases, an organisation runs the risk of being liquidatcd. We know that the of the Statement of Comprehensive upper part Income reflects the organisation's operational affairs, and it is here that operating risk exerts its most direct influence. The factors likely to cause an operating loss may be included under a common heading of operationalor occupational hazards. For Cxample, in the agricultural industry, and more specifically in farming,operating erera risk would include factors such as droughts, floods, hailstorms, and livestock and Crop discases. These factors are the ones that would contribute to unstable EBIT part. nndl n and possible financial loss. ASCS Each industry will, of course, be characterised by its own peculiar operating haz give ards and risks. In some industries, unstable EBIT could be caused by fluctuations ira in demand, such as the secasonal demand for goods or an unpredictable demand as ater in the fashion industry. Finally, there is the risk of rapid obsolescence,for example in the field of technology.All these factorswould contribute in varying degrees to tor ctl reductions in EBIT, and the astute investor should be aware of them. tpend Financial risk The definition of financial risk can be formulated by referring to the lower part of o are the Statenment of Comprehensive Income, taking special account of EBIT and the financial break-even point (the point where full settlenment of all inancial obligations dscu occurs, i.e. the paymentof interest, tax and preference dividends). Financial risk may be defined as the chance that EBIT will not be high enough to cover the organisa Sopera tion's financial obligations. This means that the interest due on interest-bearing debt., as well as income tax, might not be paid. Should this occur,the organisation faces rabl certain liquidation, and the ordinary shareholders will ultimately lose. From what we have discussed so far, the two main sources of financial risk would appear to be, firstly, a too-high operating risk (resulting in an EBIT which is too low and unstable) and, secondly,a too-high debt/cquity ratio (resulting in the erosion of EBIT, especially by high interest payments). Financial risk would thus be aggravated by unstable EBIT and toohigh a ratio of long-term debt capital in the capital structure. Both operating risk and financial risk therefore combine, and become total risk. Concluding remnarks 222 The prudent financial manager will acquaint himself with the operating risks pre Van Schaik vailing in the industry in which he finds himsclf. Likewise, the investor should be Publishers aware of these risks before he invests in an organisation in a particular field.  Risk and leverage, and break-even analyss 13 fieldi of credit management,the Inthe credit manager shoulders a similar He must decide whether or not to grant credit, for cxample to a responsibility. farmer, knowing that there or maize is a possibility that the farmer will not whcat his accounts until he has able toscttle after sold his crop -that is, if his crop partially or completely already been destroyed by one or more the agri not of has which farmers facc. A good hazards credit manager will, of course,try to cultural wherever possible through extensions the credit his debtors period without of help his own organisation'sfinancial welfarc. jcopardising TING LEVERAGE OPERA of operating leverage Definition case of financial leverage, operating levecrage is used in a similar way in As in the certain results which arise from certain other changes. Also, just to magnify order leverage relates to the lower part the Statement of Comprehensive of as financial part, so operating leverage relates to the upper part, the the inancial Income, Operating leverage can thereforce be defincd as the capacity to part. operational operating to magnify the effects of changes in sales on in fixed costs use increases in sales, there will thus be a proportionately greater rate a given change EBIT: For profit (EBIT).This change in EBIT will become progres- change in operating increases more and of more. of fixed operating costs as the proportion Sively greater can operate cither positively or ncga Re to note that operating leverage careful sales (or operating risk), as cxplained inthe iely. depending on the stability of section. previous costs? What are operating let us first discuss the impli the definition of operating leverage, Before discussing book, For the purposes of this or total operating costs. cations of operating costs, two clements, namely will be assumed to consist of only total operating costs fixed and variable operating costs. costs only, not to assumed to relate to operating Variable costs are generally to mcan the same as variable financial costs, and so variable costs will be taken to both operating and the other hand,can relate operating costs.Fixed costs, on to qualify these differences For this reason, we must be careful inancial costs. in this chapter, for the sake of convenience However, whenever we discuss costs. costs" costs", “fixed costs" and "variable of *total We shall use the simple terms costs", “fixed oper terms, namely “total operating ather than referring to the full ating costs" and variable operating costs» Fixedcosts 223 in amount over a given peri- , do not Fixed costs are the costs that normally change od, usuually the costs gencrally consist such components as of Van Schaik ©Ashers financial Fixed year. rent on premises, and electricity depreciation on fixed managers' salarics, assets,  analysis and break-even and leverage, nc nothing, these fixed 13 Risk produces cOsts Chapter organisation change the can mnust if the of directors Even the board amount of sill water, by capacity and thercby fxed and decision Only a production of time and not increasing be met. for example by are expanding therefore a function over a given period, of production and depre volume Therea costs, costs than Fixed unchanged production vol. costs remaintotal. ciation. is that fixed costs is, fixcd their are -that on confusion sbou no cfect causes mcans that if more units are ume has that sometimnes unit. This occasionally An aspecct cost per words. the fixed amount produced, as a fixed In other of belower. of units, thus reducing the fixed the measurcd unit will costS per COSt per the fixed cost number unit will increase if unit he divided by a greater the fixed cost per fewer units are is now Likewise, why organisations strive to and sold. the reason increase produced sold. (Thisis fixed costs per unit, which in turn will sales, phe and their help to us produced so reduce total fixed costs are generally more and deviation, Viewed as a produce Apart from this ther stabilise EBIT.) period. over a certain fixed amount star Variable costs costs. Variable costs are all those costs is variable COSts clement total of out time and work studies and by The other by carrying inchuding been determincd essentially the costs of raw that have costs are materials costs (input production and input we discover, for instance, that each unit costs studies, Through these raw materials and wages. Variable costs will and labour). a fixed amount to produce proportion to in terms production of volume, which is why they are described to the rising number of : varyin direct incrcase in proportion will therefore Variable costs variable. units produced. thus a function of production volume costs) are costs (unlikefixed to the rate of Variable In dircct proportion of time: they increase and decrease and not of raw materials. be wages and the cost duction. Examples would Concluding remarks under very important to these twokinds of cost, and it is Many people confuse that variable cOsts are really a fvedj stand the differences between them. Remember are a fixed total anL011t year, whereas fixed costs cost per unit over the financial over the same ycar. Demonstrating operating leverage of the definition of operating leverage, we Before we consider the implications action. Let us suppose that we are operating lever in should first demonstrate the A fixed costs in Organisation con two organisations, A and B. The considering in Organisation B.In such a case, stitute a higher proportion of total costs than assets in its of fxed 224 A would, for example, have a larger proportion Organisation This would raise Orga Van Schaik asset structure and hence a higher depreciation amount. OPublishers sation A's fixed costs to a higher level than those of Organisation B.  Risk and leverage, and break-even analysis we could say that words, Organisation A is 13 other B, which in turn would more In be more capital labour intensive Organisation thus result in varying intensive. These han WOuld proportions of fixed two organisation 's ability to and variable structures a particular limit its fixcd costs. to a certain costs mnore TheretorC, would depend, exXtent, on its asset effectively structurc. another one seldom finds However, in than ofmechanisation, organisations that are almost entircly age this intcnsive. Labour demonstrating operating leverage The graphs lever may be adequately offthe operating demonstrated by making use cach of the organisations. The graphin The action for Figure 13.1 illustrates one structure of Organisation A, and thc graph in Figure of graphs, 13.2 labour-intensive structure of Organisation B. We shall assume fur the capital-intensive la the are operating in the same industry and that, in both -rhatboth organisations illustrates ther costs and the selling price per unit will therefore remain con- total operating volume. The main difference betwcen the two organisa- Cascs, any production at A will have a higher proportion of fixed costs and a stant Organisation will bethat tions of variable costs thaan Organisation B. lower proportion these graphs. You will see that costs and income are reflect- two us consider Let while the number of units produced and sold is reflected on thhe Y-axis, edin rand onthe X-axis. about these two organisations, let us suppose that the assumptions Let 12 units within a us certain period. to produce and In satisfying sell the capacity to Rl00, and the both have income from the 12 units amounts that the gross organisations. Within to R80 in both also suppose plus variable) amount the (i.e. fixed costs will bear rel- total costs of R80, the fixed and variable of thetotal costs above. the compass as mentioned in each organisation, to R40 and the remaining erant proportions A, fixed costs amount In the Inthe case of Organisation variable costs. is the total the total costs of R80, amount up costs amount of R40,making total variable fixed costs amount to R10 and B, of fixed costs case of Organisation assumption concerningthe amount the to R70 (R80 - R10). From presentation of cach case is plotted to accom see how the graphic. In each case, we line modate the two situations. A, and the total cost by linc line is represcnted incomeis exactly both graphs, the income total cost line, In the income line intersects that point. B. Where the nor loss at ine is neither profit means that there in both graphs it cqual to total costs. This point and break-even primary break- This point is known as the operating to as the may be referred the At this point, S Tepresented by point X. This point point Y. found at only even point is to cover point. A secondary break-even issufficient income line. Here, income is insuf- 225 intersects the fixed cost means that Income line more, which o the organisation's fixed costs and nothing Van Schaik Publishers CIent to cover variable costs.  Chapter 13 Risk and leverage, and break-even analyss Organisation A, using a Figure 13.1 Operating leverage in high fixed operating costs ratio R100 A (Income) R80 B(Total R75 costs) R70 Y R40 F(Fixed costs) E(Total variable costs) X 4,8 8 9 12units Figure 13.2 Operating leverage in Organisation B, using a low ratio fixed operating costs of Y R100 A (lncome) R80 B(Total R74 costs) E (Total variable R62 D Costs) R10 F (Fixed costs) RO 1,2 4,0 9 12 units Conclusions aboutthe graphs Now pay particular attention to thefollowing remarks: even if these two orga sations fail to produce and any sell units of thcir product, fixed costs must 226 paid - that fixed costs are there as a fixed still is, liability. On the other hand, while Van Schaik organisations do not produce and sell any units, variable costs will be zero in Publishers be cases because variable costs are directly related to units produced and sold.  Risk and leveragn, and break-ven arasis 13 are produced and sold, thercforc, total costs will Ino units thc Variable cost linc, E, begins at R0 fxed consist only of that rcason, (zero rand) on the For organisations begin to costs. As sOOn as the producc and scll units oftheir prod costs incrcase with cach unit produccd and sold. The Araph. Variable line: n0 incomc is generated if no samc may be cts, income units arc sold, and ofthe atthe RO point on the therefore stid line also begins graph. the income remark rclates tothe variable cost linc, E, tinal and the total cost The are added to fixed costs, the line, B. costs variable total cost linc starts at R40 on When for Organisation A and at R10 on the Y-axis for Organisation B. Costs theYaxis at R40 and R10 respectively, because to start even if the necd organisations do not and sell any units, the fixcd cOsts still need to be paid. For produce example, in the A, total costs amount to R40 when there Case of Organisation is no production of units. For every unit produced and sold thereafter, total and sale costs begin to the amount of the variable costs - that is, the rise by number of units multiplied cost per unit. Note that Organisation B's variable by variable cost line runs more and hence more closely tothe income line than that of Organisation stecply A. Consequently, by reducing productionand sales, Organisation B would be able to variable costs, and hence total costs, faster than reduce Organisation A would. Which is the better organisation? A decision on which of these two organisations would represent the better invest ment would depend on a number of variables, such as stability of incomeand demand, and profitability,. These variables will usually influence the value of the organisation'sshares and hence shareholders' wealth. When we takethese variables into account, they simply indicate the effect of risk on profitability. We shall now determine which of the two organisations is the riskier when production and sales levels vary. In terms of the number of units that must be produced and sold,Organisation A must sell the cquivalent of 4.8 units in order to cover its fixed costs. In other words, when fixed costs amount toR40, then at point Y, income also amounts to R40. Since the variable costs incurred in producing and selling 4.8 units have not yet been covered,the organisation is actually showing a loss to the extent of the current variable costs – that is, the difference between points Y and Z in thecase of Organisation A. Bythesame token, OrganisationB must sell only the equivalent of 1.2 units for income to cover fixed costs. From this we scethat OrganisationA must exert far more cffort than OrganisationB merely to cover fixed costs. In cffect, Organisation A must sell the cquivalent of 3.6 more units (4.8 - 1.2) than Organisation B to meet fixed costs. In being its forced to produce and sell more of its goods to cover fixed costs, Organisation A runs a greater riskthan Organisation B of being faced win problemsthat could arise to prevent the additional production and sales. 227 Ihis situation is similarto the occurrenceof risk in time. In terms of risk in OVan Schaik time, the Publishees further into the future a forecast is made or the longer a creditor must  analysis Chapter 13 Risk and leveage, and break even is the chance his account, the greater that wait for his debtor to sertle the time span and Some prob loss, hcnce both the to causc financial lem could arise of risk. level of directly affect the level production the break-even points at may be applicd to X. The same reasoning nceds to sell B units to break even, while Organisation Organisation A must scll eight units as only This means that Organisation A must scll twice as many for Organisation unstable as a result B should income be of order to break even. Therefore, offer the safer investment of thetwo operating risk, Organisation B would appear to fewer products to cover costs. However,ifbecause it necds to produce and sell low and EBIT relatively stable, then opera ing risk were comparatively so the soundness of an Organisation A proposition, would be the more profitable organisationor depends essentially on the degree of an investment proposition operating risk. Implicationsof operating leverage stable in organisations and B. By suppose that income A Let is us observing A offers the better oper- ating leverage, we see that Organisation investment of the EBIT which are related two Fixed costs may be used to nmagnify changes in to changes in sales. In terms of the definition of operating leverage, Organisation A is using fixed costs to a greater degree than Organisation B is. Let us suppose that Organisation A is currently selling nine units. The amount of profit being made from the sale of nine units is the difference between income and total costs at points C and D. If we extended lines from points C and D ot Y-axis, the profit would be the cquivalent of R5 (R75 R70). However, sunn - that Organisation A increases sales by 33.3% to 12 units. Profit would now becon R20 (R00-R80), the difference between points A and B. Inthis way, proft bas increased by the following: (R20 - R5) x100 = 300% or 3 times R5 The implication of this change in sales and the change in EBIT is the following: in terms of the definition of operating leverage, an increase of 33.3% in sales resulted in a correspondingchange of 300% in EBIT. This means that for a certain change in sales, there was a proportionately greater change in EBIT. The magnification of EBIT in this way is evidence of the operating lever in action. Since theresults were all positive amounts, we may conclude that the operating lever was operating positively. So long as unit sales exXCeed those at the break-even point at X, operating leverage will always show a positive tendency, resulting n profñt. Conversely,as soon as sales fall below the break-even point, operating lever age will diminish and soon become negative, while profits will decline, and escalat- ing losses willeventually be the result. 228 Further to the remarks in thelast paragraph, let us see how the operating lever ninc Van Schaik affects the affairs of Organisation B. Here sales are also increased by 33.3% from Publishers A. units to 12 units. Profit is calculated in the same way as in the case of Organisation  Risk and leverage, and break-even analysis 13 of nine units amounts to at sales R12(R74- R62), the difference between The profit At l2 C:and D. units, profitamountsto R20(RI00 - R80),the difference points points A and B. Thecharnge in profitis thus found to be as betwecn follows: (R20- RI2)x 100 66.67% R12 for a 33.3% change in sales, Therefore, Organisation B magnified (or increased) by only 66.67% compared with Organisation A's 300%. In EBIT Organisation leveragc was also positive, but the lever B's casc, operating opcrated to a lesser in the case of Organisation A, so in terms of the than definition, Organi- extent A experienced the greater degree of operating leverage solely because of its sation fixed costs, As a result., extensive use of Organisation A cxhibited thc greater more profitability. degree of of the changes in and EBIT rclates to the rate Another implication sales of At sales of nine units, Organisation A's profit amounted to R5 while that return. B amounted to R2. When 12 units were sold, Organisation A's of Organisation are of return increascd progressively faster than that of Organisation B. Organisa ion A's profit rose rapidly from R5 to R20, while Organisation B's profit rose at a slower ratefrom to R20. R12 The implication for OrganisationA isthat profits increase progressively faster for verY unit sold above the break-even point at X. Should sales fall below the brcak even point, then losses will accelerate at progressively grcater rates. In Organisation R's case, both profits and losses will accelerate at slowerrates than those of Organ A. isation This variability in rates is caused by the degree of operating leverage (DOL), which in turnis influenced by theamount of fixed costs expended on the organi sation's operations. In the event of severe fluctuations in EBIT owving to operating risk, Organisation A would bcmore vulnerable to financial problems than Organi sation B would. Should sales provide a stable EBIT, then Organisation A would be the more profitable organisation. Concluding remarks Assumptions about the graphs The information two graphs is based on impracticaland theoretical used in these assumptions simply to demonstrate a point more clearly. In practice, and in accor dance with general economic principles, there is an interaction between supply and demand. Let us suppose that a certain article is being supplicd to the market.As sales increase, the income line rises steadily. At some stage, in practice, demand might decdline and supplywould exceed demand. The priceper unit would fall because of the oversupply and income would begin to decline. However, in these two exam 229 Ples this does not happen. The income line continues to rise without any sign of Van Schaik Publishers POssible decline. If wewere to apply these practical aspects toour two graphs, their  analysis Chapter 13 and break-even Risk and leverage, theoretical assumptions, we are By making these able would change. graphic forms more clearly. leverage to demonstrate operating financial leverage and operating The relationship between one, we note that opcrating 12 and also in this In both instances, they lever. From discussions in Chapter cach other. are related to other are leverage which arise from related age and financial certain results taken from the changes,. concerncd with magnifying in results have their origin Statement Furthermore, both concepts that operating leverage relates to the difference Income, with Income while financial of Comprehensive of Comprehensive lever- part of the Statement is based on their the uppcr Finally, their relationship respective the lower part. costs in age rclates to costs and fixed financial stimulating the fixed operating uses of fixed costs, action of the two levers. it is clear that the of their characteristics, operating From this brief summary lever the secondary one. We note also and the financial and hence also On lever is the primary lever, operating leverage, risk an influence on exerts f only that operating financial risk influences on leverage. Similarly, financial risk and financial leverapge Th risk or on operating it has no cffect at all on operating to onero. leverage; cial risk and financial leverage are both subject for this is that financial reason and operating leverage. fu ing risk connection with these explanation in aspect that requires some A final by algcbraic means. The cos the determination of the break-even point This graphs is by calculation. w thus far about the graphs may be verified clusions drawn use of break-evenanalysis. shall do in the next section by making BREAK-EVEN ANALYSIS Introduction a graph to break-even point by using only It perhaps not sufficient to find the is as also draw our conclusions to calculate it, and then plot it. We must also be able we must to calculate the brcak-even point, we did in the previous section. In order analysis. This technique begins with a simpl use a technique called break-even profit or EBIT. approach to calculating operating Calculating operating profit (EBIT) units of a certain article. The selling price per u Let us suppose that we have 100 the fixed co is R12 and the variable cost per unit is R8. Let us also suppose that from the sale of the 100 uni amount to R300.What amount of EBIT will result The total sales valuc would be R1 200(100units x R12). Total variable co would beR800 (100units x R8). We could now set this calculation out as tollo EBIT = total income -variable costs – fixed costs 230 - RI200 – R800 – R300 OVan Schaik = R1200 – (R800 + R300) Publishers =Rl00  Risk and leverage, and break even analysis 13 isquite simple and purely arithmetic. Let us rearrange the calcula- The caleulation way: following inthe (R12- R8)- R300 tion =100 units x -100 units (R4)-R300 EBIT - R400- R300 -RI00 changed anything,and we still arrive at the same answer.In have not really that the amount R4 known the marginal income per We this :c calculation, contribution note per unit, which of is is as derived from the figures in the brackets, betweenthe sclling price per unit andthe vari- or unit - R8). The difference (R12 namely is therefore the marginal income per unit. Remember that these per unit able cost as per umit. qualified are always derive a sim- we could figures symbols for the figures in this calculation, By substituting for calculating EBIT. Let us use the following symbols: pleformula =number of units produced and sold P =selling price per unit = variablecost per unit (P- )=marginal incomeper unit =fixed costs substituted for figures, we findthat: Therefore,when symbolsare EBIT =N (P- )-F related calculations. our basic formulafor other also This is profit of R100, how many would we have units If the sale of 100 units yiclds a rearrange the formula even? By algebraic transposition, we could to sell to break wve break-even point. In other words, and derive a new one for calculating the EBIT of R0 (zero rand) where ncither for N which will provide must find a value the break-even point we make shown. To derive a formulafor a profit nor a loss is the following algebraic transposition: EBIT =N(P- )-F= 0, which is the break-even point equation and so Therefore, when EBIT =0, EBIT is climinated from the algebraic we have the following: N= (P -V)