# Variable Cost increases in direct proportion to Volume Fixed Costs do not change as Volume changes (in a relevant range).

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1 Variable Cost increases in direct proportion to Volume Fixed Costs do not change as Volume changes (in a relevant range). If we are in business and we are selling something our price is going to be larger per unit than our costs are per unit and as a result our revenue stream (sales) is going to incline more rapidly than our total costs line. Before our sales line reaches our total cost line we are in the LOSS TERITORY. In this region our total costs are greater than our total sales revenue. If our sales are greater than our total costs we are in PROFIT TERITORY. And at the point were sales and total costs intersect is called the BREAK EVEN POINT. There is no profit or loss at the break even point. ACCT323, Cost Analysis & Control Lecture 3 Page 1

2 That point could be quoted in terms of the volume (number of units) which must be achieved to reach this point. Or it could be quoted in terms of the dollars of sales revenue needed in order to break even. ACCT323, Cost Analysis & Control Lecture 3 Page 2

3 Recall that our Traditional Method of doing an income statement is: Traditional Model Sales \$ 10,000 COGS \$ 6,000 Gross Profit (GP) \$ 4,000 Operating Expenses -MKTG \$ 2,000 -G & A \$ 1,000 Total Operating Exp. \$ 3,000 Operating Income \$ 1,000 Note that the Traditional Model is GAAP and is used in industry and is useful for it s intended purpose. The problem with the Traditional Model is that COGS is a combination of Fixed and Variable Costs. There are certain variable costs and certain fixed costs in COGS as well as in marketing and G&A. If we wanted to do a Cost Volume and Profit analysis we couldn t do it utilizing the Traditional format because there is a mixture of fixed and variable costs in each of the groupings. Instead we have to reform our income statement. Lets say that we examine our costs categories and find the following mixture of fixed and variable costs: Traditional Model Sales \$ 10,000 Variable = \$ 4,000 COGS \$ 6,000 Fixed = \$ 2,000 Gross Profit (GP) \$ 4,000 Operating Expenses Variable = \$ 1,200 -MKTG \$ 2,000 Fixed = \$ 800 -G & A \$ 1,000 Variable = \$ 200 Total Operating Exp. \$ 3,000 Fixed = \$ 800 Operating Income \$ 1,000 \$ 5,400 \$ 3,600 We can now group all the variable costs together and all the fixed costs together and we would be in much better shape ACCT323, Cost Analysis & Control Lecture 3 Page 3

4 Contribution Margin Format Per Unit Sales \$ 10,000 \$ Variable Costs \$ (5,400) \$ (5.40) Contribution Margin \$ 4,600 \$ 4.60 Fixed Costs \$ (3,600) Operating Income \$ 1,000 # units sold = 1000 Now take our SALES and subtract the sum of the VARIABLE COSTS, this gives us the CONTRIBUTION MARGIN. Subtracting FIXED COSTS from CONTRIBUTION MARGIN gives us OPERATING INCOME. Now say we have sold 1000 units. Lets do a per unit calculation. We find our AVERAGE SALES PRICE is \$10 per unit. \$5.40 per unit is our AVERAGE VARIABLE COSTS and \$4.60 is the contribution margin per unit. Remember, we DO NOT calculate a per unit costs for our FIXED COSTS because fixed costs are not per unit related! Not related to the number of units. This isn t to say it would not be a useful number for something, just not for what we are doing. Now we see in Contribution Margin Format our per unit numbers showing us that we are selling for \$10 per unit but for every unit that we sell we have to incur a variable costs of \$5.40. This lowers our contribution margin to \$4.60 which means that every unit that we sell is actually only contributing \$4.60 toward covering our fixed costs and going on to earning us a profit. FORMULAS Operating Income = Sales Variable Costs Fixed Costs = (Quantity * Unit Sale Price) (Quantity * Unit Variable Costs) Fixed Costs = Q * (USP UVC) FC OI = Q * UMC FC Where: UCM = Unit Contribution Margin = USP UVC Sales = Quantity * Unit Sale Price Variable Costs = Quantity * Unit Variable Costs USP = Unit Sale Price UVC = Unit Variable Costs ACCT323, Cost Analysis & Control Lecture 3 Page 4

5 Know the Quantity and Break Even formulas. Now add a T for Target and solve for Quantity Q = FC + TOI UCM At the Break Even Point the Target Operating Income is \$0.00: Q BE = Break Even Quantity FC + 0 UCM Find the break even quantity in our example: Q BE = = FC UCM Always show at least 1 decimal place FC + TOI = UCM 4.60 = This says that we must sell units to reach the Break Even Point. We can also use this formula to find the break even quantity for a given Target Operating Income by plugging that number in. For example, if we want a TOI of \$10,000: FC + TOI \$10,000 Q BE = = UCM 4.60 = 2,956.5 Remember in this example we had sales of \$10,000 on 1000 units sold for \$10 per unit sales (i.e., \$10 sale price). Now consider the percentage of Contribution Margin to Unit Sale Price: Contribution Margin 4.60 = = 0.46 = 46% Per Unit Sales (Sale Price) 10 This says 46% per unit sold went toward covering the contribution margin. Now we will find the Break Even Sales Point: (where TOI = \$0) In our example: FC SALES BE = C/M as % of Sales SALES FC + TOI 3, BE = = C/M as % of Sales 0.46 = \$ 7,826 This says we must reach \$7,826 in Sales to reach the break even point. ACCT323, Cost Analysis & Control Lecture 3 Page 5

6 So there are 2 ways of coming up with Break Even Point: 1) Solving for Break Even Point in terms of Quantity (number units sold). 2) Solving for Break Even Point in terms of Sales (\$ of sales). To solve for BEP required to reach a certain operating income just solve with the desired target operating income (non-zero). ACCT323, Cost Analysis & Control Lecture 3 Page 6

7 Here we are asking the question, what happens if there is some percent misestimation in items such as volume, variable costs, sales price, fixed costs. The purpose of One at a Time Sensitivity Analysis is NOT to evaluate the scenario possibilities, it is to evaluate the sensitivity of the variable to the bottom line. There is something called a Scenario Analysis in which you assume a certain scenario and then do a projection based on what you think will happen in that scenario and how the company might position itself in that certain scenario. The Four Horseman of Profitability: Volume Variable Costs Fixed Costs Sales Price To do this we take the original base case and compare it to the modifications. Say we need to increase our profitability s and the company wants to know how sensitive the bottom line is to a 10% change in volume. We do the analysis in one direction (positive) and hypothesis that the change is the absolute value and that it can go plus or minus. In our example we will explore a 10% increase in the various components. One at a Time Sensitivity Analysis +/- 10% +/- 10% Unit +/- 10% Unit +/- 10% Base Volume Sale Price Var. Costs Fixed Costs Costs Change Change Change Change Sales 10,000 11,000 11,000 10,000 10,000 Variable Costs (5,400) (5,940) (5,400) (5,940) (5,400) Contribution Margin 4,600 5,060 5,600 4,060 4,600 Fixed Costs 3,600 3,600 3,600 3,600 3,960 Operating Income 1,000 1,460 2, Average from Base 0 +/ /- 1,000 +/- (540) +/- (360) 10% Volume Change What happens to Sales under a 10% volume increase? It goes up 10%! What happens to our variable costs? They also go up by 10%. Contribution Margin goes up 10%. Fixed costs DO NOT CHANGE. The result is that the 10% increase/decrease in sales generates a increase/decrease 460 change from the base. 10% Unit Sales Price Change Start with the original data again and change only the one variable under consideration. Sales go up. Variable costs STAY THE SAME because the volume didn t go up! We are only changing the price and that does not effect the number of units we produce. Fixed costs does not change. In this case we see the \$1,000,000 change in sales do to the increase in per unit sales price works it s way down to the bottom line. The increase is pure margin. That is why pricing is so important. The opposite would have happened if there had been a decrease in unit sale price. Pricing decisions are very important because they impact the bottom line dollar for dollar. ACCT323, Cost Analysis & Control Lecture 3 Page 7

8 10% Change in Unit Variable Costs Sales do not change. Unit Variable Costs increase by 10% and contribution margin changes as a result. Fixed Costs remain the same. As a result of all this Operating Income is decreased by 540 to % Change in Fixed Costs Sales and variable costs will not change. Fixed costs go up by 10%. This gives us \$640 on the bottom line, a decrease of 360. Now we ask what happens if there is a beneficial change in ALL of the four profitability parameters at the same time? This is closer to a scenario analysis because all four variables are changing. We see here what effect a change in all for of the underpinnings of profitability can have: Volume, Price, Variable Costs, Fixed Costs. Volume up 10%, Unit Sales Price up 10%, Unit Variable Costs down 10%, Fixed Costs down 10%. What is our operating income going to be? Sensitivity Analysis: Beneficial Change In All 4 At Once Base Vol + 10% USP + 10% UVC - 10% FC - 10% Costs Change Change Change Change Total Sales 10,000 x 1.1 x 1.1 = \$ 12,100 Variable Costs (5,400) x 1.1 x 0.9 = \$ (5,346) Contribution Margin 4, Fixed Costs 3,600 x 0.9 = \$ 3,240 Operating Income 1, Average from Base 0 + 2,514 The 1.1 multiplier for Volume Change appears twice; once to reflect it s own increase (first line) and again as part of the Unit Variable Costs increase (second line). This is because Unit Variable Costs are calculated based on Volume, so we must show the increase in Volume in our calculation. When you increase VOLUME you must also increase VARAIBLE COSTS. All disciplines must get involved to make these kinds of changes; marketing for volume, manufacturing for variable costs, operating people for fixed costs, pricing, product design, product differentiation, tapping new markets. What this gives us is a quantitative assessment of what could be. Making it happen is a whole other aspect. ACCT323, Cost Analysis & Control Lecture 3 Page 8

9 We will be learning the Weighted Average Method only. Up until this time what we have been doing is known as Job Order Costing. This is a technique which is used when the projects are individually unique and they have to be costed individually. Example would be a custom shop, someone gives you a set of specifications, you build to the specs and cost it as you build it for the direct material, direct labor, and overhead. But we wouldn t use job order costing if we were manufacturing bottles of Snapple or anything else which involves high volumes of identical product. Instead we would use what is known as Process Costing because all the units go through the same process. We will use the below book case as an example. Direct materials are added at the end of the process. It goes through the drying and packaging process. When it comes into this process there is no material added, that has been done in the ACCT323, Cost Analysis & Control Lecture 3 Page 9

10 previous process, all it s doing is drying. Once it s dry near the end of the process they add material in the form of packaging. Key is that it is added at the end of the process. What we are describing is really divided into two parts; the Physical Flow and the Costs. Physical Flow Units WIP - Beginning 1,250 Started / Added During Process 5,000 Conversion Units to be Accounted For 6,250 X-Fers In D/M Costs Completed & Transferred Out 5,250 5,250 5,250 5,250 WIP - End 1,000 1, Units Accounted For 6,250 6,250 5,250 5,650 1 See footnote b above. % completion for D/M is an unknown units transferred in from prior process (called Started / Added above). Units to be Accounted For is the sum of WIP-beginning and transfers in. So at the beginning there are 6,250 units, these will be accounted for through the process. Now at the end of the process there are 5,250 completed and transferred out and 1,000 remaining as work in process. The sum of these are the units accounted for, 6,250. Consider that we have two sets of units which are not on the same basis. One is Units Whole & Complete (transferred out) and the others are still in WIP and they are not complete. That means they are at different stages of completion. But regardless of the stage of completion of a unit, at the end of the period the process must stop and the number still in process must be determined. What we want to know is what is the equivalent units in each category. As far as the units which were completed and transferred out they were completely done, 100% complete in every category (transfer in, direct material, conversion) (by definition). Now consider WIP-Ending; in order to be WIP at the end they must have been fully transferred in, so that s 100% complete. Regarding footnote 1 and b above. There are footnotes on the beginning and ending WIP. In our case we are not covering the FIFO method which examines beginning inventory, so disregard that footnote. Footnote b says that transferred in costs were 100% complete (we know), direct materials were? % complete, and conversion costs were 40% complete. The question mark wants us to go to the information given in the problem and find out at what point do we put direct material into the process. When is it added, when do the laborers apply material? We know from the statement of the problem that the only material they add is packaging and it is not added until the end of the process. So if the units we are examining are only 40% complete than we know we have not yet added direct material. So with regard to direct material they were 0% complete. With regard to conversion costs we find in the problem statement they were 40% complete so they have 1000*.4 = 400. Now we do the sums and find our equivalent units (listed as units accounted for). 6,250 transfer in, 5,250 direct material, 5,650 conversion costs. Now we move on to the dollars, the COSTS. Basically the format is the same. ACCT323, Cost Analysis & Control Lecture 3 Page 10

11 Conversion Costs Total X-Fers In D/M Costs WIP - Beginning 38,060 = 29, ,060 Costs Added During Process 159,600 = 96, , ,400 Costs Added During Period 197,660 = 125, , ,460 Equivalent Unit Costs \$ = \$ \$ \$ 8.40 Completed & Transferred Out 174,300 = 105, , ,100 WIP - End 23,360 2 = 20, ,360 Costs Accounted For \$ 197,660 = 125, , ,460 2 Solved for by difference. Notes Equivalent Unit Costs = Costs Added During Period / Units Accounted For Conversion Costs include Direct Labor and Overhead. Completed & X-ferred Out (Costs) = Completed & X-ferred Out (Phy) * Eqv. Unit Costs WIP End (Costs) = WIP - End (Phy) * Equivalent Unit Costs Equivalent Unit Costs Transfers In: \$125000/6250 units = 20 (6250 is Units Accounted For line in Physical) Direct Material: \$25,200/5250 units = \$4.80 Conversion Costs: \$47,460/5650 = \$840 At this point in our process the results are telling us is that the transfers in were transferred in at a cost of \$20 per unit, we ve incurred \$4.80 in material and \$840 in conversion costs. CONVERSION COST INCLUDE DIRECT LABOR AND OVERHEAD Now we will assign the costs to those units which were completed and transferred out. First are the units which were WIP Ending, and that gives us our cost of accounting. The point is to get the last two lines. We will take the Completed and Transferred Out (Phy) multiplied by Equivalent Costs which gives us Completed & Transferred Out (Costs). Same for other lines. Then the Total column is the sum of the Transfers In, Direct Material, and Conversion Costs columns. Both sheets together: ACCT323, Cost Analysis & Control Lecture 3 Page 11

12 Physical Flow Units WIP - Beginning 1,250 Started / Added During Process 5,000 Conversion Units to be Accounted For 6,250 X-Fers In D/M Costs Completed & Transferred Out 5,250 5,250 5,250 5,250 WIP - End 1,000 1, Units Accounted For 6,250 6,250 5,250 5,650 1 See footnote b above. % completion for D/M is an unknown. Costs Total X-Fers In D/M Costs WIP - Beginning 38,060 = 29, ,060 Costs Added During Process 159,600 = 96, , ,400 Costs Added During Period 197,660 = 125, , ,460 Equivalent Unit Costs \$ = \$ \$ \$ 8.40 Completed & Transferred Out 174,300 = 105, , ,100 WIP - End 23,360 2 = 20, ,360 Costs Accounted For \$ 197,660 = 125, , ,460 2 Solved for by difference. Finally, the sum of \$ is the total costs we had to account for. In the Homework we will go beyond the pure computation of the numbers and give us a picture of how critically import tis is to understanding a lot about profitability. There are many very important things we can get out of a schedule like this. We will be amazed! ACCT323, Cost Analysis & Control Lecture 3 Page 12

13 Homework Ch 3 pb 19, 20 Both are break even analysis Given revenues, var & fixed costs as a starting point, that s there budget for the year. Asked to compute the budgeted operating income under each of the following deviations from that budget. Do like things in one exercise, for example, 1 & 2 are asking for 10% inc or dec in CM holding revenues constant. Figure out what the game plan is for that change, why are they asking us to do that change. What are the implications for an operating change that they might make. Also, just do 1 instead of 2 because the answer is plus or minus. Same for 3 & 4, 5 & 6. just doing 1, 3, 5, 7, 8. In addition: 1) compute the present break even point (will have to compute it in sales dollars, no unit info). 2) determine what level of sales is required to achieve a profit of \$5,000,000. 3) what would happen to the bottom line if there is a 10% beneficial change in every variable Similar. Computer the BEP in units and revenue. Compute the impact of a 10% beneficial change for every variable Very similar problem to what we did in class. Retain the class format, book s may be a little different. He gives us the line items (row headings) and he gives us the information (numbers, statement of problem). We have to know where to plug the stuff in. ACCT323, Cost Analysis & Control Lecture 3 Page 13

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