Case16-3BillFrench - Case 16-3: Bill French Note: This case...

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Unformatted text preview: Case 16-3: Bill French Note: This case is unchanged from the Eleventh Edition. Approach This case requires quite a few calculations, but it is a good case for introducing students to the uses and limitations of break-even analysis. It can be used to discuss many of the hidden assumptions involved in such an approach. Some instructors also find it a good vehicle for discussing some of the human problems arising when a young, well-educated person begins working in a business. Finally, at The University of Michigan we have found it useful to defer this case until Chapter 26, when we teach several cases on linear programming: Bill French can be used as an introductory case to raise the issue of what product mix is optimal given resource and/or sales volume constraints. Comments on Questions Question 1 There is undoubtedly a long list of assumptions that can be related to this, or any, break-even analysis. Part of the problem of dealing with analyses of this sort is that they take on the characteristic of being static even though the form of presentation might lead one to believe that here is a moving, dynamic analysis that allows for a variety of changed conditions. To an extent this is true; but there are many conditions that are assumed to be constant. It is to the assumed constants that the students must ultimately direct their attention. For instance: 1. French has had to assume that the variability of the variable costs is constant. French has thus assumed a relatively constant level of efficiency for machines and direct labor over all portions of the range of operations. Whether or not this is a valid assumption in a practical sense is highly questionable. 2. Similarly, there is an assumption that the fixed costs are truly fixed over the full range of operations that has been pictured. In fact, some fixed costs are likely to be step functions over this range. 3. The calculation of a break-even point based on sales assumes that there will be a reasonably constant relationship between the production and the sales pattern. Were this not the case, the spread between the patterns would lead to an incurrence of costs to be carried in inventory, and the full contribution suggested by the chart may not be realized. 4. Along somewhat the same vein, the assumption (and a basic one in either aggregate or product -line analyses) that the sales mix will remain constant is a crucial one. 5. And, obviously, there is considerable reliance in French's analysis that sales prices will remain constant. Considering the objections of the participants at the meeting, it is easy to s ee where French's failure to make explicit his assumptions got him into the position of appearing to be a naive, inexperienced "whiz kid." Question 2 Calculation of various break-even points: 1 Situation #1: Allowing for 10 percent increase in variable costs and $60,000 per month increase in fixed costs, but not holding any dividend or retention requirements against operations, a simple break-even calculation (neither profit nor loss) comes out to be: Fixed costs of operating .................................................................................................................................. $3,690,000 Aggregate variable unit income, Chart 1, line 3 minus line 5 ........................................................................ $3.23 Break-even units required, $3,690,000 / $3.23 ................................................................................................ 1,142,000 units Ratio of variable income to sales, V.I. = $3.23; S. P. = $6.95......................................................................... .4647 Break-even dollar volume required, $3,690,000 / 0.4647 ............................................................................... $7,940,000 Situation #2: No allowance for 10 percent increase in variable costs, no dividend requirement, no earnings retention goal. In short, allow for change in product mix, for increased fixed costs, and change in "C" sales pricethen calculate point of no profit-no loss. Fixed costs of operating................................................................................................................................... $3,690,000 Aggregate unit variable income, Chart A, line 5 ............................................................................................. $3.56 Break-even units required, $3,690,000 / $3.56 ................................................................................................ 1,036,500 units Ratio of variable income to sales, SP. = $6.95, V.I. = $3.56 ........................................................................... .5122 Break-even dollar volume required, $3,690,000 / .5122 ................................................................................. $7,204,000 2 CHART I Aggregate Product ―A‖ Product ―B‖ Product ―C‖ Line Last Yr. Next Yr. Last Yr. Next Yr. Last Yr. Next Yr. Last Yr. Next Yr. Unit Capacity ......................................................................................................................................................................................... 1 2,000,000 2,000,000 Unit Achievement .................................................................................................................................................................................. 500,000 2 1,500,000 1,750,000 600,000 400,000 400,000 400,000 950,000 Unit Sales Price ...................................................................................................................................................................................... $2.40 3 $7.20 $6.95 $10.00 $10.00 $9.00 $9.00 $4.80 Total Sales Revenue............................................................................................................................................................................... 4 $10,800,000 $12,160,000 $6,000,000 $4,000,000 $3,600,000 $3,600,000 $1,200,000 $4,560,000 Variable Unit Cost ................................................................................................................................................................................. $1.50 5 $4.50 $3.72 $7.50 $8.25 $3.75 $4.125 $1.65 Total Variable Cost ................................................................................................................................................................................$750,000 6 $6,750,000 $6,517,500 $4,500,000 $3,300,000 $1,500,000 $1,650,000 $1,567,500 Fixed Costs ................................................................................................................................................................$1,560,000 7 $2,970,000 $3,690,000 $960,000 $960,000 $1,560,000 ............................$450,000 $1,170,000 Income ................................................................................................................................................................................................... 8 $1,080,000 $1,952,500 $540,000 $(260,000) $540,000 $390,000 -0$1,822,500 Income Taxes (50%) ................................................................................................$(130,000) 9 $540,000 $976,250 $270,000 .............................................................................. $270,000 195,000 -0$911,250 Dividends ............................................................................................................................................................................................... 10 $300,000 $450,000 Retained ................................................................................................................................................................................................. 11 $240,000 $526,250 Changes incorporated in modification of Exhibit 3: (1) (2) (3) (4) (5) (6) (7) Volume of Product "A" reduced by one third, Volume of Product "C" increased by 450,000 units, Selling price of Product "C" doubled, Variable cost per unit, by individual product lines, is increased by 10% of old level, Fixed costs increased by $720,000 and charged (arbitrarily) against Product "C", Taxes are charged at 50%, Dividends are budgeted (regular plus special) at $450,000. Comments on derivation of figures in Chart 1: (a) Aggregate unit selling price obtained by cross-adding line 4 (unit sales, revenue for "A," "B," and "C"), cross-adding line 2 (units sold for ―A,‖ ―B,‖ and ―C‖), and dividing the sum for line 4 by the sum for line 2. Line 3 does not, obviously, cross-add. (In class, I also derive the $6.95 amount as the weighted average of the three individual prices, using product mix proportions as the weights.) (b) Variable unit cost in aggregate obtained by cross-adding line 6 (total variable cost for "A," "B," and "C"), cross-adding line 2 (units sold for "A," "B," and "C"), and dividing the sum for line 6 by the sum for line 2. Line 5 does not, obviously, cross -add. (Again, l also derive this as a weighted average.) CHART II Variable unit costs without increase of 10% (union demands): Line Aggregate "A" "B" "C" Variable unit costs................................................................3.39 1 $ ...................................................................................................... $7.50 $3.75 $l.50 Units expected next year ................................................................................................00,000 2 1,750,000 400,000 4 ............................................................ 950,000 Total variable costs expected ..................................................................................................................................................... 3 $5,925,000 $3,000,000 $l,500,000 $1,425,000 Selling price per unit .................................................................................................................................................................. 4 $6.95 $10.00 $9.00 $4.80 Variable unit income (contribution) ........................................................................................................................................... 5 $3.56 $2.50 $5.25 $3.30 Variable total income (contribution) ................................................................................................3,135,000 6 $6,235,000 $l,000,000 $2,100,000 $ .......................................... Derivation: Line l—from Exhibit 3, for individual products Line 2—from Chart I, line 2 (next year) Line l—(aggregate)line 3 (ag.) / 2 (ag.) Line 4—from Chart 1, line 3 (next year) Line 5—line 4 minus line 1 (except aggregate) Line 5—(aggregate) line 6 (ag.) / 2 (ag.) which then equals line 4 (ag.) minus line 1 (ag.) Situation #3: Calculation of a break-even point under changed conditions of cost, both variable and fixed, and volume and selling price that will, after tax, provide exactly what has been provided with no extras. Coverage required: Fixed costs ................................................................................................................ $3,690,000 Regular dividends ..................................................................................................... 600,000 (pretax) Earnings retention..................................................................................................... 300,000 (pretax) Required ............................................................................................................................................................... $4,590,000 Aggregate unit variable income (situation #1) ..................................................................................................... $3.23 Break-even units required..................................................................................................................................... 1,421,000 Ratio of variable income to sales (situation #1) ................................................................................................... .4647 Beak-even dollar volume required ....................................................................................................................... $9,877,000 In a manner similar to the procedure used in the first three situations here, the student can make break even approximations under a variety of assumed conditions and for the several products either individually or in the aggregate. Chart III is a capsule summary of some possible calculations. 11 CHART III Fixed Costs or Demand a b c d e f g S.P. B.E. B.E. - V.C.= Units $ Volume V.I. Required V.I. / S.P. Required Situation #1.......................................................................................................................................................................... $3,690,000 $3.23 1,142,000 .4647 $7,940,000 Situation #2.......................................................................................................................................................................... $3,690,000 $3.56 1,036,500 .5122 $7,204,000 Situation #3.......................................................................................................................................................................... $4,590,000 $3.23 1,421,000 .4647 $9,877,000 No extra dividend; no union increase; increased fixed costs; retain (A.T.) $150,000 ......................................................................................................................................................... $4,590,000 $3.56 1,289,000 .5122 $8,961,000 Pay extra dividend; no union in increase; increased fixed costs; retain (A.T.) $150,000 ......................................................................................................................................................... $4,890,000 $3.56 1,374,000 .5122 $9,547,000 Allow union increase; pay no extra dividend; increased fixed costs; retain (A.T.) $150,000 ............................................................................................................................................... $4,590,000 $3.23 1,421,000 .4647 $9,877,000 Pay extra dividend and union increase; increase fixed costs; retain (A.T.) $150,000 ......................................................................................................................................................... $4,890,000 $3.23 1,514,000 .4647 $10,523,000 Question 3 Two points (in addition to factors already mentioned) should be recognized by the student considering a shift of capacity from product "A" to "C": 1. While the ratio of variable income to sales price is much higher for "C" than for "A" (66% against 18%), this is in part compensated for by the lower sales price of "C." 2. While the per unit dollar contribution for "C" is higher than for "A" ($3.15 against $1.75), the number of units that can be sold is a critical factor. Since the "A" contribution is 56 percent of the "C" contribution, this would mean that the company can afford to gain in "C" units only 56 percent of the number of "A" units that it gives up. Similarly, in viewing the amount of capacity that can be added for "C," we must consider (in addition to the compelling factors that do not come directly under the cost-revenue measurement) the amount of variable income available to pay for the added capacity and to return a reasonable profit at the same time. Here the analysis wanders into the area of return on investment, but the student may wish to sketch out some figures. On the basis of a per unit contribution of $3.15 from "C," an addition that would yield 100,000 additional units of "C" annually must not cost more than about $300,000 by the time amortization and profit (at a proper rate of return) are considered. Question 4 Based on the numbers of Exhibit 3, the individual product break-even volumes are as follows: Pdt. "A" $960,000 $10.00 - $7.50 = 384,000 units or $3,840,000 Pdt. "B" $1,560,000 $9.00 - $3.75 = 297,143 units or $2,674,000 Pdt. "C" $450,000 $2.40 - $1.50 = 500,000 units or $1,200,000 1,181,143units or $7,714,000 Versus 1,100,000 units or $7,920,000 on an aggregate basis. 12 Students find this "discrepancy" puzzling. Usually a number of students make the intuitively reasonable speculation that the discrepancy is caused by fixed costs not being assigned "correctly" to the three products; they surmise that if total fixed costs were allocated to products based on, say, unit marginal income or total revenues, the individual break-even volumes would add to the aggregate break-even volume. These reasonable speculations, however, are not true. I once proved mathematically that the sum of the individual break-evens will equal the aggregate if and only if all products have equal marginal incomes per unit (i.e., equal unit contributions). But that obviously is not an interesting case, because product mix is irrelevant in such a case. Although we have not yet covered joint cost allocations, I suggest to students that reasonable cost accountants could differ on the "correct" assignment of fixed costs in Exhibit 3 to individual produce, thus casting doubt on the usefulness of break -even volumes for individual products if significant joint fixed costs are involved. I now suggest the conceptually correct way to consider the multiproduct situation. For purposes of graphical illustration, assume a company has only two products, with these characteristics: Product1 Product2 Unit pace (pi) ................................................................................................................................................................. $ 5 $ 7 Unit variable cost (vi) .................................................................................................................................................... $ 2 $ 3 Unit contribution (ci) ..................................................................................................................................................... $ 3 $ 4 Direct fixed costs(Fi)) ................................................................................................$25,000 $15,000 ................................................... Joint fixed costs(Fi) ....................................................................................................................................................... $20,900 Sales volume(xi) ............................................................................................................................................................ Xl X2 EXHIBIT A 13 Then the formula for gross income (I) is: I= – F1 + (P1 V1 )X1 (p2 v2 ) x 2 F2 - Fj Pdt. 1 Contrib. Pdt. 2 Contrib. Pdt. 1 ―Direct‖ Margin Pdt. 2 ―Direct‖ margin Or, for the illustrative numbers, I = 3x1 + 4x2 – 60,000 (x1,x2 > 0) This makes it clear that instead of a break-even volume, there are virtually infinite x1, x2 combinations (i.e., product mixes) that will make I = 0 (or make I = any amount). Graphically, we have a series of ―isoprofit‖ lines, one line for each value of I, the slope of which is a function of the relative per -unit contributions. The isoprofit line for I = 0 shows all break-even product mixes. (See Exhibit A, above.) The instructor can push to this point, whether or not linear programming is to be taught. If teaching LP, the example can now be extended by adding a couple of resource constraint lines to the diagram, and asking students to think about profit maximization in that context before the Trammel Snowmobile case. Question 5 There are really two aspects of the "usefulness" question. One is, what kinds of decisions will be influenced by a break-even analysis; the other is, what insights into operations are gained in the analysis that precedes constructing a break-even chart, even if the chart itself is not used much after it is prepared? In my opinion, the break-even chart and the cost analysis required in order to prepare it are more useful for clarifying cost-volume relationships than for identifying the break-even volume per se. Nevertheless, there are certain decisions for which this type of analysis can be explicitly used; for example: 1. Given a certain complement of professional staff, how many hours of professional time at standard billing rates must a CPA firm (or any other professional services firm) bill in order to break even (i.e., recover professional salaries, support salaries, and other overhead costs)? 2. How many additional units of sales (or sales dollars) must a 30 -second ad on the Super Bowl telecast generate in order for the ad ―to pay for itself‖? 3. Given projected costs of a new commercial aircraft and an estimate of the price per plane that airlines will be willing to pay, what is the break-even volume? Is it likely that the aircraft manufacturer can in fact sell more than that number of planes? 4. If the price of a product is reduced 10 percent, how many more units must be sold to earn the same profit as at the current price? It is also important that break-even analysis not be oversold. For example, I feel that students sometimes get the impression from their marketing course that a new product introduction decision would be based on a break-even analysis. Since many such introductions require significant working capital (and perhaps fixed asset) investments, capital budgeting techniques should be used, not break-even analysis. However, as suggested by example 3 above, a break-even analysis may provide a "quick-and-dirty" look at whether it is worthwhile to go ahead and develop a full-blown discounted cash flow analysis. 14 15 ...
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