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Unformatted text preview: Case 163: 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 breakeven 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, welleducated 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, breakeven 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 breakeven 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 breakeven 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 breakeven 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
Breakeven 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
Breakeven 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 profitno loss.
Fixed costs of operating...................................................................................................................................
$3,690,000
Aggregate unit variable income, Chart A, line 5 .............................................................................................
$3.56
Breakeven 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
Breakeven 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 crossadding line 4 (unit sales, revenue for "A," "B," and "C"), crossadding 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, crossadd. (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 crossadding line 6 (total variable cost for "A," "B," and "C"), crossadding 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 breakeven 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
Breakeven units required.....................................................................................................................................
1,421,000
Ratio of variable income to sales (situation #1) ...................................................................................................
.4647
Beakeven 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 costrevenue 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 breakeven 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 breakeven volumes would add to the aggregate breakeven
volume. These reasonable speculations, however, are not true. I once proved mathematically that the sum
of the individual breakevens 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 breakeven 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 breakeven 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 breakeven analysis; the other is, what insights into operations are gained in the analysis
that precedes constructing a breakeven chart, even if the chart itself is not used much after it is prepared?
In my opinion, the breakeven chart and the cost analysis required in order to prepare it are more useful
for clarifying costvolume relationships than for identifying the breakeven 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 breakeven 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 breakeven 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 breakeven analysis. Since many such introductions require significant working capital (and perhaps
fixed asset) investments, capital budgeting techniques should be used, not breakeven analysis. However,
as suggested by example 3 above, a breakeven analysis may provide a "quickanddirty" look at whether
it is worthwhile to go ahead and develop a fullblown discounted cash flow analysis.
14 15 ...
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 Spring '08
 WORMER

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