The Portable MBA in Finance and Accounting, 3rd Edition

Cost-Volume -Profit Analysis 115

Solving for x,

We find that you must do about $1.130 million in sales to be as well-off.”
“Hmm. I’m not sure what this means. So how much of what do I have to
sell? That’s what I want to know.”
“ What we do is take the total required sales of $1.130 million and split it
by your revenue mix percentages. Given your expected mix estimates, half of
your revenues will come from sales of books, or $564,315; seven-sixteenths
from packages, or $493,776; and the other one-sixteenth from sales of hats, or
$70,539. Dividing by the selling price of each item, we can also compute the
necessary unit sales levels—7,054 books, 3,527 packages, and 1,411 hats. With
our variable cost estimates, if you meet these targets we will indeed meet the
targeted profit level (see Exhibit 3.10). In summary, we were worried that our
9,100-book target was too optimistic because price cuts were possible. With
this mix we will have to sell 10,581 books—7,054 individually and 3,527 in
packages—but one-third of them will essentially sell for around $70. This
seems more realistic if the packages are marketed correctly.”
“ What does the sensitivity analysis tell us?”
“Since the contribution percentage for the package is about equal to an
individual book, this solution is not very sensitive to variation in mix. If you
do meet your ‘optimistic’ mix projection, your contribution percentage in-
creases by less than 1%—30.1% to 30.5% (see Exhibit 3.11). As a result your

(.%) $ ,

$,

.%

$, ,

30 1 340 000

340 000

30 1

1 128 631

x

x

=

=

= (with no rounding)

EXHIBIT 3.10 Required unit revenues and sales volumes expected mix.

Books Packages Hats Mix

Per Unit Total Per Unit Total Per Unit Total Total

Expected mix 100 50 20
Revenue $80 $ 8,000 $140 $ 7,000 $50 $ 1,000 $ 16,000
Per c ent age of
total 50.00% 43.75% 6.25% 100.00%

CVP target $1,128,631
Mix % allocation $564,315 $493,776 $70,539 $1,128,631
Variable cost 71.3% 402,075 71.4% 352,697 48.0% 33,859
Contr ibution
margin $162,241 $141,079 $36,680 $ 340,000
Divide by unit
price to find
unit sales
needed Books 7,054 Packages 3,527 Hats 1,411