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28 Sensitivity Analysis Cost Analysis Originally, the bags were anticipated to cost Pioneer $1 each to produce, plus a fixed cost of
$100,000. However, increases in petroleum products necessary to produce the bags skyrocketed,
and Pioneer’s variable production cost was actually $3 per unit. Let’s see how Pioneer faired under
their agreement: * Sales
Variable costs ( 1,000,000 X $1 vs. $3)
Contribution margin ( 20% of sales)
Fixed costs
Net income $1 Scenario
$ 1,250,000
1,000,000
$ 250,000
100,000
$ 150,000 $3 scenario
$ 3,750,000
3,000,000
$ 750,000
100,000
$ 650,000 Notice the astounding change in Pioneer’s net income  $150,000 versus $650,000. Such “cost plus”
agreements must be carefully constructed, else the seller has little incentive to do anything but let
costs creep up. Sometimes you will hear a company complain about cost increases negatively
affecting their “margins;” before you assume the worst, take a closer look to see how the bottom
line is being impacted. Even if Pioneer agreed to cut Heap a break and reduce their margin in half,
their bottom line profit would still soar in the illustration. 4.6 Margin Mathematics
In the preceding illustration, the contribution margin was 20% of sales. Accordingly, variable costs
are 80% of sales. If total variable costs are $1,000,000, then sales would be $1,250,000 ($1,000,000
divided by 0.80). Download free ebooks at bookboon.com
29 CVP for Multiple Products Cost Analysis 5. CVP for Multiple Products
How many businesses sell only one product? The reality is that firms usually offer a diverse product
line, and the individual products will have different selling prices, contribution margins, and
contribution margin ratios. Yet, the firm’s total fixed cost picture may be the same, no matter the
mix of products sold. This can cloud the ability to perform simple CVP analysis. To lift this cloud
requires some knowledge of the product mix.
Let’s assume Hummingbird Feeders produces and sells a brightly colored feeding container for $15
(variable cost of production is $10, and contribution margin is $5) and a nectar formula for $3 per
packet ($1 variable cost to produce, resulting in a $2 contribution margin). Hummingbird Feeders
sells 10 packets of nectar for every feeder sold. Its fixed cost is $100,000. How many feeders and
packets must be sold to break even? To answer this question requires a redefinition of the “unit.” If
we assume the “unit” is 1 feeder and 10 packets, we would then see that each “unit” would have a
contribution margin of $25, as shown below.
Contribution Margin * Feeder
Nectar Packets
“Unit” contribution 1 item @ $5 =
10 items @ $2 each = $5.00
20.00
$25.00 To recover $100,000 of fixed cost, at $25 of contribution per “unit,” would require selling 4,000
“units” ($100,000/$25). To be clear, this translates into 4,000 feeders and 40,000 packets of nectar.
Total breakeven sales would be $180,000 (($15 X 4,000 feeders) + ($3 X 40,000 packets)). Of
course, the validity of this analysis depends upon actual sales occurring in the predicted ratio.
Changes in product mix will result in changes in breakeven levels. If Hummingbird Feeders sold
$180,000 in feeders, and no packets of nectar, they would come no where near breakeven (because
the contribution margin ratio on feeders is much lower than on the packets of nectar).
Note that one could also get the $180,000 result by dividing the fixed cost by the weightedaverage
contribution margin ($100,000/0.555 = $180,000). The weightedaverage contribution margin of
0.555 is calculated as follows: * Feeder (1 @ $15)
Nectar Packets (10 @ $3) Product
Sales to
Total Sales
Ratio (mix)
$15/$45
$30/$45 Product
Contribution
Margin Ratio
X
X $5/$15
$2/$3 Weighted
Average
Ratio
=
= 0.1111
0.4444
0.5555 Download free ebooks at bookboon.com
30 CVP for Multiple Products Cost Analysis Businesses must be mindful of the product mix. Automobile manufacturers have a broad range of
products, some at high margin and some at lower levels. If customers unexpectedly substitute
economy cars for sport utility vehicles, basic models for luxury models, etc., the resulting bottom
line impacts can be significant. Product mix can also be important for companies that sell a base
product and a related disposable. For example, a printer manufacturer may sell “unprofitable”
printers along with large quantities of high margin ink cartridges. Managers of such businesses need
to watch not only total sales, but also keep a keen eye on the product mix. 5.1 Multiple Products, Selling Costs, and Margin Management
Selling expenses are oftentimes variable. For example, a salesperson may be paid a designated
percentage of total sales. Such schemes have the potential to be counterproductive in a multiple
product setting. For example, assume that a company sells two products. Product A has a per unit
sales price of $120, and Product B has a per unit sales price of $100.
A salesperson, earning a commission calculated as 5% of total sales, would prefer to sell product A.
However, the company is better off when Product B is sold, because it has a higher contribution
impact ($30 vs. $20). As a result, when a business manager considers its program of compensation
for its sales staff, care should be given to align the interests of the sales force and the company. For
the preceding example, it may make better sense to tie the commission to the contribution effects
rather than the sales price. * S ales
Price
PRODUCT A
PRODUCT B Variable
Production
Cost $120
$100 $100
$70 Download free ebooks at bookboon.com
31 Assumptions of CVP Cost Analysis 6. Assumptions of CVP
This chapter has presented information on how to apply CVP for business analysis. Most of this
analysis is keyed to a model of how profitability is impacted by changes in business volume. Like
most models, there are certain inherent assumptions. Violating the assumptions has the potential to
undermine the conclusions of the model. Some of these assumptions have been touched on
throughout the chapter:
1. Costs can be segregated into fixed and variable portions
2. The linearity of costs is preserved over a relevant range (i.e., variable cost is constant per
unit, and fixed cost is constant in total)
3. Revenues are constant per unit and multipleproduct firms meet the expected product mix
ratios Please click the advert One additional assumption is that inventory levels are fairly constant, with the number of units
produced equaling the number of units sold. If inventory levels fluctuate, some of the variable and
fixed product costs may flow into or out of inventory, with a variety of potential impacts on
profitability. 32...
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 Fall '13
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 Management, Cost Accounting

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