CAMBRIDGE SOFTWARE CORPORATION:
QUANTITATIVE ANALYSIS
Learning Objectives:
 Benefits of product variety
 Factors limiting product variety
 Strategic considerations in product-line pricing
III. Quantitative Analysis:
We will first consider the product-line design and pricing decisions for the case when
CSC can offer only one version. In this case, the product-line design only involves
selecting the “right” version to offer. Note further that targeting/positioning decision
is synonymous with pricing decision in this case because the price selected by CSC
completely determines which of the potential 5 segments will actually buy the version
introduced by CSC. In the second part of this document, we consider the multiversion case.
(a) Single-Version Case:
Decisions Rule: Choose the version which gives the highest contribution margin
Options: (i) “Student” version; (ii) “Commercial” version; (iii) “Industrial” version
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Optimization Procedure (Managerial Logic):
The managerial logic involved in this case can be represented by the following
decision tree:
“Student”
Large
Corp
“Commercial”
Labs
Consultants
“Industrial”
Small
Business
Students
In the decision tree, there are two levels of decisions/optimizations. The first level
involves selection of the model to introduce. The second level decision is the
targeting/positioning/pricing decision. In the figure above, Consultants refers to the
fact that targeting includes Consultants and more high-end segments (i.e. Large
Corporations and labs). Note that with any decision tree analysis, to reach a
conclusion, we have to work backwards. The managerial thought process involves the
following steps:
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Step 1: Suppose CSC introduces “student” version, what is the optimal price?
What are the relevant costs at this stage of decision making?
 segment development cost
 variable cost (per unit)
Why is product completion cost NOT a relevant cost at this stage?
Because, CSC management has already (hypothetically) committed itself to producing
“student” version. As such, it is a “sunk” cost because irrespective of the # of
segments served, CSC has to incur it if this version is introduced at all.
Economic Trade-off: unit contribution-margin vs. volume (# segments served);
choose the unit price which gives the maximum total contribution
Total Contribution = Unit PriceVolume - Segment Dev. Cost(s)
NOTE: Since CSC introduces only one version, individual consumers have only two
options: to buy or not to buy the version given CSC’s price and their willingness-topay (economic value). Can the optimal price of CSC be different from $ 50, $ 100, $
150, $ 175 or $ 200? (These are the willingness-to-pay of the 5 segments for
“student” version.)
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Table 1: Contribution Analysis for Modeler “Student” Version
Price
Segments
Served
Unit
Contribution
Seg. Dev.
Costs
Demand
$ 200
$ 175
Consultants
Consultants
Small Bus.
Consultants
Small Bus.
Large Corp.
Consultants
Small Bus.
Large Corp.
R&D, U Lab.
Consultants
Small Bus.
Large Corp.
R&D, U Lab.
Students
$ 185
$ 160
$ 200,000
$ 400,000
20,000
35,000
Total
Contribution
(‘000s)
$ 3,500
$ 5,200
$ 135
$ 550,000
40,000
$ 4,850
$ 85
$ 650,000
42,000
$ 2,920
$ 35/$ 15***
$ 950,000
542,000
$ 8,020
$ 150
$ 100
$ 50
***
CSC sells to student segment through college book stores which get 40 % commission
so that CSC nets only 60 % of the sale price of $ 50.
 The optimal price for “student” version is $ 50 at which all the 5 segments are served
and the Total Contribution from this version is $ 8,020,000.
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Step 2: Derive the Total Contribution IF CSC instead offered “commercial” or
“industrial” version (Note: CSC management has already figured out its optimal
pricing policies in these contingencies.)
Table 2: Results From Contribution Analysis For
“Commercial” and “Industrial” versions
Version
“Commercial”
“Industrial”
Optimal Price
$ 225
Segments Served
Consultants
Small Bus.
Large Corp.
R&D,U Lab.
Consultants
Large Corp.
R&D,U Lab.
$ 600
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Total Contribution
$ 7,750,000
$ 14, 805,000
Step 3: Choose the versions which gives the maximum Net Total Contribution (net of
estimated product (version) completion cost). Why is product completion cost a
relevant cost at this decision stage?
e.g. CSC should choose “student version” if
Optimal TCstudent - $ 100,000 > Optimal TCcommercial - $ 200,000
and
Optimal TCstudent - $ 100,000 > Optimal TCindustrial - $ 500,000
Table 3:”Optimal” Choice of Versions
Version
Optimal Price
“Student”
$ 50
“Commercial”
$ 225
“Industrial”
$ 600
Segments Served
Consultants
Small Bus.
Large Corp.
R&D,U Lab.
Students
Large Corp.
R&D,U Lab.
Consultants
Small Bus.
Large Corp.
R&D,U Lab.
Consultants
Net Total
Contribution
$ 7,920,000
$ 7,550,000
$ 14, 305,000
 CSC should offer the “Industrial” version in the single-version case. The optimal
“targeting/positing” involves serving the three high-end segments viz. Large
Corp., Labs and Consultants segments. With this product line design and
targeting, the optimal price is $ 600.
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(b) Multi-Version case:
Note that in the single-version case, CSC chooses to introduce the “Industrial”
version and serve only the 3 high-end segments. Even though Students segments (@
500,000) is by far the largest segment, CSC chose to ignore it because the negative
price effect (reduction in unit contribution) outweighed the positive volume effect
(demand expansion).
Is there some other way to include the Students segment?
What about offering 2 versions of Modeler, with Students segments buying one
version and other segments buying the other version?
Now, for 2-version case, there are two options: (1) “Industrial” and “Commercial”
versions; and, (2) ) “Industrial” and “Student” versions. We will consider the second
option i.e. “Industrial” and ‘Student” versions first because of the following
considerations: The logic for including a second version is to include the large
“students” segment. Now, observe that in the single-version case, if CSC were to
introduce “Commercial” version, it would have ignored the “students” segment
because the incremental contribution (net of segment development cost) was negative
at $ 1,730,000.
How should one approach the problem of optimal targeting/pricing, given that
CSC is introducing “Industrial” and “Student” versions?
To ensure that Students segment buys the “Student” version, it must be priced at
$50. What about the price of the “Industrial” version? Recall that in the single-version
case, the optimal price was $ 600 and the target segments were Large Corp., Labs and
Consultants. Would these segments still buy the “Industrial” version at $ 600 given
that they can buy “Student” version as well (i.e. CSC can not restrict these consumers
from buying “Student” version)?1
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Note that in same cases, firms can and do prevent sale e.g. special student and senior citizen discount is
available only to these specific segments by requiring student ID or proof-of-age
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Below are the “consumer surplus” (i.e. willingness-to-pay minus price) for the
two versions of the 3 high-end segments (recall that, in the single-version case, if
CSC were to introduce “Industrial” version, optimal targeting excluded the Small
Business segment):
Table 4: Consumer Surplus with “Industrial” version @ $600 and “Student”
version @ $50
“Student” version
“Industrial” version
Large Corp
$100 (= $150 - $50)
$1900 (=$2500-$600)
Labs
$ 50 (=$100 - $50)
$1400 (=$2000-$600)
Consultants
$ 150 (=$200 - $50)
$ 0 (=$600-$600)
From Table 4, it is clear that while Large Corp and Labs will continue to buy
“Industrial” segment, Consultants segment will “switch” to “Student” version because
they get more surplus with that version.
What price should CSC charge for “Industrial” version, given that “Student”
version is priced @ $ 50?
Clearly, $ 600 is not “optimal” anymore because at this price, Consultants are not
buying the “Industrial” version. Recall that in the single-version case, CSC reduced
the price of “Industrial” version up to $ 600 (willingness-to-pay for “industrial”
version for Consultants segment) because the positive volume effect offset the
negative price effect up to the Consultants segment. Any further reduction was suboptimal. What about a price of $ 450 for ‘Industrial” version? Note that at this price,
the Consultants are indifferent between the two version. This changes the contribution
from the Consultants segment and the conclusion from our earlier Contribution
Analysis (Table 2) that “Industrial” version should target Consultants segment is no
longer valid. Another thing to note at this point is that in the single-version case, if
Consultant did not buy the “Industrial” version, unit sales of 20,000 (segment size)
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was “lost”. In the 2-version case, however, these consumers can now buy the low-end
“Student” version and so sales is not “lost” altogether.
To answer the question of optimal pricing for “Industrial” version, we first
compute the Maximum Price that these 3 segments will pay for “Industrial” version,
given that they have the option of buying “Student” version @ $ 50. We use the
following formula:
Maximum Price for
“Industrial” version
=
Willingness-to-pay (EV)
for “Industrial” version
- Surplus from
“Student” version
Table 5: Maximum Price for “industrial” version consistent
with consumer “self-selection”
Surplus from
“Student” version
Maximum Price for
“Industrial” version
Large Corp
$100
$2400 (=$2500-$100)
Labs
$ 50
$1950 (=$2000-$50)
Consultants
$ 150
$450 (=$600-$150)
With these “effective” willingness-to-pay for “Industrial” version (which is different
from EV), the total contribution analysis for “Industrial” segment yields:
Table 6: Revised Contribution Analysis for Modeler “Industrial” Version
Price
Segments
Served
Unit
Contribution
Seg. Dev.
Costs
Demand
$ 2400
$ 1950
Large Corp.
Large Corp.
R&D, ULab.
Large Corp.
R&D, U Lab.
Consultants
$ 2365
$ 1915
$ 150,000
$ 250,000
5,000
7,000
Total
Contribution
(‘000s)
$ 11,675
$ 13,155
$ 415
$ 450,000
27,000
$ 10,755
$ 450
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 The optimal price of “Industrial” version is $ 1950 and the optimal
targeting/positing for this high-end version is the 2 high-end segments viz. Large
Corp. and Labs.
 Net Contribution from “Industrial” version is $12,655,000.
 The other 3 segments buy “Student” version generating a net contribution (net of
product completion cost) from this version of:
Table 7: Revised Contribution Analysis for Modeler “Student” Version
Demand
Consultants
Unit Contribution
20,000
Small Business
$ 35
15,000
Total Contribution
(Net of Seg. Dev. Cost)
$ 500,000
$ 35
$
325,000
Students
500,000
$ 15
$ 7,200,000
Less:
Product Completion Cost
$ 100,000
Net Total Contribution:
$ 7, 925, 000
By offering two versions, Cambridge software earns a total net contribution of
$20,580,000, an increase of $6,275,000 versus the optimal single product offering.
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