NPD Practices
NEW PRODUCT FORECASTINGPart III: Translating Penetration Estimates into Long Run Salesby Jeffrey Morrison, Director of Modeling Hquifax Corporation ([email protected]
Table 1: AnTlual Sales ofa Similar Product (Actllals)
A B C 0AetuaJ Square of
Non Actual Cumulative CumulativeCumulative Cumulative Sales Sales
Sales Sales ILag 1 YearI ILag 1 Yearl
Year) 150 150 0 0Year 2 400 550 150 22,500
Year 3 1,225 1,775 550 302,500
Year 4 1,675 3,450 1,775 3,150,625
Year 5 1,700 5,150 3,450 11,902,500
Year 6 1,710 6,860 5,150 26,522,500
Year 7 1,650 8,510 6,860 47,059,600
Year 8 800 9,310 8,510 72,420,100
Year 9 50 9,360 9,310 86,67(l,100
Year 10 1 9,361 9,360 87,609,600
Forecastcrs have always struggled
with how best to develop realisticprojections in an environment
where historical data and adequate
market research may be scarce. Although
new product forecasters are faced with
even more challenges in this area, some
statistical modeling techniques used toanalyze mature products can be applied
to new products to provide valuable insight
into long run market acceptance. This is
the last article in a three part series dis
cussing quantitative forecasting tech
niques for new product forecasting.
In the last article (Visions, October 1999;page 1:{), we looked at Jim who had recently
been promoted to Product Manager in a na
tional sports eqUipment company, ABC Ath
letics. The research group had just completed
the development of a new golf ball that travels 2()<)'{) further than anything on the mar
ket. The financial people needed a ten-year
forecast for demand and revenue. One of
Jim's main tasks in his new job was to de
velop a sales forecast that he could sell as
"believable" to the very conservative vice
president of Finance. By using some reIa
tivelystraightforward regression techniques
and information from a survey, ,Jim was able
to develop a variety of "what-if' scenarios
related to the anticipated long run market
penetration for the new product. Now Jim's
task is to translate those long run penetra
tion estimates into unit sales over time.
INTRODUCTION TO DIFFUSIONANALYSIS
Substantial literature exists on the dynamics of new product innovations. These dy
namics often refer to the rate of new prod
uct acceptance into the market as it.'> diffusion. Although no single diffusion framework
provides all the answers, Rogers (1962) was
one of the earlier pioneers describing new
product diffusion as a five stage process:
• Awareness
• Interest• Evaluation
• Trial• Adoption
In general, Rogers saw diffusion as theprocess by which an innovation "is com-
municated through certain channels over
time among the members of a social sys
tem." Another pioneer in this field, Frank
Bass (19(l9). describes the diffusion pro
cess as a result of two independent driv
ers: mass media and word of mouth. The
mass media influence covers those consumers interested in the "latest and greatest"aspect.'l of product.,> and services. This mar
ket segment's purchase decision is theo
rized to be externally derived - specifically
from media advertisements that generate
awareness. On the other hand, the word of
mouth influence is theorized to be much
greater - reflecting the internal communi-
cation dynamics among consumers. When
placed in a mathematical framework, the
Bass theory provides one of several fore
casting solutions for new product diffusion.
THE BASS MODELIn the last article, Jim was able to de
rive a market penetration rate of 43% from
the survey data, given the average price
of the product and demographics of the
target market. Well, today is ,Jim's lucky
day. He just uncovered historical sales data
on an older product which he thinks might
mimic the life cycle of his new product.
Jim decides to use the Bass model to esti
mate the two components of new product
diffusion: the coefficient of innovation and
the coefficient of imitation. In the Iitera-
ture, these coefficients are simply referredto as p (mass media) & q (word of mouth).
If he had not been able to find data on a
similar product, Jim would have had to usc
some industry values for p & q referred to
in the Bass literature.
Table 1 shows the older product's historical unit sales for the last 10 years.
Notice from columns A &B that it is a fully
mature product - completing all phases of
the product life cycle: Introduction,
Growth, Maturity, and Decline. Specifically,
the saturation level occurs at year 6 with
annual sales of 1,710 units. By year 10,
new sales were about zero and the prod-
uct line was soon discontinued.Now that we have some historical data
from a similar product, we are ready to
estimate p & qwithin the Bass frameworkusing linear regression. The dependent
variable is specified as Column A in '1able
1 - actual Non-Cumulative Unit Sales. The
explanatory variables are simply trans
forms of the history - lagged one period.
The first of these variables is shown in
Column C - Cumulative Unit Sales (Lagged
1 year). The second variable (Column D)
is the square of the first variable. That's
it! All Jim has to do now is simply run the
regression.
Now we use the regression coefficient.'l
(lable 2) to calculate p & q and compute the
Bass predictions for the similar product:
PDMA VISIONS APRIL 2000 VOL. XXIV NO.2 29
-
Bass Forecast Equation of Non-Cumulative Unit Sales t =p * (lifetime sales - cumulative sales (L-l) ) + q *
( cumulative sales (L.I/ lifetime sales) *( lifetime sales- cumulative sales (t-II )
Non-Cumulative Unit Sales= 442.41 + .691 *X1 -.0000782 *X2
R Square 0.901305673Number of Observations 10
Coefficients
Intercept 442.4115Xl Variable (Column C -Thble1) 0.691179X2 Variable (Column 0 -Thble1) -.0000782
Table 2: Regmssion RcsuUs:
Step 1: Identify lifetime unit sales ('rable 1 col. B)Step 2: Calculate p = Intercept / lifetime unit sales
Step 3: Calculate q = p + coefficient of Xl
= 9,361= 0.047261
= 0.738441
FORECASTING NEW PRODUCT SALES WITH THEBASS MODEL:
Now ,Jim is ready to forecast unit sales for his new product. With the coefficient of innovation (0.047261) and thecoefficient of imitation (0.188441) from the similar product, he simply has to make a guess at the total lifetimesales for his new product. If the potential industry sales
over the next 10 years is 10,000,000 golf balls and the survey indicates the new product will attain about a 43% penetration, the lifetime expected sales would be 4,300,000.The forecast equation is the same as before, but with differ
ent a value for lifetime sales:For example, for the first period forecast, non-cumula
tive unit sales are:
Bass Forecast Equation for
Non-Cumulative Unit Sales I = I =0.047261 *(4,300,000-0) + 0.738441 *
(0/4,300,000) * (4,300,000-0) = 203,222
Table 4: New Pmduct Forccast (Non-Cumulative Unit Sales)
As shown in 'Iable 3, the Year 1 Non-Cumulative Sales equal the intercept(442). The second period fitted value, then, would be calculated as follows:
Non-Cumulative Unit Sales t = 2 =0.047261 *(9,361-442) + 0.738441 * (442/9,361) * (9,361-442)
= 733
Year 1 Year 2 Year 3 Year 4 Year 5203,222 336,593 526,290 744,907 891,722
Year 6 Year 7 Year 8 Year 9 Year 10816,846 508,584 200,892 54,876 12,580
NonCumulative Unit Sales
Figure 1: Fitted Ir.'i. Actual Unit Sales
ADDITIONAL FORECASTING SOLUTIONS:Although the Bass Model has shown some very encour
aging results in the past, it is dependent on a number ofassumptions such as:• Market potential of the new product remains consistent
over time.
• Diffusion of an innovation is independent of all other in-novations and is binary.
• Nature of innovation does not change over time.
• There are no supply restrictions.• Product and market characteristics do not influence dif
fusion patterns.9 108
•
•...... - Predicted I
• Aetuals r-
p-
2
•
2,500
2,000
1,500
1,000
500
0 •
How well did the model do in fitting the historical sales for the similar
product? As seen in Table 3 and Figure 1, fitted sales are indeed close.
3 4 567Years Since ProdUCtL"1l1TIch,___________ _ ..J
Table 3: Annual Golf Ball Sales a Similar Pmduct (Fitted)
A B C DActual Fitted
Non Non Actual FittedCumulative Cumulative Cumulative Cumulative
Sales Sales Sales Sales
Year 1 150 442 150 442Year 2 400 733 550 1,175Year 3 1,225 1,146 1,775 2,321Year 4 1,675 1,622 3,450 3,943Year 5 1,700 1,941 5,150 5,884Year 6 1,710 1,778 6,860 7,662Year 7 1,650 1,107 8,510 8,769Year 8 800 437 9,310 9,207Year 9 50 119 9,360 9,326Year 10 1 27 9,361 9,353
And although easy to compute, the model's simplicity is a
2-edged sword. For example ...
• How do we make adjustments to the forecast if our marketing plan is significantly different than others in thepast?
• How do we account for known pent-up demand (pre-seiling) in the forecast?
• How can we input assumptions as to the symmetry of theproduct life cycle?
• Can we revise the forecast based upon latest market conditions and purchases?
• What about competition?
Fortunately, additional techniques are available that fo
cus on the S-shaped pattern of the pl'oduct life cycle. Someare based on various formulations of the Logistic and
Continued on page 41
30 PDMA VISIONS APRIL 2000 VOL. XXIV NO.2
PDMA CONFERENCE REVIEWContinucd from pagc J4
Anyone interested in more information about this issue may find the follow
ing resourees interesting:
• Von Hippel, Eric Sources of Innovation, Oxford University Press, 1994
• Lead User Concepts web site at http://www/leaduser.com
• "Creating Breakthroughs at 3M", by EI'ic von Hippel, Stefan Thomke and Mary
Sonnack, Harvard Business Review, September-October 1999. pp. 47-57
the workshop is that a business needs to
look at mUltiple analyses of a portfolio
prior to making critical project
prioritization decisions. Looking at only
one analysis can yield misleading results.
The second workshop, conducted by
Rich Moore, President and CEO of Inte
grated Development Enterprise, Inc. (IDe),
MANAGED INNOVATION?Continued from pagc 26
rative and regulated process, such as the
Lead User System, has been adopted at 3M
quite smoothly. 3M's on-going measurement
and value assessment process finds that
even the most productive "traditional
method" inventors (those prestigious aM
scientists whose reputations were built by
using the traditional, "inventor in the lab"
method of innovation) credit the Lead User
System with enriching their own pursuit of
innovation. These scientists, and other mem
bers of the 3M Lead User teams, have de
veloped a more grounded appreciation of the
fact that novel concepts are often found, and
will continue to be found, in the interactions
that take them out of the lab, out of the com-
a software solution provider, was entitled
"Hands-On IT-Enabled Portfolio Manage
ment." It discussed how new web-enabled
product-development applications are finally giving management the right tools to
manage and accelerate the portfolio on an
enterprise-wide basis. This workshop
clarified and defined the role of IT in port-
pany and even out of their industries.
From "shadowing" a third world user to
understand where their process strengths
and weaknesses exist, to working with pro
fessional theatrical mask makers to better
understand human skin properties, the
folio management and gave participants a
vision of how portfolios will be managed
in the new millennium.
The learnings participants took back to
their organizations from the conference
can be applied immediately making thisan extremely valuable event for all PDMA
members.
Lead User System provides a proven discipline for profitably leveraging resourees
inside and outside of 3M for models, exper
tise and future competitive advantages.
©2000 ASI Associates
NEW PRODUCT FORECASTINGContinued from page 80
Gompertz curves - diffusion frameworksallowing a more detailed extraction of key
components of the process. For example,
it would be advantageous to input assumptions about the product's half-life, life cycle
symmetry, pent-up demand, and the most
recent unit sales in forecasting futurc de
mand. Since these key components are
specified in the model structure, the ana-
Iyst would have the flexibility to change their
assumptions to better integrate marketing
plans into the forecast. The mathematics
of these routines can be programmed in
SAS, Fortran, C++, or Visual Basic. How
ever, some packages like LifeCast Pro are
designed with excellent GlJI interfaces for
use by product managers, financial ana
lysts, and business forecasters.
References:(1). NEW PRODUCT DIFFUSION MODb'LSINMARKEJ'ING: A REVJb'WAND DIRRCTJONFOR RESEARCH. by Vijay Mahajan, EitanMuller, and Frank M. Bass. Journal ofMarketing. Vol. 54 (January 1990), pp 1-26.(2). NEWPRODUCTDEVELOPMENT: MANAGING AND FORECASl1NG FOR STRATEGIC SUCCESS. By Robert J. Thomas, JohnWiley & Sons (1998). pp 189-195.
If you would like an Excel spreadsheet of the Bass Model, please
contact Jeff Morrison at [email protected]
PDMA VISIONS APRIL 2000 VOL. XXIV NO.2 41