NPD Practices

NEW PRODUCT FORECASTINGPart III: Translating Penetration Estimates into Long Run Salesby Jeffrey Morrison, Director of Modeling Hquifax Corporation (jeffmorrison@equifax.comj

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 jeff.morrison@equifax.com

PDMA VISIONS APRIL 2000 VOL. XXIV NO.2 41