July 13, 2004
Editor's Note: This column by Scott Ellis and Steve Kakouros
of Hewlett-Packard Co. is the latest in a series of contributed editorial
columns. Readers interested in authoring future contributed columns
can click here to see the Guidelines for Editorial Submissions page.

Setting Warranty Policy for Products That Generate Annuity Streams:

Most warranty-management analysis concerns warranty as cost, the effect of warranty on customer satisfaction, or the signaling impact of warranty on customers. This article describes a study where the focus was not on the product under warranty, but rather on the effect that warranty length might have on the sales of related peripherals and supplies.

by Scott Ellis and Steve Kakouros

The problem we describe originated as part of a widespread cost-cutting trend within the high-tech consumer electronics industry. In the past 5 to 10 years, stiff competition and constantly leapfrogging technological developments have forced manufacturers to review line-item costs as never before in order to remain both competitive and profitable. At the start of our project, Hewlett-Packard's printer manufacturing group was under pressure to reduce warranty costs. One way to cut those costs is by reducing the length of the warranty period.

These sales generate annuity streams for the manufacturer as long as the product remains in operation. However, cost savings from a shorter warranty period must be weighed against potential lost profit from reduced annuity streams. A shorter warranty policy might cause products to drop out of active use sooner, and the cost savings from a shorter warranty policy therefore might be outweighed by the lost annuity profits.

Determining the right length to offer is a matter of balance between what customers want and what the manufacturer can afford. At the time, HP's standard warranty length for all printers was one year. The question was: what would happen if HP shortened the warranty to three months?

Warranty costs included call-center costs for services such as technical support, as well as hardware repairs or replacements. By reducing the potential number of support calls and repairs, HP's hardware group estimated that they could achieve substantial savings simply by reducing the warranty period. It seemed like a reasonable cost-cutting move.

The hardware group was happy -- but the printer supplies organization was not. At HP, the printer and supplies markets were large enough that separate organizational and financial structures had emerged to support them. It was the hardware organization that bore the warranty costs, but it was the supplies group that stood to lose revenue if the shortened warranty policy caused more printers to drop from the installed base.

The supplies group argued that reducing the warranty period would lead to customer dissatisfaction and have a negative impact on the market for printer supplies. For a printer with an average operational life of 1-3 years or sometimes even more, anything that stood to reduce that span could potentially reduce the supplies annuity stream by a corresponding number of months.

Who was right? No one really knew. It was an extremely emotional issue. Eventually the supplies organization turned to the Strategic Planning and Modeling (SPaM) team. SPaM is a small team of operations research specialists within HP. Its mission: to provide support to HP businesses seeking to improve their efficiency, cost-effectiveness, and profitability by making better, more data-driven decisions.

Project Inception

The first step in the project was to involve people from both the supplies and the printer (hardware) organizations, so that both sides would eventually agree on the outcomes. The second step was to clearly frame the problem and design an objective, analytical model to serve as the focal point for answering trade-off questions. Finally, we also created a software tool to visually demonstrate these trade-offs to people outside the immediate project team. These steps were essential to achieve the wide-scale acceptance needed to help successfully implement our new decision-making process.

The biggest challenge was isolating the potential revenue impacts of warranty changes from revenue impacts that were due to other factors. Customers decide to buy new printers for many reasons that have nothing to do with warranty. To identify warranty-driven revenue impacts, we needed first to establish a credible relationship between the warranty length and sales of printer supplies. Our work took place in several phases:

  1. Framing the trade-off.
  2. Bounding the problem to establish maximum risk.
  3. Modeling trade-offs for different warranty cost levels and products.

Step 1: Framing the Trade-Off

At first the problem was a heated debate about "warranty length versus lost customers." The supplies group claimed that HP stood to lose a large portion of its customers from shorter warranties, while the hardware group argued that warranty wasn't even that important at purchasing time. Before we could perform any quantitative analysis, we had to identify what we were really comparing and define the elements that drove each side of this equation.

On the one side, we had warranty cost savings. Where did these cost savings really come from, how do we calculate them, and how large are they? Warranty costs were measured as a cost-per-call based on the number of calls received per product, divided into the total cost of running the call centers. The other key driver was the cost of product repairs.

On the other side, we had lost profit. What were we really worried about losing? Was it lost customers, lost units, or lost supplies sales? Associating "lost customers" with "lost profit" was difficult because customers experiencing technical difficulties could do any number of things if they could not get free support under warranty; not all questions or problems would result in a unit dropping out if the question went unanswered. Furthermore, a unit could drop out for any number of reasons, only one of which might be the inability to obtain free support.

Characterizing customer behavior at the time of purchase was also important. How might the warranty change affect a potential new customer who was choosing among several similar products? Would a customer who would otherwise have chosen the HP product still buy that same product with a shorter warranty? The news here was encouraging: according to HP's market research, printer warranty is not among the top ten factors influencing printer purchasing decisions; it only becomes important if a customer experiences a problem. This is particularly true for low-end products.

Step 2: Bounding the Problem

There was one piece of information that we needed but didn't have: the dropout probability. This was the likelihood that a printer would drop out of the installed base, if a potential warranty event occurred and the problem was not resolved immediately, for free. We had the dropout rate for the total installed base, and we had the change in the warranty installed base. What we needed to establish was the relationship between this warranty base reduction and a corresponding change in the total decay rate.

What we essentially did was to narrow the scope of this unknown to an acceptable level for a rough-cut analysis that would let us know when a warranty change was clearly a bad idea. Thus we asked: what is the maximum number of units we could lose? Bounding the problem shows how we scoped the number down using our available data.

Figure 1: Bounding the problem

Although we are using purely illustrative data, two main points must be emphasized: Most units never experience a support call at any point during their life, and of these calls, only some of the units are at risk for early dropout.

To illustrate, let's use some sample numbers. Let's say that for Product Line X in the North American Region, 100,000 units are shipped during the first year of the product's life. Of these units, 10% experience a warranty event within the one-year warranty period. At this point, we know that the maximum number of units at risk to drop out of the installed base is 10,000. Of this original group of 10,000 customers who called the support center, we can then eliminate several categories.

First, we can eliminate anyone who has had the printer less than three months. These customers would be covered under either a 12-month or a 3-month warranty policy, and thus the revenue from these units is not at risk from a policy change. For illustration purposes, let's say that this represents 20% of the calls received, or 2,000 units. Another fraction of the calls are customers who are willing to pay for technical support on a per-call or subscription basis. These customers are also not affected by warranty policy change, since they will not drop out under either policy. Let's say that paid support calls make up 10% of the calls received for Product Line X, thus eliminating another 1,000 units.

A further percentage of calls are the "free anyway" calls -- customers who aren't really entitled to free warranty support, but for one reason or another, receive it anyway. In our example, this represents 10% of the calls, or another 1,000 units.

This eliminates 40% of the original 10,000 calls received, or 4,000 units. Our problem thus concerns the remaining 6,000 units, which are those units experiencing a warranty event between 3 and 12 months of service. This represents the portion of the printer installed base that are potentially at risk for earlier drop-out under a shorter warranty policy. Out of total lifetime shipments, this is around 6%, shown as the "max" in Figure 2. This step is important because it bounds the problem. If a member of one of the organizations felt that 20% of the customers could be affected by a change in warranty policy, we could clearly show that this could not be the case.

Figure 2: Lost profit vs. warranty savings, per unit

Step 3: Modeling The Trade-Offs

Next, we need the total lost profit for the maximum dropout rate. We need to consider the average age of that first warranty event, in order to get the average number of months lost. This would be applied to the at-risk units, starting with the maximum dropout probability (every unit experiencing a warranty event between 3-12 months drops out). The average number of months lost can then be used to calculate the average supplies revenue lost, and that can be rolled up to a total lost profit as shown in Figure 3.

We can't quite predict what percentage of at-risk customers would drop out, if a warranty event occurred between three and 12 months and they couldn't get free support. However, we can draw a "line in the sand" from the maximum lost profit to the zero line and see where it crosses the warranty cost savings line. This allows us to model what-if questions using different warranty cost savings amounts, for products with different annuity profit margins.

Figure 3: Comparing products by profitability

Depending on where on the X axis a product falls (i.e., how many units drop out of the installed base), the average lost profit per unit over the lifecycle will vary compared with the expected warranty cost savings.

As this figure shows, for a high-profit product, the lost annuity stream profit from a small number of units could wipe out the warranty cost savings fairly quickly. For a low-profit product, on the other hand, the lost profit might never even cross the warranty savings line; thus, reducing warranty costs for that product might make sense. For the "middle-of-the-road" products, more research would be needed, since the profit/loss likelihood isn't clearly in favor of one course or the other.


The results of this analysis showed that the benefit from the proposed warranty length reduction for the product in question was very sensitive to even the least disturbance of the printer supplies revenue. This result was at odds with many people's intuitive reasoning. In order to communicate our results more effectively, we created a scaled-down version of our initial model in a spreadsheet. Everyone could play with this model and understand the logic behind it without having to gather extensive data or conduct multiple calculations. It was this tool that allowed both the hardware and supplies organizations to agree on how to approach warranty policy changes.

In this case, retaining the longer warranty policy was clearly the better solution, and this decision was accepted by both hardware and supplies groups.

Modeling the Installed Base

This sidebar presents the thinking and the methodology behind our installed base modeling. We developed a method to generate a picture of the current installed printer base, validate our baseline against marketing data on the installed base that actually existed in the field, and then explore ways of modifying that installed base based on inputs that included warranty length.

Our baseline case was the actual printer installed base with the standard, 12-month warranty. This meant projecting the total printer installed base from existing sales data, as shown in Figure 4. This number could then be compared against market research data regarding the printer installed base to validate our other installed-base projections.

Figure 4: Printer installed base, baseline

We also had to consider only the printer base that would be affected by the change in warranty policy. The average printer life span was known from market research data. Of that life span, the first three months were covered in either case, and anything over a year old would not be covered regardless of which warranty policy was in effect. So, the only portion of the installed base we were concerned with were units that were between 3 and 12 months old (Figure 5).

Figure 5: Printers at risk

Economic Impact

Next, we had to ask how much these "at-risk" printers, those between 3-12 months, were worth in terms of total annuities. The total installed base represented the annuity pool. By taking the supplies revenue, which was known, and applying it to the total installed base, we could calculate the average monthly revenue that each operational unit could be expected to generate. The decay rate was the rate at which printers would drop out of the total installed base. It was really the impact of the warranty change on this decay slope that we were investigating.

The warranty installed base was that portion of the total installed base that was under warranty at any given time. What happens to the total installed base if, as is shown in Figure 6, that warranty base shrinks?

Figure 6: Printer installed base change

In order to establish the change that was driven by warranty, we needed to identify how much of the decay was driven by factors other than warranty.

What information did we have?

  • Past printer shipments. For this study, we focused on one product line and one region.
  • Average printer life. This was derived from supplies forecasts and extensive market research, and represented the length of time that a printer would be generating ink revenue.
  • Monthly dropout rate. This is the percentage of total life cycle shipments that is expected to drop out of the installed base each month.
  • Average supplies revenue per unit, per month.
  • Warranty event likelihood (per unit). A warranty event is a customer service call that represents a situation where the printer may stop generating ink revenue.
  • Average printer age at first event. This is the average number of months after purchase at which first warranty event occurs (if it occurs).

Modeling Methodology

This section contains technical notes on our modeling methodology. In this case, we want to obtain a curve representing the installed base (IB) as a function of warranty length (WL), and to be able to assign different weights to the impact of the warranty length. In order to model the deltas between IB for different warranty length, we must generate the curves with key inflection points representing "turning points" in the model.

Based on shipment data, we can generate the cumulative installed base as shown in Figure 7.

Figure 7: Cumulative installed base

To obtain the actual installed base, we apply a decay rate (DR) obtained from marketing data on the average printer life. This decay rate is driven by many factors, only one of which is warranty length. Our problem is to determine how much weight to give to warranty length as an influencer of the decay rate. We do this by designing an equation that will:

  • Generate a valid installed base when compared with marketing data
  • Allow us to change the weighting of the warranty period as well as its actual duration

A sample equation is shown in Figure 8. The x and y in the figure are for illustrative purposes, and represent factors such as customers who might discard a unit in order to upgrade to a newer model.

Figure 8: Applying decay rate

We model the "turning points" which are:

  • When the ramp-down begins, i.e., when the actual installed base departs from the cumulative installed base and begins to decline.
  • The point where warranty length is no longer relevant. For example, in the baseline case, this point would occur one year after the product is no longer being sold.

In Figure 9, these turning points are shown as A and B, respectively.

Figure 9: Turning points

This allows us to use three separate event modeling equations to generate one curve. Each event model simulates units dropping out of the installed base. In the first event model, warranty is not a factor because for the first 3 months of the product's life, all printers will be under warranty. In the third event model, no one is under warranty, so warranty is also not a factor. It is in the second event model that we measure deltas related to the warranty change.

Each turning point, measured from the beginning of shipments, signals the change from one event model to the next one. Assuming that the change in warranty policy affects the point in time at which each turning point occurs, and assuming that we know the weight to assign to the warranty length as opposed to other factors, we can generate a prediction of the new installed base under different warranty policies (Figure 10).

Figure 10: Turning point shift with warranty lengthy

About the Authors

Scott Ellis is the Director of HP's Strategic Planning and Modeling group (SPaM). SPaM helps the HP businesses make better data-driven decisions in the areas of supply chain, forecasting and planning, warranty, and related areas. During his years at SPaM, Scott has worked with many HP businesses on a wide range of complex business problems. He has also served as the supply chain architect for HP's low-end server business. Before HP, Scott worked for three years as a consultant at McKinsey & Company. He has a bachelor's degree in government and economics from Harvard University and an MBA from Stanford.
Steve Kakouros is a Process Technology Manager at HP's Strategic Planning and Modeling group (SPaM), where he works with different HP divisions to improve their business processes through rigorous analysis and state-of-the-art technologies. He has extensive experience in supply chain management at HP, with his most recent research being focused on forecasting and planning, as well as product warranty and reliability. His article entitled "Part Tool, Part Process" on inventory optimization at HP, was published in Operations Research/Management Science Today. Prior to working with SPaM, he had consulted with Oracle and SPOAR investments. Steve has a M.S. in Operations Research from Stanford University and a Diploma in Applied Mathematics from Aristotle University, Thessaloniki, Greece.

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