Issue No. #2 21 November 2000 ISSN: 1532-1886

Making a Bundle with Bundling (Part 1) by Carl Wright

Bundling is selling a quantity of a single product or a group of one or more products to customers. Typically, the cost of the bundle is lower than the item by item cost of the bundle parts. The practice has a long history in retail sales. For example, the “baker’s dozen” gives thirteen donuts for the price of twelve. This is “quantity bundling”.

It resembles volume discounting because you pay a lower average price when you buy in quantity, but volume discounting doesn't guarantee a level of revenue to the service provider. Volume discounting rewards me with reduced costs when I consume a certain amount or combination of services. Bundling rewards the service provider when I don't use all the services I purchase.

The source of the added revenues for service providers is the situation where customers agree to purchase a bundle of services but then don't consume them. I'm sure that I'm doing that with my cellular phone provider, but I've been too busy to worry about it. Have you had this experience? For the service provider there is a balancing act between the revenue benefit they receive against the increased potential of losing a customer from resentment.

Many wireless service providers sell “cross-product bundles” when they provide voicemail services packaged with their airtime minutes. These simplify the buying decision for customers. They also muddy the comparison of whether the bundle is a good deal. I find it harder to compare the costs of the services I get to an alternative.

We cover an example of quantity bundling in this issue.

My Encounter With Quantity Bundling

My example of making money with bundling comes from my own experience. I live in an area of Michigan where the local phone service is provided by Verizon (formerly GTE). Verizon is the victim of this comparison only because they serve my home area. Many other service providers also price services with quantity bundling. This example shows how Verizon increases revenues by offering these bundles.

When I moved into my home and turned on phone service, I was given the choice between “Value Pak-60"' and their Unlimited local service. The “60” package cost $11.36 per month, gave me sixty paid-for local calls and charged four cents for each call beyond the sixty already paid-for. The Unlimited service cost $14.48 and has no additional charge for local calls. I selected the “Value Pak-60” plan.

Over several months, I noticed that I often made less than twenty local calls, but paid for sixty of them. I called my customer service representative and learned that there is an “Econo Pak-0”. Today, I can’t recall if I was given the opportunity to get Econo Pak-0, but I’m left feeling that I was steered into the Value Pak-60 plan. With Econo Pak-0, I pay $9.29 per month and four cents for every local call.

Plan Name

Monthly cost

Cost per call


Econo Pak-0


Four cents per call

$9.29 monthly access fee + four cent per call charges

Value Pak-60


Four cents per call after sixty calls

$9.29 monthly access fee + $2.07 for the first sixty local calls + four cents per call after sixty local calls



Zero cents per call

$9.29 monthly access fee + $5.18 for an unlimited number of local calls

The tariff involved can be found at This is a PDF document that requires Acrobat Reader. The prices are found on “5th Revised Sheet 3.1”. My community (Saline, Michigan) is in the rate group 4 column.

When Does a Plan Become A Lower Cost Choice?

The Value Pak-60 plan lowers the cost per call to $0.0345 from $0.04. This represents a drop of 13.75%. A Value Pak-60 customer doesn’t save any money versus the Econo Pak-0 until they exceed 51 calls. The cost per call for the unlimited calling plan varies according to the number of calls made. The Unlimited plan customer starts to save money versus the other plans when they make more than 138 phone calls.

A Model of the Impact of Quantity Bundles

I've included an Excel spreadsheet which shows the actual costs of local calls for customers in these plans based on their level of calling activity. The spreadsheet is either a ZIP file (43kb) holding the spreadsheet or the plain MS Excel spreadsheet (105kb). The spreadsheet also includes a model of company revenues and how quantity bundles can increase them.

How Much Can I Add To Revenues?

As provided the model shows how revenues can be increase by more than 15% by bundling from the base revenue. The base revenue is charging for all calls the highest per call fee of $0.04 per call in the Econo Pak-0 plan. You can adjust the populations of subscribers between the plans and the standard deviation and average of the customer populations in the plans.

Why Do People Like Bundles?

It is valuable to look at the different ways in which a bundle is valued.

Why Do Service Providers Like Bundles?

It’s The Population

The population of customer behavior to which you apply the quantity bundle offers is the primary determinant of the success and revenue benefit of the bundle. This description doesn't try to project the impact on customer behavior that a bundle can have. You can create a bundle offer that delivers huge revenue gains to your company, but if your bundle offer doesn't provide enough actual and perceived benefit to the customers, you will lose them to your competitor or discourage service usage (reduce revenues).

You get these increased revenues/earning when the bundles offered and accepted by customers charge for more services than are actually used. The following chart shows examples of how this might be done.

Figure 1. Relationships between quantity bundles and the population of customer calling activities

The diagram above uses a simple Normal distribution of call calling profiles to illustrate how the bundle can relate to the profile. The vertical bars represent the number of customers who make a specific number of local calls per month. The bars go from left to right as the number of local calls per month increases. Actual customer behavior distributions won't be as orderly, but will likely resemble this distribution.

The height of the yellow box shows the number of calls for which a customer is charged when they sign up for the quantity bundle.

The first diagram applies a quantity bundle below the profile peak of local calling usage. This choice increases revenues for less than half of the population of customers, but since the bundle offers a cost savings to the rest of the customer population, you should get more customers to sign-up. The added revenue from those making less calls than the bundled number of calls is counterbalanced by the savings earned by the rest of the customers. This saves more money for more customers, but the next alternative may end up being more popular.

The second diagram puts the bundle boundary beyond the middle of the distribution. This increases the number of customers who see their usage level contained within the offered bundle. They are able to more accurately estimate their total spending. Their spending with the bundle will likely be higher than it would be without the bundle, but the customer gains greater confidence in their estimate of service costs. The service provider gets revenue increases on both sides of the customer distribution.

You can do a detailed model of your customers behavior and get the optimal bundling, but I expect that you'll need to select bundling numbers that appeal to your customers. If you offer Value Pak-78, you create questions in your customers about why "78". You will get fewer questions if the number is "70" or "80".

Cross-Product Bundling

Cross-product bundling will be covered in a future issue.

Rating Matters Definitions

cross-product bundle n. 1. a combination of products that are available separately, but are offered together, such as a “ski and boot package” v. 1. to To group together two or more products into one product offering, such as “the software was bundled with the computer.”

quantity bundle n. 1. a quantity of a product that is sold at a specific price and that is paid for regardless of consumption of the product (examples are airtime packages from wireless carriers and potatos by the bag)

More About Rounding

The example about the impact of rounding on revenues in Rating Matters Issue No. 1 reminded one of our subscribers about his own experience with rounding's importance. My thanks to Mr. Leonard J. Mignerey, Vice President Software Development, DST Innovis, for sharing the following story.

"When I was a young developer in the early 80's, I had an assignment where I was responsible for the maintenance of a payroll system at The Catholic University of America in Washington D.C. I was working on an enhancement that happened to impact the rounding logic and I was mired in determining just how far I needed to carry the rounding to insure accurate totals. I received a call from the Director of Payroll inquiring as to why I was spending so long on the enhancement. After receiving my explanation, he informed me that "the pennies didn't matter." So I took a stab and delivered the project. A month later I received a phone call from the same director who was inquiring as to why the payroll was off by approximately $50,000 as memory serves... Needless to say, I then received the time to properly figure out the rounding issue."

I quizzed Leonard about how the amount got to be so large. I figure that if the rounding error was just one cent each time you rounded that you'd have to have 5,000,000 events. He answered.

"Ah, you forget the most important fact, this happened while I was a 'young developer'. So I don't remember all of the details. However, when you consider full-time faculty, part-time faculty, student workers (student aid), full-time staff, part-time staff; all with different pay scenarios... you do end up with a large number of employees. Some of us got in the habit thereafter of using, "pennies don't matter" as a mantra when somebody was being stubborn concerning the resolution of relevant details."

The source of rounding errors is often the use of decimal or floating point numbers in programs when processing money amounts. Since computers work in the binary number system and convert back and forth from decimal, each calculation has the potential of creating small errors. It's been my experience that the safest course lies in processing money amounts as integer amounts of the smallest money quantity (i.e. pennies, centimes, etc.) and never having fractional amounts totaled. If you apply any percentage calculations to the money amounts, you'll create fractional amounts. Your processing algorithm must then have rounding rules appropriate to the business problem to maintain quality results.

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