|Issue No. #1||24 October 2000||ISSN: 1532-1886|
Adventures In Rounding
Many years ago a consultant with whom I was impressed told me a story. It might be an urban legend, but he had been in IT management at McCaw Cellular. I believed him without asking for names and dates.
He told me that a chief financial officer at a cellular company became enamored with the attractiveness of offering six second call duration rounding to their customers. He was replacing the more common sixty second rounding. He deployed this change in rounding without adjusting for its effects. I asked if it was really true. He assured me that it was and then continued the story by telling me that after the revenue drop in the first month, the sixty second rounding was returned and the chief financial officer was let go.
A Rough Estimate of the Revenue Effect of Rounding
It was easy for me to imagine the revenue effect by looking at the results of rounding on an average phone call. The average phone call is between three and four minutes. If the cost of the call is the same for every minute, then every average call is charged for four minutes. This last minute represents twenty five percent of the revenues of the company. If you switch to six second rounding (tenth of a minute rounding), your revenues can drop from 22.5% to 2.5%.
How do I figure that? If the call is rounded to 3.1 minutes from 4.0 minutes (four minutes equals forty tenths of a minute), you lose 9 of 40 tenths of a minute you would charge for. This is 22.5% of call revenue. If the call is rounded to 3.9 minutes from 4.0 minutes, then you only lose the charge for one tenth of a minute. This is 2.5% of call revenue.
It's The Ratio That Matters
The impact of rounding is relative to the ratio between your average unrounded value and your maximum rounding amount. In the case of telephony with sixty second rounding, the ratio is roughly 3.5 versus 1.0. When you switch to six second rounding, the ratio goes to 3.5 versus 0.1. The following diagram illustrates the impact graphically.
Figure 1. The colored portion shows the "rounding zone" where extra revenue comes from.
Two Models of the Impact of Rounding
Associated with this issue is a MS Excel spreadsheet in a Zip file(54kb) or an MS Excel spreadsheet(158kb) with two specific models of rounding's impact on a telecommunications company. I used a statistically normal population of calls over which the rounding rules are applied. This allows you to see the whole company effect of rounding on revenues. The model is full of flaws, but still illustrates the impact of rounding on revenues.
The spreadsheet shows the results from sixty second rounding. To see the results for six second rounding, just change the rounding interval at the top of the spreadsheet.
The spreadsheet shows an overall revenue increase for sixty second rounding from one second rounding of 16.28%. The increase of revenue from six second rounding is only 1.3%. Switching to six second rounding from full minute rounding drops about 15% of revenues from the monthly billing.
Notes on Rounding from Jim O'Neill, a regular columnist of Billing World magazine
Orange, a cellular company, launched in the UK many years ago with "One second billing" and was very successful in weaning customers away from British Telecom.
In 1992, a midwestern cellular company was the first U.S. company to bill airtime in 30 second initial and 6 second intervals after that. Very successful at it too.
A New York congressman is calling for the elimination of full minute rounding.
Rating Matters Definitions
Rounding v. the process of taking actual measures and converting them to a specified degree of accuracy, such as "sixty second rounding", "penny rounding"; adj. an object related to the rounding process, such as "rounding factor", "rounding rule".
Rounding factor n. a value that identifies the degree of accuracy desired from a rounding process, such as "to the penny", "to the second".
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2000 Service Level LLC
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This issue was corrected from the version sent to subscribers. The ratio "3.5 to 0.1" was incorrectly stated as "3.5 to 0.01".