Account question

profileDee Redd


This is a cost-volume-profit, opportunity cost problem. Some customers will switch and some customers

will not. The cost-volume-profit structures are different between the two sets of customers, and we do

not get to choose how many customers will switch to automated billing. The customer chooses. The

revenue is the same between sets of customers, so let’s describe only the costs :

Existing cost structure: $40,000 + $0.20 * 100,000 bills

After implementing:: $50,000 + $0.04 * billsSwitchers + $0.20 * billsNonswitchers

Total bills: billsNonswitchers+ billsSwitchers= 100,000

The question will be how many billsSwitchers should there be to keep the total cost after the

implementation no higher than the existing cost structure.

Problem statement:

Beta has an opportunity to automate some of the billing process so that customers can use a direct

account deduction. Moving to an automated billing process is voluntary for customers and Beta does

not know what percentage will move.

There are currently 100,000 customers. The cost of the billing process, as currently constituted, is

$40,000 of annual fixed cost and $0.20 per bill. Automating the billing will result in a total of $50,000 of

annual fixed cost, which is to say that some of the prior fixed cost will continue and Beta will need new

software and equipment. Variable costs for any automated bill will drop to $0.04 per bill.


How many customers must switch to the automated billing process to make the investment