## Special Report

Finding the Lowest Cost Option

If you're buying goods or services you're frequently faced with trying to choose the cheapest approach where there are both fixed and variable costs. For example, Madison Bank offers a checking account for \$25 per month and \$0.10 per check. Chatham Bank offers a similar account for \$40 per month but only \$0.04 per check. Cellular providers, rental companies, etc. often have a similar approach to pricing. Which is the cheapest? The higher the volume of checks written, calls made, etc., the better off you'll be with the service providing the cheapest per unit rate. While it's obvious the lowest cost choice depends on your volume, finding that breakeven point can be a long trial and error process. Fortunately, if the relationship isn't too complicated, there's a simple formula you can use to find that breakeven point.

Look at the example above. There are four pieces of information:

```               Fixed Cost 1           = \$25      = F1
Variable Cost 1        = \$0.10    = C1
Fixed Cost 2           = \$40      = F2
Variable Cost 2        = \$0.04    = C2

```
The total cost of an account at a bank, etc. is equal to the fixed cost plus the variable cost times the number of checks written. Assume that V stands for the volume or number of checks written. The total cost of a bank account at Madison would then be equal to:

```               F1 + (V x C1)

```
If we know the fixed and variable costs of both accounts, we can write an equation to solve for the volume. It's

```                    F1 - F2
V = ---------
C2 - C1

```
Now, simply plug into the formula:

```
25 - 40      -15
---------  =  ----- = 250
.04 - .10     -.06

```
The breakeven point is 250 checks per month. If you write more than that you should take the account at Chatham bank (the one with the \$40 monthly fee). If you write less than that, stick with Madison.

Here are some points to keep in mind:

• When plugging into the equation, the numerator and denominator should both be either positive or negative. If one is positive and one negative, either you've made a mistake or one of the options doesn't make sense. See the next point.

• If both the fixed and variable costs are less with one option, you don't need the formula. That's the best choice. If both the fixed and variable costs are higher than the other option, you want to avoid that choice.

• If your volume is above the breakeven point, the correct choice is the one with the higher fixed fee. If your volume is below the breakeven point, the lowest cost option is the one with the higher per unit charge.

What if there are more variables? For example, monthly charges for an account at Cold Spring Bank include a fixed fee of \$25 per month, \$0.10 per check and \$0.07 per deposit item.

There's no simple formula you can use in this case. The best approach is to compare the total cost of one account with the total cost of another at your normal volume.

For example, using the numbers just above and assuming 40 checks and 100 deposited items per month, the total cost of an account at Cold Spring would be:

```
Fixed Cost + (No. Checks x \$0.10) + (No. Deposits x \$0.07)
```
or:
```               \$25 + (40 x \$0.10) + (100 x \$0.07) = \$36

```
Then find the total cost for a competing account using the same approach. You can incorporate more variable costs using the same approach. To compare a number of accounts you can write an equation using a computer spreadsheet.

If there are multiple variables, you may not have to evaluate all of them. That's true if they're equal in the competing options. For example, the cost of redepositing a check is \$15 at Madison and \$15 at Chatham. Just ignore this cost.

If you have to deal with an additional variable, you might decide to incorporate it as an additional fixed cost. For example, redepositing a check at Madison is \$15 and \$17.50 at Chatham. You average 2 such checks per month. Just add the difference of \$5 (\$2.50 per check x 2 checks) to the fixed cost of a Chatham account.

Two other points. Be sure to reevaluate your options periodically. At least once a year where the potential savings are relatively small; maybe every 6 months where the savings are larger. Your volume of transactions can change, as can the vendor's prices.

And don't forget to look at other considerations, particularly if the formula produces a breakeven point closest to your volume level. For example, it doesn't make sense to use a bank across town to save \$3 per month.

Copyright 2007 by A/N Group, Inc. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is distributed with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional service. If legal advice or other expert assistance is required, the services of a competent professional should be sought. The information is not necessarily a complete summary of all materials on the subject.--ISSN 1089-1536