Home Accounting Cost Analysis: Managerial and Cost Accounting

# Sensitivity Analysis

The only sure thing is that nothing is a sure thing. Cost structures can be anticipated to change over time. Management must carefully analyze these changes to manage profitability. CVP is useful for studying sensitivity of profit for shifts in fixed costs, variable costs, sales volume, and sales price.

## Changing Fixed Costs

Changes in fixed costs are perhaps the easiest to analyze. To determine a revised break-even level requires that the new total fixed cost be divided by the contribution margin. Let's return to the example for Leyland Sports. Recall one of the original break-even calculations:

Break-Even Point in Sales = Total Fixed Costs / Contribution Margin Ratio \$2,000,000 = \$1,200,000 / 0.60

If Leyland added a sales manager at a fixed salary of \$120,000, the revised break-even would be:

\$2,200,000 = \$1,320,000 / 0.60

In this case, the fixed cost increased from \$1,200,000 to \$1,320,000, and sales must reach \$2,200,000 to break even. This increase in break-even means that the manager needs to produce at least \$200,000 of additional sales to justify their post.

## Changing Variable Costs

In recruiting the new sales manager, Leyland became interested in an aggressive individual who was willing to take the post on a "4% of sales" commission-only basis. Let's see how this would change the breakeven point:

Break-Even Point in Sales = Total Fixed Costs / Contribution Margin Ratio \$2,142,857 = \$1,200,000 / 0.56

This calculation uses the revised contribution margin ratio (60% - 4% = 56%), and produces a lower break-even point than with the fixed salary (\$2,142,857 vs. \$2,200,000). But, do not assume that a lower break-even defines the better choice! Consider that the lower contribution margin will "stick" no matter how high sales go. At the upper extremes, the total compensation cost will be much higher with the commission-based scheme. Following is a graph of commission cost versus salary cost at different levels of sales. You can see that the commission begins to exceed the fixed salary at any point above \$3,000,000 in sales. In fact, at \$6,000,000 of sales, the manager's compensation is twice as high if commissions are paid in lieu of the salary!

What this analysis cannot tell you is how an individual will behave. The sales manager has more incentive to perform, and the added commission may be just the ticket. For example, the company will make more at \$6,000,000 in sales than at \$3,000,000 in sales, even if the sales manger is paid twice as much. At a fixed salary, it is hard to predict how well the manager will perform, since pay is not tied to performance.

You have probably marveled at the salaries of some movie stars and professional athletes. Rest assured that some serious CVP analysis has gone into the contract negotiations for these celebrities. For example, how much additional revenue must be generated by a movie to justify casting a high dollar movie star (versus using a low-cost unknown actor)? And, you have probably read about deals where musicians get a percentage of the revenue from ticket sales and concessions at a concert. These arrangements are likely based on detailed calculations; what may seem foolish is actually quite logical in terms of a comprehensive CVP analysis.

## Blended Cost Shifts

Sometimes, a business will contemplate changes in fixed and variable costs. For example, an airline is considering the acquisition of a new jet. The new jet entails a higher fixed cost for the equipment, but is more fuel efficient. The proper CVP analysis requires that the new fixed cost be divided by the new unit contribution margin to determine the new break-even level. Such analysis is important to evaluate whether an increase in fixed costs is justified.

To illustrate, assume Flynn Flying Service currently has a jet with a fixed operating cost of \$3,000,000 per year, and a contribution margin of 30%. Flynn is offered an exchange for a new jet that will cost \$4,000,000 per year to operate, but produce a 50% contribution margin. Flynn is expecting to produce \$9,000,000 in revenue each year. Should Flynn make the deal? The answer is yes. The break-even point on the old jet is \$10,000,000 of revenue (\$3,000,000/0.30), while the new jet has an \$8,000,000 breakĀ­even (\$4,000,000/0.50). At \$9,000,000 of revenue, the new jet is profitable while continuing to use the old jet will result in a loss.

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