Sensitivity Analysis and Margin of Safety

Learning Objective 5 Explain how sensitivity analysis helps managers cope with uncertainty

determine the effect on operating income of different assumptions

Sensitivity analysis is a “what if” technique managers use to examine how an outcome will change if the original predicted data are not achieved or if an underlying assumption changes. The analysis answers questions such as “What will operating income be if the quantity of units sold decreases by 5% from the original prediction?” and “What will operating income be if variable cost per unit increases by 10%?” For example, companies such as Boeing and Airbus use CVP analysis to evaluate how many airplanes they need to sell in order to recover the multibillion-dollar costs of designing and developing new ones. The managers then do a sensitivity analysis to test how sensitive their conclusions are to different assumptions, such as the size of the market for the airplane, its selling price, and the market share they think it can capture. The analysis helps visualize the possible outcomes and risks before the company commits to funding a project.

Electronic spreadsheets, such as Excel, enable managers to systematically and efficiently conduct CVP-based sensitivity analyses and to examine the effect and interaction of changes in selling price, variable cost per unit, and fixed costs on target operating income. Exhibit 3-4 displays a spreadsheet for the GMAT Success example.

Screenshot of a spreadsheet shows the analysis of CVP relations which depict the number of units required to be sold at $200 to earn a particular target operating income.

The number of units to be sold are calculated by dividing the sum of fixed costs and target operating income by contribution margin per unit. The contribution margin per unit is obtained by subtracting the per unit variable cost from 200 dollars. The details in dollars are as follows:

1. Fixed costs: 2,000

(a) Variable cost per unit: 100

Number of units when Target operating income is
- 0 equals 20 (Breakeven point)
- 1,200 equals 32
- 1,600 equals 36
- 2,000 equals 40

(b) Variable cost per unit: 120

Number of units when Target operating income is
- 0 equals 25 (Breakeven point)
- 1,200 equals 40
- 1,600 equals 45
- 2,000 equals 50

(c) Variable cost per unit: 150

Number of units when Target operating income is
- 0 equals 40 (Breakeven point)
- 1,200 equals 64
- 1,600 equals 72
- 2,000 equals 80

2. Fixed costs: 2,400

(a) Variable cost per unit: 100

Number of units when Target operating income is
- 0 equals 24 (Breakeven point)
- 1,200 equals 36
- 1,600 equals 40
- 2,000 equals 44

(b) Variable cost per unit: $120

Number of units when Target operating income is
- 0 equals 30 (Breakeven point)
- 1,200 equals 45
- 1,600 equals 50
- 2,000 equals 55

(c) Variable cost per unit: $150

Number of units when Target operating income is
- 0 equals 48 (Breakeven point)
- 1,200 equals 72
- 1,600 equals 80
- 2,000 equals 88

3. Fixed costs: $2,800

(a) Variable cost per unit: $100

Number of units when Target operating income is
- 0 equals 28 (Breakeven point)
- 1,200 equals 40
- 1,600 equals 44
- 2,000 equals 48

(b) Variable cost per unit: $120

Number of units when Target operating income is
- 0 equals 35 (Breakeven point)
- 1,200 equals 50
- 1,600 equals 55
- 2,000 equals 60

(c) Variable cost per unit: $150

Number of units when Target operating income is
- 0 equals 56 (Breakeven point)
- 1,200 equals 80
- 1,600 equals 88
- 2,000 equals 96

Using the spreadsheet, Emma can immediately see how many units she needs to sell to achieve particular operating-income levels, given alternative levels of fixed costs and variable cost per unit that she may face. For example, she must sell 32 units to earn an operating income of $1,200 if fixed costs are $2,000 and variable cost per unit is $100. Emma can also use cell C13 of Exhibit 3-4 to determine that she needs to sell 56 units to break even if the fixed cost of the booth rental at the Chicago fair is raised to $2,800 and if the variable cost per unit charged by the test-prep package supplier increases to $150. Emma can use this information along with sensitivity analysis and her predictions about how much she can sell to decide if she should rent the booth.

An important aspect of sensitivity analysis is margin of safety:

$\begin{array}{rcl} Margin of safety & = & Budgeted (or actual) revenues - Breakeven revenues \\ Margin of safety (in units) & = & Budgeted (or actual) sales quantity - Breakeven quantity \end{array}$

The margin of safety answers the “what if” question: If budgeted revenues are above the breakeven point and drop, how far can they fall below budget before the breakeven point is reached? Sales might decrease as a result of factors such as a poorly executed marketing program or a competitor introducing a better product. Assume that Emma has fixed costs of $2,000, a selling price of $200, and variable cost per unit of $120. From Exhibit 3-1, if Emma sells 40 units, budgeted revenues are $8,000 and budgeted operating income is $1,200. The breakeven point is 25 units or $5,000 in total revenues.

$\begin{array}{l} Margin of safety & = & \begin{matrix} Budgeted \\ revenues \end{matrix} - \begin{matrix} Breakeven \\ revenues \end{matrix} = $ 8,000 - $ 5,000 = $ 3,000 \\ \begin{matrix} Margin of \\ safety (in units) \end{matrix} & = & \begin{matrix} Budgeted \\ sales (units) \end{matrix} - \begin{matrix} Breakeven \\ sales (units) \end{matrix} = 40 - 25 = 15 units \end{array}$

Sometimes margin of safety is expressed as a percentage:

$Margin of safety percentage = \frac{Margin of safety in dollars}{Budgeted (or actual) revenues}$

In our example, $margin of safety percentage = \frac{$ 3,000}{$ 8,000} = 37.5 %$

That is, revenues would have to decrease substantially, by 37.5%, to reach breakeven revenues. The high margin of safety gives Emma confidence that she is unlikely to suffer a loss.

If, however, Emma expects to sell only 30 units, budgeted revenues would be $straight $ text 6,000 end text$ $inline style begin inline style left parenthesis straight $ 200 thin space text per unit end text cross times 30 thin space text units end text right parenthesis end style$ and the margin of safety would equal

$Budgeted revenues - Breakeven revenues = $ 6,000 - $ 5,000 = $ 1,000$

$\begin{matrix} Margin of \\ safety percentage \end{matrix} = \frac{Margin of safety in dollars}{Budgeted (or actual) revenues} = \frac{$ 1,000}{$ 6,000} = 16.67 %$

That is, if revenues fall by more than 16.67%, Emma would suffer a loss. A low margin of safety increases the risk of a loss. Emma would need to look for ways to lower the breakeven point by reducing fixed costs or increasing contribution margin. For example, could she charge a higher price without reducing demand or could she purchase the software at a lower cost? If Emma can neither reduce her fixed costs nor increase contribution margin and if she cannot tolerate this level of risk, she will prefer not to rent a booth at the fair.

Sensitivity analysis gives managers a good feel for a decision’s risks. It is a simple approach to recognizing uncertainty, which is the possibility that an actual amount will deviate from an expected amount. The appendix to this chapter describes a more comprehensive approach to modeling uncertainty using probability distributions.

Watch Try It Video