### Learning Outcomes

- Demonstrate how changes in the cost-volume-profit equation affect profit.

**Sensitivity analysis** shows how the CVP model will change with changes in any of its variables (e.g., changes in fixed costs, variable costs, sales price, or sales mix). The focus is typically on how changes in variables will alter profit.

For BlankBooks, Inc., the monthly break-even point is 2,000 units, and the company must sell 2,900 units to achieve a target profit of $1,530. Let’s assume management believes a goal of 2,900 units is overly optimistic and settles instead on a more reasonable goal of 2,500 units in monthly sales. This is called the **base case**. The base case is summarized as follows in the contribution margin income statement format, using the following assumptions (the same ones we have been using):

Bindings | $5.00 | each |

Pages (preassembled, ready to bind) | $1.00 | each |

Labor per piece assembled | $2.00 | each |

Sales Salary | $2,000.00 | per month |

Commission | 3% | each |

Internet and web site | $200.00 | per month |

Production facility rent | $1,200.00 | per month |

Sales Price | $10.00 | each |

Units | $/Unit | Total | |
---|---|---|---|

Sales | 2,500 | $ 10.00 | $ 25,000.00 |

Variable costs | 2,500 | $ 8.30 | 20,750.00 |

Contribution Margin | $ 1.70 | Single Line4,250.00 | |

Fixed costs | 3,400.00 | ||

Operating income | Single Line$ 850.00Double line | ||

CM ratio | 17.00% |

Although management believes the base case is reasonably accurate, it is concerned about what will happen if certain variables change. As a result, you are asked to address the following questions from management (you are now performing sensitivity analysis!). Each scenario is independent of the others. Unless told otherwise, assume that the variables used in the base case remain the same. How do you answer the following questions for management?

- Scenario 1: How will profit change if the sales price increases by 2 percent?
- Scenario 2: How will profit change if sales volume decreases by 10 percent?
- Scenario 3: How will profit change if fixed costs decrease by 60 percent and variable costs increase by 10 percent?

Let’s assume all of these scenarios are independent of each other.

### Scenario 1: sales price increases by 2 percent

Mathematically, the increase is represented by 1.00 + 0.02 = 1.02 (the entire sales price = 1, and the increase in the price = 0.02)

Therefore, a 2% increase in sales price = $10.00 * 1.02 = $10.20.

Plugging this revised sales price into our model, we get:

Units | $/Unit | Total | |
---|---|---|---|

Sales | 2,500 | $ 10.20 | $ 25,500.00 |

Variable costs | 2,500 | $ 8.30 | 20,750.00 |

Contribution Margin | $ 1.90 | Single Line4,750.00 | |

Fixed costs | 3,400.00 | ||

Operating income | Single Line$ 1,350.00Double line | ||

Increase (decrease) over base | $ 500.00 | ||

% increase (decrease) over base | 58.82% | ||

CM ratio | 18.63% |

This shows that a 2% increase in sales price, from $10.00 to $10.20, increases the bottom line by $500, which is a 58.82% increase in profit. That indicates that our model is fairly sensitive to price increases.

### Scenario 2: sales volume decreases by 10 percent

Mathematically, the decrease is represented by 1.00 – 0.10 = 0.90 (the entire volume = 1, and the reduction in the volume = -0.10)

Therefore, a 10% decrease in sales volume = 2,500 * 0.90 = 2,250.

You could also compute this by subtracting (2,500 * 0.10) from 2,500.

2,500 * 0.10 = 250

2,500 – 250 = 2,250

Plugging this revised sales volume into our model, we get:

Units | $/Unit | Total | |
---|---|---|---|

Sales | 2,250 | $ 10.00 | $ 22,500.00 |

Variable costs | 2,250 | $ 8.30 | 18,675.00 |

Contribution Margin | $ 1.70 | Single Line3,825.00 | |

Fixed costs | 3,400.00 | ||

Operating income | Single Line$ 425.00Double line | ||

Increase (decrease) over base | $ (425.00) | ||

% increase (decrease) over base | -50.00% | ||

CM ratio | 17.00% |

This shows that a 10% decrease in sales volume, from 2,500 units to 2,250 units, decreases the bottom line by $425.00. That represents half of our income at that level, so again, it seems like our model is fairly sensitive to drops in volume.

### Scenario 3: fixed costs decrease by 60 percent and variable costs increase by 10 percent

Mathematically, the decrease in fixed costs is represented by 1.00 – 0.60 = 0.40 (the entire fixed costs = 1, and the reduction = -0.60), and the increase in variable costs is represented by 1.00 + 0.10 (the entire variable cost = 1, and the increase = 0.10)

Therefore, a 0% decrease in fixed costs = $3,400 * 0.40 = $1,360, and a 10% increase in variable costs = $8.30 * 1.10 = $9.13, which is the same as (1 * 8.3) + ( 0.10 * 8.3) = 8.3 + 0.83 = 9.13.

Plugging these revised fixed and variable costs into our model, we get:

Units | $/Unit | Total | |
---|---|---|---|

Sales | 2,500 | $ 10.00 | $ 25,000.00 |

Variable costs | 2,500 | $ 9.13 | 22,825.00 |

Contribution Margin | $ 0.87 | Single Line2,175.00 | |

Fixed costs | 1,360.00 | ||

Operating income | Single Line$ 815.00Double line | ||

Increase (decrease) over base | $ (35.00) | ||

% increase (decrease) over base | -4.12% | ||

CM ratio | 8.70% |

This shows that a 10% increase in variable costs, from $8.30 to $9.13, is not even offset by a robust 60% decrease in fixed costs, from $3,400 to $1,360. Our model is sensitive to increases in variable costs because the margin on each unit is so small.

Let’s see a side by side summary of these scenarios:

Base | Scenario 1 | Scenario 2 | Scenario 3 | |
---|---|---|---|---|

Subcategory, Assumptions |
||||

Sales price per unit | $10.00 | $10.20 | $10.00 | $10.00 |

Variable cost per unit | $8.30 | $8.30 | $8.30 | $9.13 |

Monthly fixed costs | $3,400.00 | $3,400.00 | $3,400.00 | $1,360.00 |

Sales Volume | 2,500 | 2,500 | 2,250 | 2,500 |

Subcategory, CVP Model Results |
||||

Sales | $ 25,000.00 | $ 25,500.00 | $ 22,500.00 | $ 25,000.00 |

Variable costs | 20,750.00 | 20,750.00 | 18,675.00 | 22,825.00 |

Contribution Margin | Single Line 4,250.00 | Single Line 4,750.00 | Single Line 3,825.00 | Single Line 2,175.00 |

Fixed costs | 3,400.00 | 3,400.00 | 3,400.00 | 1,360.00 |

Operating income | Single Line$ 850.00Double line | Single Line$ 1,350.00Double line | Single Line$ 425.00Double line | Single Line$ 815.00Double line |

Increase (decrease) over base | $ 500.00 | $ (425.00) | $ (35.00) | |

% increase (decrease) over base | 58.82% | -50.00% | -4.12% | |

As you can see, once the model is established, you can quickly answer a wide variety of what-if scenarios.

Sensitivity analysis shows how the cost-volume-profit model will change with changes in any of its variables. Although the focus is typically on how changes in variables affect profit, accountants often analyze the impact on the break-even point and target profit as well.

Now, let’s check your understanding of sensitivity analysis.