When forecasting revenue for your financial projections it is important to take into account any limiting factors or scarce resources the business has. Limiting factor analysis is a technique for analyzing how profits can be maximized when there are scarce resources.

## What is a Limiting Factor?

A limiting factor usually refers to any resource which the business needs to produce the products it sells. There is no point in forecasting high unit sales if the business is not capable of producing the amount it needs.

In the short term, a business will always have at least one limiting factor but might have many more, including the following.

- Production capacity
- Skilled labor
- Material supplies
- Finance capacity
- Premises such as factory/office space
- Market demand for the product

## Limiting Factor Analysis Example

### Step 1: Work out the Product Contribution per Unit

Suppose a business manufactures two products A and B, and has projected unit sales for the period of 1,000 and 600 units respectively. The first step is to work out what contribution per unit each product makes.

Contribution is simply the selling price less the variable costs.

A | B | |
---|---|---|

Unit selling price | 8.00 | 5.00 |

Unit variable costs | 3.00 | 1.00 |

Contribution per unit | 5.00 | 4.00 |

On the face of it, product A makes the higher contribution per unit and the business should simply make and sell up to the maximum sales projection of 1,000 units, and with unlimited capacity and no limiting factors, should also make and sell 600 units of product B.

### Step 2: Calculate the Contribution per unit of Limiting Factor

But what happens if there is a limiting factor, if for example production machine capacity was a scarce resource, then this would be identified as the limiting factor, and the business would need to take this into account when considering which products to manufacture.

Suppose in this example production machine capacity is limited to 2,350 hours for the period, and the products A and B take 2.00 hours and 1.25 hours to manufacture respectively. In order to ascertain which is the best way to allocate the scarce resource the business needs to calculate the contribution each product makes for each unit of limiting factor used.

The calculations are summarized in the table below:

A | B | |
---|---|---|

Unit contribution | 5.00 | 4.00 |

Production hours | 2.00 | 1.25 |

Contribution/hour | 2.50 | 3.20 |

In this example, product A contributes 2.50 for every production hour used, and product B contributes a higher amount of 3.20 for every production hour used.

Armed with this information, to make more profit, it clearly makes more sense to manufacture product B up to its maximum sales projection before manufacturing product A. Notice that this is in total contrast to the situation based on the contribution per unit where product A had the higher value of 5.00 compared to product B at 4.00.

### Step 3: Allocate the Limiting Factor to Production

Having decided the order it products should be manufactured to achieve maximum profits, the business now needs to allow for the total number of units of the limiting factor. In this example the limiting factor is machine hours, with a maximum capacity of 2,350 hours available in the period.

Product B has the highest unit contribution per machine hour (3.20) and should be manufactured first. The sales projection for product B is 600 units, and since the product takes 1.25 hours to make, the machine hours used would be 600 x 1.25 = 750 hours, leaving a balance of 2,350 – 750 = 1,600 machine hours with which to make product A.

The limiting factor of production machine hours, leaves only 1,600 hours available to manufacture product A, and since it takes 2.00 hours to manufacture one unit, the business is only capable of producing 1,600 / 2.00 = 800 units.

This is summarized in the table below.

A | B | |
---|---|---|

Product rank | 2 | 1 |

Machine hours/unit | 2.00 | 1.25 |

Production units | 800 | 600 |

Machine hours | 1,600 | 750 |

The product rank describes the order in which the products should be manufactured based on the contribution per unit of limiting factor calculated in step 2. Notice that the total number of machine hours used is the same as the maximum capacity available (1,600 + 750 = 2,350).

The original sales projection for product A was 1,000 units, the limiting factor analysis has shown that the business is only capable of producing 800 units and therefore the sales projection will need to be revised down.

## Limiting Factors and Fixed Cost

In all of the above calculations, no account was taken of fixed costs. In the short term, by their nature, fixed costs do not change and therefore cannot impact on the decisions regarding limiting factors and scarce resources. For example, if a fixed rent is paid on a manufacturing unit, the same amount will be paid irrespective of how many units or what type of units are produced. Obviously, in the long term changes can be made to the manufacturing capacity and therefore the limiting factor analysis would need to be repeated.

## Maximizing Profit and Limiting Factors

The aim of the limiting factor analysis is to indicate which products to produce in order to maximize profits. This can be demonstrated by comparing the income statement with the units based on the limiting factor analysis (800 product A and 600 product B) to an income statement based on an alternative set of production figures.

Suppose in the above example the fixed costs for the period were 5,000, then the income statement based on the analysis would be as follows:

A | B | Total | |
---|---|---|---|

Sales Units | 800 | 600 | |

Sales | 6,400 | 3,000 | 9,400 |

Variable costs | 2,400 | 600 | 3,000 |

Contribution | 4,000 | 2,400 | 6,400 |

Fixed costs | 5,000 | ||

Profit | 1,400 |

Suppose instead of the 600 units of product B shown by the limiting factor analysis, the business had chosen to produce say only 520 units of product B. Using a similar approach, the 520 units of product B would have used 520 x 1.25 = 650 machine hours, leaving 2,350 – 650 = 1,700 hours for producing 1,700/2.00 = 850 units of product A. In these circumstances the income statement would be as follows:

A | B | Total | |
---|---|---|---|

Sales Units | 850 | 520 | |

Sales | 6,800 | 2,600 | 9,400 |

Variable costs | 2,550 | 520 | 3,070 |

Contribution | 4,250 | 2,080 | 6,330 |

Fixed costs | 5,000 | ||

Profit | 1,330 |

Clearly the profit when the units are based on the limiting factor analysis (1,400) are higher than those at the alternative production levels (1,330). The limiting factor analysis has resulted in profits being maximized.

In this example only two products were considered. A similar approach can be applied to any number of products, by simply calculating the contribution per limiting factor for each product, ranking the products in order, and producing up to the maximum sales projection until the units of limiting factor are fully utilized.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.