Welcome to Limiting Factor Analysis!
In a perfect world, a business would be able to make and sell as many products as it wanted to. But in the real world, things get in the way. Maybe you don’t have enough staff, or perhaps a machine has broken down, or you can't get enough raw materials from your supplier. In management accounting, we call these obstacles limiting factors (or sometimes bottlenecks or constraints).
In this chapter, you will learn how to make the best possible decisions when you have a shortage of resources. Our goal is simple: Maximize total contribution (and therefore profit). Don't worry if this seems a bit technical at first—we're going to break it down step-by-step!
What exactly is a Limiting Factor?
A limiting factor is any resource that is in short supply and prevents a business from expanding its activities further. Think of it like a kitchen: you might have enough ingredients to bake 100 cakes, but if you only have one small oven that can fit two cakes at a time, the oven time is your limiting factor.
Common examples of limiting factors include:
• Labour hours: Not enough skilled workers or hours in the week.
• Raw materials: A shortage of wood, fabric, or specialized components.
• Machine hours: Machines can only run for a certain number of hours before they need maintenance.
• Sales demand: Sometimes, the "limit" is simply that customers don't want to buy any more!
Key Takeaway
A limiting factor is the "bottleneck" that stops you from producing more. To maximize profit, we need to use that scarce resource as efficiently as possible.
The Golden Rule of Decision Making
When resources are limited, most students make the mistake of looking for the product with the highest profit or the highest contribution per unit. In this section of the CIMA syllabus, that is actually the wrong approach!
The Golden Rule: To maximize profit when there is a single limiting factor, you must rank products based on their contribution per unit of the limiting factor.
Analogy: Imagine you have only 10 minutes to grab items in a "supermarket sweep." You wouldn't just look for the most expensive item; you'd look for the item that gives you the most value per second it takes to grab it.
Step-by-Step: How to Solve Limiting Factor Problems
If you follow these five steps, you can solve almost any single limiting factor problem in your exam:
Step 1: Calculate the contribution per unit for each product.
Remember: \( Contribution = Selling Price - Variable Costs \)
Step 2: Identify the limiting factor "requirement" per unit.
Find out how much of the scarce resource each product uses (e.g., 2 kg of wood or 3 hours of labour).
Step 3: Calculate the contribution per unit of the limiting factor.
Formula: \( \frac{Contribution\ per\ Unit}{Resource\ Required\ per\ Unit} \)
Step 4: Rank the products.
The product with the highest "contribution per unit of resource" gets Rank 1, the next highest Rank 2, and so on.
Step 5: Allocate the resource.
Use your limited resource to satisfy the full demand for the Rank 1 product first. If there is resource left over, move to Rank 2, and so on, until the resource runs out.
Quick Review: The Ranking Formula
Don't forget: Always divide the contribution by the resource used!
\( \text{Ranking Metric} = \frac{\text{Contribution (\$)}}{\text{Kilos / Hours / Litres}} \)
Real-World Example
\nLet's say a company makes two types of wooden toys: Trains and Cars. The limiting factor is wood, and they only have 100kg available.
\n\n• Trains: Contribution = \$10. Uses 2kg of wood.
• Cars: Contribution = \$15. Uses 5kg of wood.
At first glance, Cars look better because they give \$15 contribution. But let's look at the wood:
• Trains: \( \$10 / 2kg = \$5 \) per kg of wood.
• Cars: \( \$15 / 5kg = \$3 \) per kg of wood.
Decision: The company should make Trains first! They get \$5 of profit for every kilo of wood used, compared to only \$3 for the Cars.
Common Mistakes to Avoid
• Using Fixed Costs: Never include fixed costs when calculating contribution for limiting factor analysis. We only care about variable costs because fixed costs stay the same regardless of which product we prioritize.
• Forgetting Demand: You can't just make an infinite amount of the "best" product. You must stop once you reach the maximum sales demand for that product and then move to the next best one.
• Mixing up the division: Students often divide the resource by the contribution. Always remember: Money goes on top! (\( \$ \div Hours \)).
Memory Aid: The "C.U.L.R." Method
If you're struggling to remember the steps, think of C.U.L.R. (pronounced like "Color"):
1. Contribution per unit.
2. Unit of resource required.
3. Limiting factor calculation (Divide C by U).
4. Rank and allocate.
The "Make or Buy" Connection
Sometimes, if we have a limiting factor, we might consider buying a component from an outside supplier instead of making it ourselves. This "frees up" our limited resource to be used on something else.
In this scenario, we look at the extra cost of buying per unit of the limiting factor saved. We want to buy the item that has the lowest extra cost to buy, so we minimize the damage to our profits.
Key Takeaway
In make-or-buy decisions with a constraint, the goal is to save the most "scarce resource" for the least amount of extra spending.
Final Quick Review Box
• Goal: Maximize total contribution.
• Method: Rank by contribution per unit of the limiting factor.
• Fixed Costs: Ignore them (they are irrelevant for this decision).
• Steps: Calculate contribution -> Divide by resource used -> Rank -> Allocate according to demand.
You've got this! Limiting factor analysis is just a puzzle about getting the "biggest bang for your buck" (or your hour, or your kilo). Keep practicing the ranking calculations, and you'll master this in no time!