Resources are finite. A business only has so many man hours, so many square feet, and so much machinery. Over the long term, a company can expand its capacity but in the short term, it must make important decisions in order to maximize profit. Constrained resources require businesses to make decisions about which products to make and in what quantities.

How does a company decide which product is given priority over constrained resources?  We must look at how each product uses the constrained resource and maximize contribution margin per hour. Let’s look at an example.

Example #1 – Unlimited Demand

KLI Desks, Inc. makes two types of office desks,  Executive and Standing. Both desks require time in the Painting Department, but there are only 172 hours per month available currently in that department. The company can sell as many of each desk as it can make. What is the optimal product mix that would maximize profit each month?

At first glance, it would be tempting to make the standing desk, since it has a higher contribution margin per unit, but with the constraint of the painting department hours will that give KLI Desks the highest monthly contribution margin? To determine if that is true, we don’t need to calculate the contribution margin for all 172 hours. We just need to calculate the contribution margin for one hour for each product and determine which is higher.

If the Executive desk takes 15 minutes to paint, we can make 4 per hour (60/15). We can make 3 of the Standing desk per hour (60/20). Multiply the number of desks that can be made each hour by the contribution margin per desk.

Although the Executive Desk has a lower contribution margin per unit, the increased product per hour results in a higher contribution margin per hour. Therefore, we would only produce Executive desks.

What if demand for the desks was limited?

Example #1 – Limited Demand

KLI Desks, Inc. makes two types of office desks,  Executive and Standing. Both desks require time in the Painting Department, but there are only 172 hours per month available currently in that department. The company can only sell 500 of each desk per month. What is the optimal product mix that would maximize profit each month?

This example is a bit different than the last example because we cannot sell an unlimited number of desks. We can only sell 500 of each desk per month. Therefore, we do not want to make more than 500 of either desk. We know from the previous problem that we should make Executive desks first. How many hours would it take to make 500 Executive desks?

500 desks / 4 desks per hour = 125 hours required

There are 172 hours available each month which means we can make some Standing desks but how many?

172 total hours – 125 hours for Executive desks = 47 hours remaining

47 hours X 3 Standard desk per hour = 141 Standard desks

We can make 500 Executive desks and 141 Standard Desks to maximize profit. This is only because we can not sell more than 500 of either desk per month.

### Final Thoughts

When working with optimal product mix, determine which product will give you the highest contribution margin per hour of constrained resource. Then look to see if there are other constraints, for example, a limit to the number of units of either product that could be sold.

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Optimal Product Mix

One type of short-term decision that businesses frequently have to make is whether or not to accept special order requests from customers. A special order is an order that the company did not anticipate when developing its budget for the year. Therefore, this is an additional opportunity to generate revenue above sales goals. Special orders typically request a lower price than normally offered and/or might include additional costs. Often students get caught up in the lower price or lower contribution margin and want to disregard the order immediately. However, if the order will bring in additional profit, the order should be considered.

When faced with a special order decision, a company should consider the following three items:

1. Does the company have the excess capacity to fulfill this order?

Remember that a special order is an order that the company did not expect. The company must make sure that there is excess capacity to fill this order without harming the original plan developed for the year.

2. Will the order be profitable?

Typically, a special order will have a reduced price and/or additional costs. Will the price be high enough to cover the incremental costs associated with the order. Think back to overhead allocation. When overhead allocation rates were developed at the beginning of the year, they were based on the planned production. These special orders are in addition to the planned production. Therefore, fixed overhead would not be applied to these jobs. This allows the company to make the products needed for the special order at a reduced cost. Although the price might be lower, the company may be able to achieve profit on the job.

3. Will the order affect planned sales, now or in the future?

The company must insure that the special order will not hurt other sales. It is important to make sure that the customer requesting the special order does not compete with existing customers or the company itself, which would result in decreased sales at regular prices. Special orders can also lead to unhappy existing customers if they find out about the special deal you gave someone else. Careful consideration must be made when accepting special orders to protect current and future profits.

### Identify the relevant costs

In order to identify the relevant costs associated with a special order decision, we must look at the existing costs to determine which costs will be paid if the order is accepted. Previously incurred fixed costs are never relevant. The only fixed costs that should be considered are fixed costs that are incurred because of the special order. Then consider your variable costs. Are there any variable costs that will not be paid with this special order? Sometimes variable selling costs are excluded from the calculation because no sales commission will be paid on the order. These savings can help decrease the cost and increase the profitability of the job.

Carefully read the problem to ensure you have identified the relevant and irrelevant costs properly.

### Should the company accept the job?

Typically in problems you will do in class, you will only consider the quantitative factors. Use the contribution margin approach to calculate if the job will generate profit or loss:

1. Calculate the contribution margin per unit

Calculate the contribution margin (price – variable costs) per unit for the special order. Exclude irrelevant costs from the calculation.

2. Calculate the total contribution margin

Multiply the number of units in the special order by the contribution margin per unit.

3. Subtract any incremental fixed costs from the contribution margin to determine profit or loss

If there are any incremental fixed costs, subtract those costs from the contribution margin. If there are no incremental fixed costs, the contribution margin is all profit.

4. Determine if you should accept the job

If there are no extenuating qualitative issues, accept the job if it will generate additional profit. If there is a loss on the job, do not accept the job.

### Final Thoughts

These problems are not difficult. The hardest part is to identify the irrelevant costs and remove them from your calculations. Use what you have learned about contribution margin to determine if you have profit on the special order.

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Special Order Decision Making

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Target Profit

Contribution margin is one of the most important concepts in managerial accounting. It is used extensively in planning and decision making because it is much easier to use than absorption costing, especially as variables change in the planning process.

Contribution margin can be defined in a number of different ways. Contribution margin per unit is price less variable cost per unit. Total contribution margin is sales less total variable costs. These are the two definitions you will see most often for contribution margin. I like to define contribution margin as the amount from each unit that contributes to fixed cost and profit.

Let’s look back at the contribution margin income statement:

Notice that contribution margin less fixed cost is profit. In order to make a profit, total contribution margin must be greater than fixed costs. Once all of our fixed costs are paid for, any additional sales generate profit.

But how much profit? Each unit would generate profit equal to the contribution margin for that unit. If the contribution margin per unit is \$10, then each additional unit sold would provide an additional \$10 of profit.

Contribution margin is most often expressed as a monetary unit, but we can also express it as a percentage of price. This is called the contribution margin ratio. The contribution margin ratio tells us the percentage of each sales dollar that becomes contribution margin

Contribution margin ratio = contribution margin per unit / price

or

Contribution margin ratio = total contribution margin / sales

We can also look at variable cost as a ratio. The variable cost ratio tells us the percentage of each sales dollar that would go toward variable cost.

Variable cost ratio = variable cost per unit / price

or

Variable cost ratio = total variable cost / sales

As long as price and variable cost remain the same, these ratios will remain the same. It does not matter if the company sells 10 units or 1 million units, the percentage of each sale that becomes contribution margin or does to cover variable costs is the same.

Let’s look at an example to illustrate how to calculate contribution margin and these ratios.

Example #1

Hangout Limited, LLC sells one product priced at \$40 per unit. The variable costs (direct materials, direct labor, variable overhead and variable selling) is \$25 per unit. Calculate the contribution margin per unit, the contribution margin ratio and the variable cost ratio.

We know that contribution margin is price less variable cost. Therefore, contribution margin is:

\$40 – \$25 = \$15

That means that for every unit we sell, \$15 will go to cover fixed cost and profit. Once the fixed costs are paid, \$15 per unit becomes profit.

Now calculate the ratios. We’ll start with the contribution margin ratio. Contribution margin ratio is contribution margin per unit divided by price per unit.

\$15 / \$40 = 37.5%

What does that mean? For every dollar of revenue the company brings in,  37.5% or 37.5 cents will become contribution margin. This also tells us that 37.5% of every sale is available to pay fixed costs or generate profit.

The variable cost ratio is variable cost per unit / price.

\$25 / \$40 = 62.5%

This tells us that for every unit sold, 62.5% will go to cover variable costs.

These ratios are important as we start to look at planning and decision making using contribution margin.

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Contribution Margin

The contribution margin income statement is a very useful tool in planning and decision making. While it cannot be used for GAAP financial statements, it is often used by managers internally.

The contribution margin income statement is a cost behavior statement. Rather than separating product costs from period costs, like the traditional income statement, this statement separates variable costs from fixed costs.

The basic format of the statement is as follows:

Variable costs, no matter if they are product or period costs appear at the top of the statement. Fixed costs are treated the same way at the bottom of the statement. It is helpful to calculate the variable product cost before starting, especially if you will need to calculate ending inventory.

Let’s run through an example to see how the income statement is constructed. We will use the same figures from the absorption and variable product cost post.

The first thing to remember about any income statement is that the statement is calculated based on the amount of product sold, not the amount of product produced. Therefore, this income statement will be based off the sale of 8,000 units.

To calculate sales, take the price of the product and multiply by the number of units sold.

Sales = Price X Number of units sold

Sales = \$100 X 8,000

Sales = \$800,000

Next, we need to calculate the variable costs. In the absorption and variable costing post, we calculated the variable product cost per unit.

This covers the product costs, but remember we must include all the variable costs. There is also \$5 of variable selling cost that should be included. Multiply the total variable cost per unit by the number of units sold.

Total variable cost = Variable cost per unit X Number of units sold

Total variable cost = (\$44 + \$5) X 8,000

Total Variable Cost = \$392,000

Contribution margin is the amount of sales left over to contribute to fixed cost and profit. Contribution margin can be expressed in a number of different ways, including per unit and as a percentage of sales (called the contribution margin ratio). In the contribution margin income statement, we calculate total contribution margin by subtracting variable costs from sales.

Total contribution margin = Sales – Variable costs

Fixed costs include all fixed costs, whether they are product costs (overhead) or period costs (selling and administrative). One thing that causes the contribution margin income statement and variable costing to differ from the traditional income statement and absorption costing is the fact that fixed overhead is treated as if it were a period cost. All fixed overhead is expensed in the period it is incurred. Under absorption costing, fixed overhead is attached to each unit. Therefore if there are units that are not sold, a portion of the fixed overhead ends up in inventory. That is not the case when using variable costing.

Total fixed overhead = \$48,000 + \$112,000

Last step: subtract fixed costs from contribution margin to calculate operating income.

#### Final Thoughts

The contribution margin income statement is all about behavior. Remember the format and ignore the traditional (absorption) income statement. Most students that have trouble with this statement try to relate it back to what is happening on the traditional income statement. Throw out what you know about the traditional income statement when doing the contribution margin income statement. Focus on the format of this statement and you should be fine.

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The contribution margin income statement