There are several things to be careful about when making decisions that depend on understanding costs behavior. Want to touch briefly on some of those. Costs that behave one way for one organization might behave another way for another organization. Let's think about the T-shirt maker example that we started with. As I described it, the labor cost behaved like a fixed cost during the normal course of the year. The company employed one employee and this employee works full time regardless of the number of T-shirts the company makes and he's paid a fixed salary. Now consider a different T-shirt maker that has one person available to work as needed, but rather than being paid as a full time employee, this employee is paid a certain amount for each T-shirt he makes. This T-shirt company's labor costs are variable costs. They increase and decrease proportionately with changes in the number of T-shirts made. A second thing to be careful about is that the cost function that we derive is valid only for a certain range of activity. When we estimate the relationship between cost and activity levels or estimate the cost function, we do so using past data about cost and activity for different levels of activity. But we only have data for the organization's typical activity levels to use in our estimate. So our estimate is valid only within that range of activity. That range of activity is something that we call the relevant range. In our T-shirt company example, we have data for activity levels that range from about 4500 T-shirts to about 16000 T-shirts. Now, if activity level exceeds what the organization typically sees or if it falls below the typical activity level, our costs predictions may not be accurate. For instance, if the company decides to produce substantially more T-shirts than it's typical, we may need or it may need to add additional capacity like adding a second shift, adding some equipment, or adding people. And these can increase the organization's fixed cost. So we may not be able to reason- reasonably or reliably estimate or predict costs for activity levels outside of that relevant range with the equations that we've derived. A third thing to be careful about is that costs that are fixed in the short term, may be variable in the long term. Some similarities with what we've just talked about. While many cost may appear fixed based on the past data that we used to assess them. That data may be based on relatively short time horizons. And note that when we start thinking longer term, managers have to open them, have open to them many more options than they do in the short term. For example, over the longer term managers again might decide to increase production substantially by increasing the organization's production capacity. So over the longer term, and over a greater relevant range of activity levels, costs that are fixed in the short term might actually look variable in the longer term. Consider that T-shirt maker and the one full time employee that makes the T-shirts. That cost is fixed in the short term for a relevant range of the units that are being produced. But once the company opens itself up to ramping up production in the long term, we start to realize that the T-shirt maker may have to hire additional employees to support that increased production. So over a very wide range of activity and time even some of our fixed costs appear to vary with the level of activity. Fourth thing to be careful about. Beware of per unit costs. Let's return to our graphs of variable cost and fixed costs. Recall that these graphs show what happens to total variable costs and total fixed cost as activity or the number of units increase. Now what would a graph of variable cost per unit and fix cost per unit look like? Well, notice the difference in the graphs related to variable costs. Total variable costs increase as the number of units increases, and it increases the same amount for each additional unit. And incidentally that's why the graph of the total variable cost is a straight line. Now let's notice the difference in the graph related to fixed costs. Total fixed cost stay the same as the number of units increases. But notice that the fixed cost per unit decreases as the number of units increases. Now why does that happen? Well, because we're dividing a constant amount a fixed cost, by an increasing number of units. Here's something interesting. I can also depict these relations in a two by two matrix that you might find helpful. Notice that as the number of units increase, the variable costs increase in total, okay, they increase in total, but they stay the same per unit. And as the number of units increase, fixed costs stay the same in total, but they decrease per unit. So another way to capture that. Now why is it important to understand? As a manager you will make many decisions where cost is an important factor. Making those decisions using unitized or per unit cost can sometimes lead to poor decisions because using unitized fixed costs, treats those costs as if they were variable. And here's an example. Suppose you're the T-shirt maker and your variable costs are $4 per T-shirt and your total fixed cost of $40000. Now suppose you typically sell 10000 T-shirts per month. So your fixed costs per unit are also $4, right? They're the $40000 fixed cost divided by the 10000 units. And so then your total cost per unit are $8. The $4 variable cost plus the $4 fixed cost. Now, if you increase the number of T-shirts to 12500 instead of 10,000 T-shirts, your variable costs per unit will still be $4. Remember they stay the same per unit regardless of the number of units but your fixed cost, per unit would not be $4 any longer. It would be $3 and 20 cents per unit. The $40000 in fixed cost divided by the 12500 units. And your total cost per unit would be the 7.20. $4 variable cost plus a 3.20 fixed cost. So what's the takeaway here? Well, be aware of working with unitized or per unit cost. Be careful not to assume that fixed cost per unit and total cost per unit stay the same across different levels of activity. So when you have a decision that involves choosing between alternatives that have different levels of activity, don't unitize the fixed cost in your analysis. The next thing I want to issue a caution about is, cost may vary based on something other than the number of units. Now so far in the course we've considered variable cost as those that vary based on the number of units. So we've assumed that changes in the number of units produced or number of services provided lead to proportional changes in costs. Examples of such costs were the cost of raw materials, sales commissions paid on a per unit sold basis. However, there may be other measures of activity other than units that drive costs to increase or decrease. Here are some examples. Suppose another company pay sales commission, but instead of paying it based on the number of units sold like our T-shirt maker did, it pays based on revenues, then the cost of commission, while still variable varies based on revenues not the number of units. Another example. Some activities may be performed for a group or a batch of units rather than for each individual unit. In these cases the cost of that activity may vary with the number of batches of units produced rather than the number of units produced. Examples of these costs might include the cost of setting up machines or equipment, to get them ready to produce a new group or batch of units, or the cost of inspecting the same number of pieces from each batch of units after they're produced, or even the cost of processing a customer's order. And still another example. Some activities may be performed for an entire product line rather than for a group of units or for each individual unit. And these cases the cost of that activity will vary with the number of product lines produced rather than the number of batches or the number of units produced. Examples of these costs can include research and development costs that are associated with a product line, or maybe the cost of advertising for a product line would be another example. So what's the take away here? Well, variable cost do not always vary with the number of units. Be alert to that possibility that other drivers of those costs may exist and use those drivers as the activity when estimating your cost equations.
