Temporal Equations in TDABC Cost Models

In the previous article titled "TDABC: The Revolution of ABC Models," I explained what time-based costing models are and their advantages over traditional ABC costing models. If you are not familiar with what ABC costing models are, I invite you to read my article "What is ABC Costing?" 

The TDABC model uses time as its main cost driver instead of the large number of drivers that a traditional ABC model might use. By doing so, we kill two birds with one stone: we avoid the complexity of creating a layer of activities where we first assign resources, and at the same time, we prepare the allocation to cost objects. This approach allows us to develop much simpler models that can still incorporate the full complexity of the business. 

But Why Use Time as a Driver? 

The advantage of using time as a driver is that, on the one hand, practically all processes can be expressed in terms of costs per unit of time, determining a cost per hour or per minute. On the other hand, it also allows us to determine idle capacity. 

In oversimplified terms to make it easy to understand, if, for example, a unit of 2 people each earning $3,000.00 per month, this unit has a monthly cost of $6,000.00. And if they work 40 hours per week for 4 weeks = 160 hours per month, multiplied by 2 people = 320 hours available, equivalent to 19,200 minutes. Therefore, $6,000.00 divided by 19,200 minutes = $0.3125, which is the cost per minute of that department. 

Now, continuing with our oversimplified example, suppose these two people handle calls that average 9 minutes each. Their monthly capacity would be 2133 calls (19,200 / 9). Now, if during the month they processed only 1760 calls, we can conclude two things: a. The cost of calls was $4,950.00, which is equal to $0.3125 x 1,760 calls x 9 minutes per average call. b. The cost of idle capacity was $1,049.06, which is the result of (2133 - 1760) = 373 calls not made * 9 minutes per average call = 3,357 minutes * $0.3125 cost per minute of the department. 

Experience indicates that for an average employee, it is much easier to determine the average time in minutes it takes to perform an activity than the total time it takes for that activity over the course of a month. Of course, it depends on the type of activity, as the higher the position in the company, the longer the activities tend to take, whether weeks or even months. 

Temporal Equations: Reducing Complexity 

To explain temporal equations, first, let's understand the problem they solve. Imagine an IT process that breaks down as follows: Processing a support ticket, which includes the following possibilities in any combination. On the right side, the average time in minutes it takes to perform that action is listed. 

1. Initial Review (10)

1.1. Requires clarification from the client (20) 

1.2. Requires supporting documentation (35) 

2. Identify the problem (25)

2.1. In-depth review of the case (120) 

2.2. Requires review by a specialist (190) 

3. Develop the Solution (120)

3.1. Extra permits must be requested (20) 

In this process, there are 8 possibilities that can occur when handling a ticket. Although in practice, some may not apply, theoretically, we would have 64 possible combinations. In a traditional ABC model, we would be forced to generate 64 objects to assign each of these possibilities. 

>> TDABC: The Revolution of ABC Cost Models <<

However, in a TDABC, this dilemma is very easily resolved with a temporal equation such as the following: 

In this way, instead of creating 64 objects, we have a single temporal equation, which, for each ticket processing transaction, can capture each of the combinations. To do this, simply add the minutes of each activity as they apply. This way, a great complexity of possible combinations can be managed without increasing the complexity of the model. 

Tips for Building the Temporal Equation 

Although it seems complex, it is very simple. We can break it down into two basic steps. 

Standard Process Time 

This would be the time it takes to perform the process in its most common version. In the previous example, the standard process could be determined as follows: 

This would give us a response time of 155 minutes for the standard process of Processing a support ticket. 

For those low-cost support processes, it is enough to determine the standard time as the driver to use. However, in high-cost processes, it is advisable to break down the temporal equation into those variables that are relevant to determine the cost. 

>> Key benefits of defining your processes <<

Extended Standard Process Times 

When, in addition to the steps of the standard process, additional steps are required, such as if supporting documentation is needed (add 35 minutes), or if a specialist review is needed (add 190 minutes). In this example, the equation is expanded as follows: 

If there are additional steps, they are simply added to the temporal equation, so that all the complexity of the business can be captured in the equation. 

Some Practical Recommendations 

Despite its great advantages, it is not necessary to use temporal equations throughout the cost model. Here are some aspects to consider where it makes more sense to use them. 

Prioritize the Most Expensive Processes 

In cost models, I always recommend applying the Pareto principle to prioritize which processes are worth investing time and effort in developing the model. Typically, the most expensive processes are prioritized. 

Clearly Define the Process Scope 

It is essential to be clear about the start and end of the process. This ensures that the temporal equation covers only those steps that belong to the process to be costed and does not overlap with other processes. 

Use Variables for the Calculation of Drivers That Are Available 

"If it is not practical, it doesn't work." For the work with temporal equations to be truly applicable, we need to record those variables that trigger greater time consumption. In our previous case, it is necessary to know if during the processing of the ticket a client clarification was required or if additional permissions had to be requested since these factors add extra minutes to the ticket processing. If these variables are not recorded, other variables must be sought to help determine this time consumption. For example, whether a ticket is of high, medium, or low complexity. 

Start with Simple Equations 

I always recommend that cost models be iterative, and in each iteration, if necessary, increase the complexity where required. Therefore, temporal equations, in the first iterations, should be as simple as possible. Then, if justified, more variables can be added. 

What Happens if We Assign Actual Times Instead of Estimated Times? 

If we have an ERP that records each of the times of the temporal equation in each transaction, it would logically make sense to use those times, right? Well, the answer is not so simple. 

On the one hand, using actual times is very simple since we have this data, and it is not surprising that many companies opt for this practice. So, what's the problem? Well, the issue here is that idle capacity of resources would not be considered, which is precisely what we calculated in the first example. And this is valuable data to consider. By using actual times, we are somehow also incorporating potential biases that may go unnoticed if idle capacity is not considered. In any case, if both sides of the coin are desired, an additional scenario can always be created where one of these alternatives is chosen. 

The TDABC model represents a significant evolution in activity-based costing, providing a simpler and more precise methodology by using time as the main cost driver. The implementation of temporal equations allows for managing the inherent complexity of business processes without the need to create multiple cost objects, which facilitates the direct allocation of resources to cost objects. 

By capturing all possible combinations of activities, temporal equations simplify the model and enable a more detailed and realistic cost analysis. This approach not only optimizes costing accuracy but also facilitates the identification of idle capacities, helping organizations improve operational efficiency. 

In practice, it is advisable to start with simple equations and, based on needs and results obtained, increase complexity iteratively. Additionally, it is essential to clearly define the process scope and prioritize the most expensive processes to maximize the return on time and effort invested in model development. 

The great advantage of implementing TDABC lies in its adaptability and the possibility of using available variables for the calculation of drivers. Although using actual times may seem like a logical option, it is important to also consider idle capacity to obtain a complete and accurate view of operational efficiency.