# 12 Variance Analysis

Stijn Masschelein

While the previous chapter focused on how the budget is set, in this chapter I will show how an organisation can use the budget at the start of the year and compare it to the actual results. The purpose of this comparison, or variance analysis, is to provide feedback on the progress of the strategic plan during the budgeting period, assess the success of the strategic plan at the end of the period, and evaluate the performance of employees. The main advantage of the variance analysis is that the organisation can use the objective financial information to quantitatively estimate deviations from the plan and break the overall deviations down in smaller parts. It does not have to solely rely on subjective knowledge to evaluate the plan and the employees. Still, as we will see, subjective knowledge is going to be important in how the organisation should interpret the calculations.

The rest of this section builds on a case study that I have used when teaching this material: Easy Business Company Limited. The case describes how Sindy Sin starts a new recruiting agency in China in 1998. After economic reforms, China was in an economic boom until a relatively short-lived international financial crisis hits the economy. Sindy starts her business at the time where firms are still keeping close tabs on their cost structure but they are starting to hire again. Sindy’s business is one of many established and new recruiting agencies that provides services to match firms and job seekers.

Table 12.1: Planned Variable Costs and Revenues Easy Business
Category Revenue and Cost per Position
Revenue 2,000
Sales Bonus 300

## Level 1: Static Budget Variances

From the information above, we can calculate the planned budget and we are going to compare it to the actual costs and revenues that are given in the next table. The planned budget calculations are the planned positions filled times the variable revenues and costs or:

• $\textrm{revenues} = 250 \times 2,000$
• $\textrm{bonus} = 250 \times 300$
• $\textrm{advertisements} = 250 \times 100$

The difference between the budget and the actual results is calculated in the level 1 variance analysis and the differences are called static budget variances. The variances are denoted by (F) for favourable variances and (U) for unfavourable variance. Variances are favourable when actual revenues exceed the budget and when actual costs are lower than in the budget. Unfavourable variances happen when sales are lower and costs are higher than budgeted.

Actual Static Budget Variance Planned Budget (1) (2)  = (3) – (1) (3) 225 25 (U) 250 405,000 95,000 (U) 500,000 63,000 12,000 (F) 75,000 27,000 2,000 (U) 25,000 90,000 10,000 (F) 100,000 315,000 85,000 (U) 400,000 275,000 25,000 (U) 300,000 40,000 60,000 (U) 100,000

The actual operating income of 40,000 RMB is 60,000 RMB lower than in the planned budget. The level 1 analysis splits the differences up over the different revenue and cost components which helps Sindy to figure out why operating income is lower than expected. It is easy to see that part of the explanation is that Sindy could only fill 225 positions compared to the 250 positions she expected to fill. The total variable and fixed costs are lower than expected which dampens the effect of the decreased sales.The lower variable costs should not come as a surprise because she filled less positions the variable costs are expected to go down. In order to improve the profitability of Easy Business, Sindy will want to know whether the lower sales are the main reason for the drop in profits or whether there are also other explanations. The level 2 analysis in the next section will try to disentangle the sales drop from other factors.

## Level 2: Flexible budget variances.

The flexible budget calculates budgeted costs and revenues with the actual output for the year instead of the budgeted output. In other words, the flexible budget adjusts the original budget after the fact for the actual number of positions filled instead of the budgeted number of positions filled. This allows us to calculate at the end of the budgeting period what the budget would have been if we correctly predicted the actual output for the year. If we then find any deviations between the flexible budget and the planned budget, we know that these come from the sales volume. If we find any deviations between the flexible budget and the actual results, we know they cannot be because of the sales volume. This is exactly what Sindy wants to figure out after the static budget analysis in the previous section.

The flexible budget for the variable costs is calculated as 225 times the unit variable costs in Table 12.1. The fixed costs are by definition not expected to change when the output changes. As a result, the flexible budget fixed cost is the same as the budgeted fixed cost. The variable components of the variable budget can then be calculated as follows:

• $\textrm{revenues} = 225 \times 2,000$
• $\textrm{bonus} = 225 \times 300$
• $\textrm{advertisements} = 225 \times 100$

The resulting flexible budget is shown in column (3) of the next table.

Actual Flexible Budget Variance Flexible Budget Sales Volume Variance Planned Budget (1) (2) = (3) – (1) (3) (4) = (5) – (3) (5) 225 – 225 25 (U) 250 405,000 45,000 (U) 450,000 50,000 (U) 500,000 63,000 4,500 (F) 67,500 7,500 (F) 75,000 27,000 4,500 (U) 22,500 2,500 (F) 25,000 315,000 45,000 (U) 360,000 40,000 (U) 400,000 275,000 25,000 (F) 300,000 – 300,000 40,000 20,000 (U) 60,000 40,000 (U) 100,000

The difference between the planned budget and the flexible budget in column (4) is called the sales volume variance and it is a measure of how much of the variance between the actual operating income and the budgeted operating income can be explained by the difference in positions filled. The total effect of the drop in positions filled is a decrease in the contribution margin by 40,000 RMB which is two third of the total decrease in operating income. I want to highlight that it makes most sense to look at the total contribution margin and not at variable revenues and costs separately for the sales volume variance because the only change is the sales volume and all variable components are changing proportionally to the sales volume by definition.

The difference between the actual results and the flexible budget is called the flexible budget variance and is calculated in column (2) of Table 12.3. The flexible budget variance for the revenues indicates that even accounting for the lower than expected positions filled, Easy Business lost 45,000 RMB in sales compared to the the planned budget. This difference must be the result of a lower sales price per position filled. The actual price per position filled of 1,800 RMB [1] is indeed lower than the planned price of 2,000 RMB in Table 12.1. Similarly, we can see that the flexible-budget variance is favourable for the bonus which means that the average bonus per position is lower than planned. In contrast, the advertisement variance is unfavourable which means that the average advertisement cost is higher than the planned advertisement costs. These findings are also supported by the actual unit costs in Table 12.4. Finally, the variance for the fixed costs shows that Easy Business had 25,000 RMB lower fixed costs than expected. All in all, the results show that the remaining third of the variance between expected and actual income is driven by a lower than expected price per position filled which are partly offset by significant cost savings in fixed costs.

Table 12.4: Actual Variable Costs and Revenues Easy Business
Category Revenue and Cost per Position
Revenue 405,000 / 225 = 1,800
Sales Bonus 63,000 / 225 = 280

There are a number of possible explanations for the lower sales and the consequent sales volume variance. Maybe the competition of other recruiting agencies has been harsher than expected or the labour market was less hot than expected and firms did not have that many positions to be filled. Or the sales people were not willing to work hard enough to fill positions because they did not receive a high enough bonus (RMB 1,800 instead of RMB 2,000). While Sindy cannot directly control the competition and demand, she can control the bonus she pays. The variance analysis gives her a tool to evaluate whether it is worthwhile to increase the bonus for sales staff if it leads to more positions filled. Because the variance analysis is quantitative, she can directly compare the cost of increasing the bonus to the benefits of more sales. This is one of the key advantages of the variance analysis. It is easy to quantitatively compare costs and benefits.

## Level 3: Price variances and efficiency variances.

The level 3 analysis separates the flexible cost variance in a price variance and an efficiency variance. The price variance of a variable cost is the additional costs of an increase in the cost price per input. The efficiency variance quantifies the cost of consuming more of the underlying input per unit of output. In the case of Easy Business, the input is the number of words, the cost price per unit of input is the price per 10 words, and the unit of output is the number of positions filled. In other words, the price variance reflects the effect of an increase in the cost per word in the advertisement (not the additional cost of the advertisement itself!). The efficiency variance reflects the cost of using more or less words per advertisement. We use the information in Table 12.5 to calculate the price and efficiency variance.

The price variances in Table 12.5 are calculated as follows. First, we need to calculate the total number of inputs necessary, i.e. the total number of words in the advertisements. For the flexible budget, the actual numbers filled (=225) times the budgeted number of words per advertisement (=50) gives the total number of words. That is, under the assumptions of the flexible budget, Sindy expected to need 11,250 words for advertisements. The actual number of words used is calculated as 225 times 80 which equals 18,000. The efficiency variance is the difference between these two numbers, RMB 13,500, and it quantifies the total cost of using more words per advertisement, keeping the cost price per word the same. The price variance is the difference between the total actual cost and the actual number of units used, times the budgeted price per 10 words, RMB 9,000 [2]. It quantifies the decrease in the cost of advertisement because of the lower cost price per word. The variances split up the effect of using more words (efficiency variance) than expected at a lower cost per 10 words (price variance).

Actual Results Price Variances Actual Inputs Efficiency Variances Flexible Budget (1) (2) = (3) – (1) 225 225 225 18,000 – 18,000 6,750 (U) 11,250 15 20 20 27,000 9,000 (F) 36,000 13,500 (U) 22,500

There is more than one potential explanation for the efficiency variance. The positions may have been more complicated and needed more words to advertise. Or alternatively, Sindy was not careful in crafting the advertisements and used too many words. The price per words might have been lower because Sindy found a cheaper outlet to put the advertisements in and the change of outlet could also be the reason for the lower number of positions filled. A variance analysis cannot attribute the variance to one of these causes but what it can do is quantifying whether a change in the original plan was good or not. In this case, whether the favourable price variance in the advertisement was worth the unfavourable sales-volume variance. The latter is RMB 40,000 (U) versus a RMB 9,000 (F) price variance. If Sindy moved to a cheaper outlet than her savings are definitely not worth the loss of 25 customers.

As outsiders it will always be difficult for us to understand, what the deep underlying reasons are for the budget variances. These questions can be better answered by managers and employees with specific operational knowledge. For instance, Sindy might have heard from applicants that they learn about the position through other means than the outlet and they normally only check the traditional newspapers. A common refrain of this book is that formal systems, like budget variance analysis, always need to be complemented with specific knowledge from employees. The question is not whether objective or subjective knowledge is superior. Most meaningful decisions will involve both types of knowledge.

## Budgets, Variance Analysis, and on-Financial Measures.

I want to add one little addendum to this chapter. Traditional management accounting tools such as budgets have often been criticized for being too focused on financial measures such as profits and cost prices. The variance analysis in the previous section shows that judicious use of budget variances is not just about profits and variances. It can also help to link cost overruns to operational measures and help identify the causes of bad performance. This book will further discuss the Balanced Scorecard as a tool to
explicitly include non-financial measures and causal links in management accounting systems. The existence of more modern tools like the Balanced Scorecard should not overshadow that budgets can already incorporate productivity measures like the number of words per advertisement.  The strength of variance analyses is that it allows to compare the size of different variances to make explicit trade-offs.

1. We can calculate the unit sales price as $\frac{405,000}{225}$
2. $18000 \times \frac{(20 - 15)}{10} = 36000 - 27000$