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Exam

The role of this appendix is to provide a somewhat more formalized

methodology for the calculation offlexible budget variances.

FLEXIBLE BUDGET EXPENSE VARIANCES

The first step in flexible budgeting is to establish the flexible budget for

the actual output level. That is, we must determine what we would have

expected to spend if we had known in advance the output level that

would actually occur. Because of variable costs, we would have

budgeted more resources if we knew service levels would be higher andless resources if we knew they were going to be lower. For example,

consider an excerpt from the variance report for the Millbridge High

School for August.23

Town of Millbridge High School August Variance Report

Actual

Budget

Variance

Books

$120,000

$100,000

$20,000 U

The actual spending was $120,000. The budgeted cost was $100,000.

Suppose that the budget assumed that there would be 2,000 students,

but 2,100 students enrolled. Assuming that the purchase of textbooks

would be expected to vary in direct proportion with enrolled students,

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the budget called for planned spending of $50 per student (i.e., $50

2,000 students = $100,000).

For 2,100 students at $50 per student, $105,000 would have been

budgeted for supplies. This is the flexible budget. It is the amount the

school would have expected to spend had the actual number of students

been known. The original budget was $100,000. The flexible budget,

which adjusts for the actual volume, is $105,000. The actual amount

spent was $120,000:

The difference between the original budget and the actual amount spent

is the total variance. This is still $20,000 unfavorable. The $5,000

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difference between the original budget and the flexible budget is the

volume variance. This volume variance is unfavorable because the

flexible budget requires more spending than was expected in the

original budget. The increased number of students may be considered to

be good or bad, depending on the attitudes of the people in the town.Regardless, from a variance reporting standpoint, the convention is to

consider increased spending to be unfavorable. Managers should guard

themselves from assuming that unfavorable variances are always bad

events.

The difference between the flexible budget and the actual amount spent

is referred to as the flexible budget variance. It simply represents all

other causes, aside from the volume variance. In this case the flexible

budget variance is $15,000. It is unfavorable, since actual spending was

$15,000 more than the flexible budget, which is the expected spending

for the actual number of students enrolled. If the flexible budget

variance and volume variance are combined, we get the total variance

for the line-item. Note that if one of these variances was favorable and

the other was unfavorable, they would offset each other, like positive

and negative numbers.

23Note that in preparation for the new school year, Millbridge orders most of its

books during August of each year. There are many other lines in the variance

report, but we will focus on just the line-item for textbooks.

FLEXIBLE BUDGET NOTATION

At this point in the analysis, we do not know much about the flexible

budget variance. It is a combination of the price and quantity variance.

We need to be able to calculate each of these two variances. To do this

we will introduce some notation. The letterAis used to refer to an

actual amount. The letterBis used to refer to a budgeted amount. The

letter Pstands for a price or rate, and the letter Qstands for a quantity.The letter iis used to stand for an input and the letter oto stand for an

output or workload.Inputsare resources consumed. These can be labor

hours, or units of supplies, or any other resource the organization pays

for. Outputsare a measure of the volume of goods or service being

produced. These can be the number of students or the number of meals

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or the number of patients.

The notation is combined to form six key variables. Pistands for the

price of the input, such as $20 per textbook. Qostands for the total

quantity of output, such as the number of students.Qi

stands for thequantity of input needed to produce one unit of output. For example, we

might expect that each year the school will buy, on average, 2.5

textbooks per pupil. The letterBin front of other letters indicates a

budgeted amount. The letterAin front of other letters indicates an

actual result. The definitions of the notation can be formalized as

follows:

BPi:

budgeted price per unit of input

BQi:

budgeted quantity of input for each unit of output

BQo:

budgeted quantity of output

APi:

actual price paid per unit of input

AQi:

actual quantity of input for each unit of output produced

AQo:

actual quantity of output

Suppose that for the Town of Millbridge High School, these six items

had the following values:

BPi:

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$20 per textbook

BQi:

2.5 textbooks per student

BQo:

2,000 students

APi:

$22 per textbook

AQi:

2.5974 textbooks per student

AQo:

2,100 students

To calculate the price, quantity, and volume variances, it is necessary to

get these six pieces of information. The three budgeted items are

generally available from the data that were used in making the originalbudget. The three actual pieces of information should be available in

most organizations. School systems will know the actual number of

students, the AQo. Also, if you buy books, you should have a record of

how many books were purchased and how much was paid for them.

The actual price paid for each book is not needed. If we know how

many books we purchased and how much we paid in total for books, we

can divide the total cost for books by the number of books to find the

average price paid per book, the APi. Similarly, we do not need to

know how many books we acquired for each student. If we know how

many books we actually purchased and how many students we actually

had, we can divide to find the actual number of books purchased per

student, on average, the AQi.

The first step in these data is to calculate the original budget in terms of

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the notation. The original budget is simply the expected number of new

books per student, multiplied by the expected cost per book, multiplied

by the expected number of students. Using our notation, this can be

shown as follows:

Original Budget

BQi BPi BQo

2.5 $20 2,000

$100,000

That is, BQi, the budgeted quantity of input per unit of output, is 2.5

new books per student; BPi, the budgeted price per book is $20; andBQo, the budgeted quantity of students, is 2,000. The total budgeted

amount for textbooks is $100,000.

The next step is to find the flexible budget. Recall that the flexible

budget is the amount that one would have expected to spend if the

actual number of enrolled students had been known in advance.

Therefore, leave the BQi at the budgeted 2.5 books per student, and

leave the BPi at the budgeted $20 per book. The only change is from a

BQo of 2,000 students to a new AQo of 2,100 students. The flexiblebudget can be calculated as follows:

Flexible Budget

BQi BPi AQo

2.5 $20 2,100

$105,000

The difference between the original budget and the flexible budget is

caused by a difference in the number of students. Other than that, the

calculations are the same. The originally budgeted amount of $100,000

can be compared with the flexible budget amount of $105,000 to

determine the volume variance of $5,000 U. Since the number of

students is higher than expected, cost will be higher than expected. This

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will give rise to an unfavorable variance. The comparison between the

original budget and the flexible budget can be shown as follows:

We can also calculate the flexible budget variance that we found earlier,

by comparing the flexible budget to the actual spending. The actual

amount spent is simply the product of the number of books purchased

per student, the cost per book, and the number of students, as follows:

Actual

AQi APi AQo

2.5974 $22 2,100

$120,000

Note that to calculate the actual cost, the actual number of books per

student, the actual price per book, and the actual number of students isused. Also note that the actual number of books per student is based on

the actual number of books acquired in total, divided by the actual

number of students. The difference between the flexible budget and the

actual amount spent was earlier described as the flexible budget

variance:

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The volume variance and the flexible budget variance add up to the

total variance for the line-item, as shown earlier. Using our notation,

that would appear as follows:

To this point, we have the same information as we had before we

started using notation. Now, however, we can go further by determining

the price and quantity variances. In order to determine these variances,

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it is necessary to derive a subcategory. This subcategory is simply a

device to allow for separation of the flexible budget variance into two

pieces: the price variance and the quantity variance. The subcategory is

defined as the actual quantity of input per unit of output, multiplied by

the budgeted price of the input, times the actual output level. In terms ofthe notation, the subcategory can be calculated as follows:

Subcategory

AQi BPi AQo

2.5974 $20 2,100

$109,091

If the subcategory calculation is compared with the actual costs, the

price variance can be determined as follows:

Note that the actual and subcategory calculations both use the AQi and

the AQo. The only difference between the two calculations is that theactual uses the APi whereas the subcategory uses the BPi. Since the

price is the only element that differs, it must be responsible for the

$10,909 difference between the two calculations. This $10,909 variance

is because books cost $22 on average, instead of $20 as expected.

To determine the quantity variance, it is only necessary to compare the

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subcategory with the flexible budget:

In comparing the subcategory and the flexible budget calculations, we

note that both use the BPi and the AQo. However, the subcategory uses

AQi, whereas the flexible budget uses BQi. So, the $4,091 difference

that is observed is the result of the fact that the number of books

purchased per pupil, on average, differed from the expected number.

Thus, we have a quantity difference. Note that this quantity difference

has nothing to do with the number of students but rather with the

number of books per student.24

Reviewing the price and quantity variances, we can look at how they

together comprise the flexible budget variance:

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Notice that adding the price variance of $10,909 U and the quantity

variance of $4,091 U results in the flexible budget variance. Recall that

the flexible budget variance and the volume variance add up to the total

variance. Figure 8-A-1shows that the three individual variances

price, quantity, and volumeadd up to the total variance for the line-

item.

FIGURE 8-A-1 Flexible Budget Variance

Analysis Model

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24

In this example we have constructed a subcategory that uses the actual quantity ofinputs per unit of output and the budgeted price of inputs. This is an arbitrary

convention. We could have instead used the budgeted quantity of inputs per unit of

output and the actual price of inputs. We would still generate a price and quantity

variance if this switch was made. However, there is an interaction effect of price

and quantity, and the answers may vary slightly if the alternative approach is used.

Recall that without flexible budget variance analysis, the total variance

for the line-item would be the only piece of information available for

analysis. There was an unfavorable variance of $20,000. Without

additional information, this variance might be attributed to the increasein the number of students. Using Figure 8-A-1, it is possible to

determine that of this total variance, $5,000 was caused by the increase

in the number of students. However, $4,091 was caused by an increase

in the number of books per student, and $10,909 was caused by either

an increase in book prices or perhaps a movement to acquiring

different, more expensive books than had been planned. We would

certainly want to investigate both the quantity and price variances to

determine more specifically why they occurred and whether any

remedial action is necessary to avoid cost overruns in the future.

In considering Figure 8-A-1, note that this calculation would need to be

done for each line-item for each department. Although that might seem

to be a large task in large organizations, it is readily converted to a

simple computer spreadsheet program. Thus, the major effort required

to calculate price, quantity, and volume variances is to input into the

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computer the six basic pieces of information needed for each line-item

(i.e., BQi, BPi, BQo, AQi, APi, and AQo).

It is also important to realize that the price, quantity, and volume

variances are merely components of the total variance for any line-item.

In Figure 8-A-1, the total variance is $20,000. Note that if we compare

the actual amount spent, $120,000, with the original budget of $100,000

in that figure, the difference is the $20,000 total variance. As we try to

understand why that total amount was incurred, the variance has been

divided into components. Note that the price variance of $10,909, plus

the quantity variance of $4,091 plus the volume variance of $5,000 add

up to the total variance.

It sometimes is not obvious whether a variance is favorable or

unfavorable. Looking at Figure 8-A-1, an easy rule of thumb is that as

one moves from the right side toward the left. larger numbers on the left

indicate unfavorable variances. If the flexible budget amount is larger

than the originally budgeted amount, the volume variance is

unfavorable. If the subcategory is greater than the flexible budget, the

quantity variance is unfavorable. This is true because as one moves

from the original budget toward the left, movement is toward the actual

result. If the actual result is larger than the original budget, then more

was spent than budgeted. Such higher spending indicates an

unfavorable variance.

(Financial Management for Public, Health, and Not-for-Profit

Organizations, 3rd Edition. Pearson Learning Solutions 14).