1. Day 17
Variance Analysis

2. “Variances”
The basic objective is to analyze the results of operations (“actuals”) to the expected or plan outcomes to better understand performance
Useful feedback if we can identify the root cause
Can also be used to measure performance and for compensation

3. Some Caveats
Variety of approaches (1, 2, 3 and 4 variance are all widely used)
Customizable, no hard and fast rule about which approach to use
Complex, we only scratch the surface
Names used to describe the same computation may vary across authors/firms, important to know the specifics of each firm’s system

4. MB – Actuals = BQ * BP – AQ * AP
How?
Key: compare Master Budget (MB) to Actuals in stages
Let’s break the numbers down a bit:
MB = Budgeted Quantity (BQ) * Budgeted Price (BP)
Actuals = Actual Quantity (AQ) * Actual Price (AP)
The difference between the two can be written as:
MB – Actuals = BQ * BP – AQ * AP
All variance computation systems try to rewrite this difference in a variety of informative ways.

5. Static (Master) Budget
An exhibit
Consider the Sonnet example in HDR
Line item
Static (Master) Budget
Revenue
9,000,000
COGS
Direct material
(2,250,000)
Direct labor
(60,000)
Less Ending Inventory -
(2,310,000)
Gross Margin
6,690,000
Direct Marketing
(450,000)
Fixed Overhead
(800,000)
Operating Income
5,440,000
Actual Results
8,692,500
(2,280,000)
(69,540) -
(2,349,540)
6,342,960
(356,250)
(810,000)
5,176,710
The master budget
Actuals
We want to analyze the difference in each line item.

6. Step 1: “Flex” the Master Budget
The difference
MB – Actuals = BQ * BP – AQ * AP
can further be written as:
(BQ * BP – AQ*BP) + (AQ*BP - AQ*AP)
We have just subtracted AQ*BP in the first parenthesis and added it back in the second!
The new term, AQ*BP, is an important “What if?”
What would the firm have expected its revenues and costs to be at the actual level of activity?

7. An important detail
Since the master budget is driven by units of output, computing AQ*BP for revenues is easy.
By contrast, computing the corresponding flexible budget “expectations” for variable costs requires just a bit more (easy to mess this up, unless one goes step by step )
First, determine the quantity of input expected to be used given the actual level of output: this is the flexible budget quantity of inputs (FBQI)
Then, compute the budgeted cost of this quantity

8. THIS IDENTITY IS IMPORTANT, SO MAKE SURE YOU “GET” IT !!
The new character FBQI
The variable inputs required to produce the actual quantity of output, FBQI (the flexible budget quantity of inputs), can be computed as
FBQI = AQO*I/O Ratio
Where I/O Ratio is the Budgeted number of input units required per unit of output
By contrast, note that AQI ≡ AQO * AI/OR.
THIS IDENTITY IS IMPORTANT, SO MAKE SURE YOU “GET” IT !!

9. Back to the Flexible Budget
Given that we know FBQI, the flexible budget amount for the input cost is simply:
FBI = AQO*I/O Ratio*BPI
With this new understanding of the flexible budget let us briefly return to the Sonnet example and compare the Master and Flexible Budgets …

10. Static (Master) Budget
A second exhibit
Compare the master and flexible budgets:
Line item
Static (Master) Budget
Revenue
9,000,000
COGS
Direct material
(2,250,000)
Direct labor
(60,000)
Less Ending Inventory -
(2,310,000)
Gross Margin
6,690,000
Direct Marketing
(450,000)
Fixed Overhead
(800,000)
Operating Income
5,440,000
Flexible Budget
8,550,000
(2,137,500)
(57,000) -
(2,194,500)
6,355,500
(427,500)
(800,000)
5,128,000
“Master”
“Flexible”
This difference in Operating Income is the “volume” variance, i.e. the impact of the difference between budgeted and actual volume of activity. We would like to know why the volume varied.

11. Step 2: Flexible Budgets vs. Actuals
Recall the flexible budget amount for input costs:
FBI = AQO*I/O Ratio*BPI
Notice that both I/O ratio and BPI are budgeted amounts. This means the actual input costs can differ from the flexible budget for two reasons:
the actual input output ratio (AI/OR, i.e., actual physical usage) may not be same as the Budgeted usage, i.e., AI/OR ≠ I/OR
the actual price of inputs may differ from the Budgeted price of inputs AP ≠ BPI

12. Step 2: Price and Efficiency
Keeping this in mind, for variable costs, we can rewrite the difference between the flexible budget and the actual outcomes as:
FBI – Actuals = FBQI * BP – AQ * AP
= (FBQ-AQ)*BP – AQ*(AP-BP)
WE HAVE AGAIN SUBTRACTED AQ*BP IN THE FIRST PARENTHESIS AND ADDED IT BACK IN THE SECOND!
This is the key substitution to not mess up!!! 
The first term is called the efficiency (or usage) variance, the second is called the price variance.
Does this usage make sense?

13. Flexible Budget Variance
The final exhibit
All of which leads directly to:
Line item
Flexible Budget
Flexible Budget Variance
Actual Results
Price Variances
Efficiency Variances
Revenue
8,550,000
142,500 F
8,692,500
COGS
Direct material
(2,137,500)
(142,500) U -
(2,280,000)
Direct labor
(57,000)
(1,140)
(11,400)
(69,540)
Less Ending Inventory
(2,194,500)
(2,349,540)
Gross Margin
6,355,500
6,342,960
Direct Marketing
(427,500)
71,250
(356,250)
Fixed Overhead
(800,000)
(10,000)
(810,000)
Operating Income
5,128,000
60,110
5,176,710
At which point, we’re ready to move on to the analysis of the volume and overhead variances, (as discussed, for example, in Chapter 8 of HDR)

14. How do we recall all this?
One thing at a time.
MB = BQO * I/O ratio * BPI
Vs.
FBI = AQO * I/O Ratio *BPI
AQO * AI/O Ratio * BPI
AQO * AI/O Ratio * API
Equations
Volume
Variance
Efficiency
Variance
Price
Variance