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Day 17 Variance Analysis.

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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


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