【正文】 aging production costs as production volume increases 11 Variance Analysis Agenda ?What is variance analysis? ?Linear variance – Ice Cream Co. ?Two ponent variance analysis – Jesse’s Brewery ?Variance analysis with more than two ponents – Boston Video ?Key takeaways 12 Variance Analysis Situation: ?Jesse’s Brewery produces highquality beers which it sells in cases ?In the past year, Jesse’s Brewery has experienced 15% revenue growth. During the same time, sales volumes and prices have both increased Question: ?Jesse’s Brewery would like to understand what percent of the revenue increase es from the increase in sales volumes, and what percent from the increase in price Two Component Variance Example Jesse’s Brewery (1 of 6) 13 Variance Analysis 1 9 9 7 1 9 9 8$ 1 7 6 .5$ 2 0 3 .5$0$ 5 0$ 1 0 0$ 1 5 0$ 2 0 0$ 2 5 0Jesse39。s Brewery Annual Revenues (Millions of Dollars)Two Component Variance Example Jesse’s Brewery (2 of 6) Case Price: Cases Sold: $ $ What percent of the $27MM increase in revenue is due to – the price increasing? – the volume sold increasing? – both the price and volume sold increasing? ? this is covariance, where part of the variance is not easily attributable to a single variable 14 Variance Analysis Volume 1998 Revenue $ 1997 Revenue Price Variance (Part of revenue change attributable to price) $ (1997) $ (1998) (1998) (1997) Price Volume Variance (Part of revenue change attributable to volume) Covariance (part of revenue change attributable to change in both volume and price) The best way to approach variance analysis problems is to use the rectangle diagrams to intuitively understand how the changes in the two variables account for the change in the overall quantity. Two Component Variance Example Jesse’s Brewery (3 of 6) 15 Variance Analysis Volume 1998 Revenue (P2 x V2) 1997 Revenue (P1 x V1) Price Variance (Part of revenue change attributable to price) P1 (1997) P2 (1998) V2 (1998) V1 (1997) Price Volume Variance (Part of revenue change attributable to volume) Co variance Step 1: Volume Variance = (V2 V1) x P1 Step 2: Price Variance = (P2 P1) x V1 Step 3: : Covariance = (V2 V1) x (P2 P1) Step 4: Allocate covariance to volume and price variance based on the proportion of the total for each variance ., if: volume variance = $2M price variance = $1M covariance = $.5M then % of $.5 is added to the volume and % is added to the price A fourstep process leads to the solution. Two Component Variance Example Jesse’s Brewery (4 of 6) 16 Variance Analysis Jesse39。s Brewery 1997 Variance Data Price per case $ $ Number of cases sold (in MM) .5 Revenues (in $MM) $ $ Step 1: Price Variance $ Step 2: Volume Variance $ Step 3: Covariance $ Revenue variance excluding covariance $ Proportions for assigning covariance Price Volume Assignment of covariance to Price Variance $ to Volume Variance $ Adjusted Variances Price Variance Volume Variance (P1) (P2 P1) (V1) (V2 V1) $ (P1 x V1) ( ) ( ) (P2P1)x(V2V1) (+) (%) (%) 63% 34% 3% 65% 35% () () () () () $ (P1 x V1) 1998 $ $ (P2) (V2) $ (V2 x P1) $ (P2 x V1) $ $ (+) (+) Variance % Here is an example of an annotated spreadsheet to determine variance. Two Component Variance Example Jesse’s Brewery (5 of 6) 17 Variance Analysis Price variance: Volume variance: Covariance: $ $ $ Proportions are 65% 35% 65% 35% to price variance $ to volume variance $ + + $ $ Price $ $ Volume Total variances: (65%) (35%) If price and volume variances are calculated correctly, then we can take their proportions to allocate covariance. Two Component Variance Example Jesse’s Brewery (6 of 6) 18 Variance Analysis Negative Covariance new (1998) (1997) $ (1997) $ new (1998) Volume Price Even if one variable decreases, the formula applies the same way. The only difference is that price va