Variance Analysis complete solutions correct answers key

 

NOTE ON VARIANCE ANALYSIS

 

Variance analysis is an analytical process for evaluating and explaining business performance by comparing it to an accepted benchmark. It is an important component of a business’ Management Control Cycle as it provides information about what is happening in the business (both good and bad) upon which management can take action.

 

Consider the following simple example:

 

A trip to Grandma’s house in Washington D.C.

Grandma offered to pay for your trip … but she’s tough! Explain to Grandma why it cost you $4.00 more than you had planned to drive to Washington from Boston:

 

                           Miles                  Gallons Gallons

                           Driven   X     per Mile   =               Used           X    $/Gallon   = Total Cost

 

PLAN               500                     1/20                    25                       $2.00                  $50.00

 

ACTUAL         540                     1/18                    30                       $1.80                  $54.00

 

VARIANCE                                                                                                              $ (4.00) Unfavorable

 

 

In this example, the process is the development of a plan and measurement of actual results against that plan. The plan becomes the benchmark. In order to explain the unfavorable $4.00 extra cost, you must evaluate each of the variables impacting that cost versus the benchmark.

 

 

The variables that need to be examined fall into 3 categories:

 

VOLUME: Typically units in a manufacturing environment but, more broadly, whatever measure of output that is meaningful for the analysis. For instance, miles would be the volume variable in Grandma’s; hours (or # billable professionals x average hours per period) would be the volume variable in a professional firm (consulting, law etc.).

 

MIX: When more than one product or service is provided, the percentage each represents of total volume is its relative mix. For instance, if plan is to sell 60 oranges and 40 apples, the planned mix is 60% oranges and 40% apples. If actual results show sale of 90 oranges and 30 apples, the actual mix is 75% oranges and 25% apples. The increase in total units sold from plan of 100 to actual of 120 would be explained in the volume variable above. There is no mix variable in Grandma’s.

 

RATE: There are many types of rate variables that can be used to explain variances. In Grandma’s, there is a gasoline utilization rate – gallons per mile – and a gasoline cost rate – $ per gallon. Other rates may include market share, sales price, labor rate per hour, material used per unit, etc.

 

 

 

 

 

This leads to three basic rules of variance analysis:

 

1.      Always change variables in the sequence of VOLUME, MIX, RATE

 

2.      Change only ONE variable at a time; once changed it stays at the new number

 

3.      When multiple rates exist, change the $ rate last so you are pricing out actual quantity

 

The following chart may help visualize the above rules:

 

                                        VOLUME          MIX              RATE 1            RATE 2

START                          Plan                   Plan                   Plan                   Plan

Step 1 Volume  Actual                Plan                   Plan                   Plan

Step 2 Mix                      Actual               Actual                Plan                   Plan

Step 3 Rate 1                 Actual               Actual               Actual                Plan

Step 3 Rate 2= END     Actual               Actual               Actual               Actual

 

** We will defer mix variances until later in the semester and focus on volume and rate variances for now.

 

There are two approaches to doing variance analysis, both of which yield the same result.

 

The first approach follows the framework in the above chart. It changes the variable to actual and re-computes the total cost. It then calculates the change in total cost from the prior line giving the variance caused by that variable. Applying this methodology to your trip to Grandma’s in Washington:                                                                                                                                                                                                    

                  VOLUME                 RATE 1       RATE 2           TOTAL                       VARIANCE   

START             500             x            1/20          x   $2.00        =            $50.00

 

Step 1                540             x             1/20          x   $2.00         = $54.00          $(4.00) Unfav.     Volume                          

Step 2                540             x             1/18          x   $2.00         = $60.00        $(6.00) Unfav.     Gals/Mile

 

END                  540                     1/18                    $1.80         = $54.00        $ 6.00   Fav.        $/Gallon

 

                                                     TOTAL VARIANCE                             $(4.00) Unfav.

 

The second approach uses the difference in each variable to calculate the variance directly:

 

Volume:            (500 – 540)        x         1/20   x           $2.00                 =  $(4.00) Unfav.         Volume

 

Gals/Mile:         540 (actual)       x (1/20 – 1/18) x             $2.00                  =  $(6.00) Unfav.         Gals/Mile

 

$/Gallon:           540                     x 1/18 (actual) x ($2.00 – $1.80)              =  $ 6.00   Fav.          $/Gallon

 

TOTAL VARIANCE                                     $(4.00)  Unfav.

 

The results are identical; the only difference is where the variance is calculated.

 

 

 

Now use the results of the variance analysis to tell Grandma what happened and WHAT ACTIONS you would take next time to avoid the cost overrun:

                           What Happened                                                    Corrective Action Plan

1.

 

 

2.

 

 

3.

 

 

                                                     “BRACKETS ARE BAD”

 

Favorable variances- spending less than plan, bringing in more revenue/profit than plan – are POSITIVE values.

 

Unfavorable variances- spending more than plan, bringing in less revenue/profit than plan – are NEGATIVE values. They are best displayed inside brackets  ( XXX.XX)

 

In order to make the variance calculations come out with the correct +/- signs, you need to use the following conventions:

 

Revenue/profit related items use  Actual  –  Budget

 

Expense related items use  Budget  –  Actual

 

 

 

 

 

Please make sure you label your variances with a “U” for Unfavorable and an “F” for Favorable

 

 

 

Process for doing Variance Analysis

Variance analysis is most commonly done between a budget and actual results – how did you do versus budget? There are many other pairings, however, for which variance analysis can be useful:

• Budget and a current forecast
• Strategic plan and budget
• Current forecast to next year’s budget
• Current actual results to prior period actual results

 

To do variance analysis, it is helpful to consider a six step process:

 

• 1. Set the benchmark (budget, strategic plan, etc.)
  2. Record the “actual” results to compare to benchmark
  3. Compute the variances
  4. Assign responsibility
  5. Determine causes of significant variances (both good and bad)
  6. Take corrective action

 

Let’s define the primary variances we will work with at this point in the semester:

 

Sales Volume Variance: Change in “unit” volume x budget contribution margin per unit. This tells you how much more or less contribution margin you should have earned as a result of the change in volume from budget.

 

Sales Price Variance:  “actual” volume x change in price. This tells you the impact your pricing actions had on the actual volume of units.

 

Material Usage Variance:  “actual” volume x change in quantity used per unit x budget cost per unit. This tells you how much more or less you should have spent on materials you actually used versus budget to make your product.

 

Material Cost Variance:  “actual” volume x “actual” quantity used per unit x change in cost per unit. This tells you how much more or less you actually paid versus plan for the materials you actually used.

 

Labor Usage (Efficiency) Variance:  “actual” volume x change in amount of time used per unit x budget cost per unit of time. This tells you how much more or less you should have spent on labor you actually used versus budget to make your product.

 

Labor Cost Variance:  “actual” volume x “actual” time used per unit x change in cost per unit of time. This tells you how much more or less you actually paid versus plan for the labor you actually used.

 

Let’s work through a simple variance analysis problem to demonstrate the six step process for doing variance analysis:

 

Sarah’s Soaps. Sarah makes hand molded soap bars for sale to gift stores in packages of 12 bars.    Her business performance      last month was:                                                                                                                                                                                      Budget (Step 1)                  Actual (Step 2)         Favorable(Unfav)

 

Units (Dozens)                   10,000                         11,000                        1,000   F

 

Revenue                                      $100,000                         $104,500                         $  4,500   F

Materials                                         20,000                         21,780                       (1,780)  U

Direct Labor                                   16,000                         18,150                       (2,150)  U

Contribution Margin    $  64,000                       $  64,570                       $     570   F

 

Revenue/Dozen                           $10.00                             $  9.50

Material Pounds/Dozen                 4.0                               4.4

Material $/Pounds                      $    .50                                      $    .45

DL Hours/Dozen                            0.20                                          0.22

DL $/Hour                                  $  8.00                           $  7.50

 

At first glance, it appears that Sarah did well, earning $570 more contribution margin than budget. But let’s do some variance analysis (Step 3) to see what really happened.

 

Sales Volume Variance =    (11,000 – 10,000) x ($10.00 – $3.60)           = $ 6,400   F  (note: Actual – Budget)

 

Sales Price Variance     =     11,000  x ($9.50 -$10.00)                    = $(5,500) U                   “           “

 

Material Usage Variance = 11,000  x (4.0 – 4.4) x $0.50                         = $(2,200) U  (note: Budget – Actual)

 

Material Cost Variance =   11,000  x 4.4 x ($0.50 – $0.45)                    = $ 2,420   F                          “             “

 

DL Usage/Effic. Var.    =    11,000  x (0.20 – 0.22) x $8.00             = $(1,760) U                   “        “

 

DL Cost Variance        =     11,000  x 0.22 x ($8.00 – $7.50)       = $ 1,210   F                “           “

 

Total of ALL Variances MUST equal $570 F !!!                                      = $    570   F    Ah hah! It does!!!!

 

So who does Sarah hold accountable for the results (Step 4)? Sales & Marketing is usually responsible for customer relationships and therefore both number of units sold to customers and price. How did they do?

 

Sales & Marketing:       Sales Volume Variance                           $ 6,400  F

Sales Price Variance                                             (5,500) U

Total                                                         $   900   F

 

They dropped the price by $0.50 per dozen and saw some favorable elasticity – an extra 1,000 units – resulting in a net improvement for the business of $900 – looks like a good job for the month.

 

Manufacturing usually has responsibility for product cost including both the acquisition of resources (raw material and direct labor in this case) and manufacturing operations. The purchasing department within manufacturing would be specifically responsible for acquisition while the production department within manufacturing would be responsible for manufacturing operations. How did they do?

 

Purchasing:                   Material Cost Variance                                        $ 2,420  F

DL Cost Variance                                                    1,210  F

Total                                                         $ 3,630  F

 

Production:                    Material Usage Variance                                     $(2,200) U

DL Usage/Efficiency Variance                 (1,760) U

Total                                                         $(3,960) U

 

So what happened? We need to go talk to the three departments and try to find out (Step 5). Clearly both Sales & Marketing did well while production had a bad month. Each department needs to explain what happened. Marketing should explain why they dropped the price – a lucky guess? Or based on a thorough market study? Sales should be able to discuss customer reaction to the price reduction – are they stocking up at the lower price and potentially reducing future purchases? Purchasing should be able to explain what was happening in the market place to drive costs per unit down – were they able to maintain adequate levels of material quality and DL staff experience? Production needs to explain why they were significantly less efficient than budget – did machines break down? Were DL less experienced than necessary? Was raw material quality off causing production and scrap problems?

 

Then, based on findings from your interviews and analysis, take corrective actions (Step 6). These will obviously depend on the results of your analysis.

 

One question many students have is “why don’t the variances add up to the total variance for each line item in the Income Statement?” The reason is quite simple. Let’s use the total material variance of $(1,780) as an example. There are three components making up this variance:

 

Volume: Sarah shipped an extra 1000 units x 4.0 pounds/unit x $0.50/pound                   = $(2,000) U

Usage: Prod’n used 4.4 pounds/unit vs. 4.0 (extra 0.4) x $0.50/pound x 11,000 units        = $(2,200) U

Cost: Purch. paid $0.45/pound vs. $0.50 (saved $0.05/pound) x (4.4 x 11,000) pounds    = $ 2,420   F

Total Material Variance                               $(1,780)  U

 

The usage and cost variances were calculated above; the volume variance is part of Sales Volume Variance.

 

 

 

Problem Assignment

                          

Let’s expand our view of Sarah’s Soaps with some additional information.

 

SARAH’S SOAPS VARIANCE ANALYSIS

 

 

Budget

Actual

Fav(Unfav)

Market Size(12 Packs)

50000

60000

10000

Sarah’s Soap 12 Packs

10000

11000

1000

Share %

20.0%

18.3%

-1.7%

 

 

 

 

Revenue

100000

104500

4500

Material

20000

21780

(1780)

Direct Labor

16000

18150

(2150)

Variable Mfg OH

15000

13860

1140

Contribution Margin

49000

50710

1710

Manufacturing

10000

11000

(1000)

Marketing/Advertising

8000

10000

(2000)

Engineering

10000

8000

2000

Administration

10000

10500

(500)

Profit

11000

11210

210

 

 

Specifically, we learn:

 

• The market for Sarah’s soap is budgeted to be 50,000 dozen per month (therefore she is budgeting a 20% market share – 10,000/50,000). The actual market for the month turned out to be 60,000 dozen
• In addition to variable material and direct labor costs, Sarah’s manufacturing operations incurs variable overhead – utilities for machinery, fringe benefits for direct labor, etc. She has budgeted this at 0.5 machine hours per dozen at a cost of $3.00 per machine hour; for the month. 0.45 machine hours were used per dozen at an actual cost of $2.80 per machine hour
• Sarah also has four categories of fixed costs with budget and actual results as follows:

Budget           Actual            

Manufacturing

10000

11000

 

Marketing/Sales

8000

10000

 

Engineering

10000

8000

 

Administration

10000

10500

 

 

Using the blank template posted on Blackboard, re-compute all the variances for Sarah’s Soaps for the month. Note: /\ in the template means change in value. Additional variances you will need to calculate are:

• Market size variance
• Market share variance (together these two equal sales volume variance)
• Variable OH usage/efficiency variance (similar to DL usage/efficiency variance)
• Variable OH cost variance (similar to DL cost variance)
• The four fixed cost variances (for this class, we will use just the raw differences as above)

 

Explain the $210 variance for the month and recommend possible corrective actions using the six step process.