End of Chapter: Cost Allocation, Customer-Profitability Analysis, and Sales-Variance Analysis

Problem for Self-Study

The Payne Company manufactures two types of vinyl flooring. Budgeted and actual operating data for 2020 are as follows:

	Static Budget			Actual Results
	Commercial	Residential	Total	Commercial	Residential	Total
Unit sales in rolls	20,000	60,000	80,000	25,200	58,800	84,000
Contribution margin	$10,000,000	$24,000,000	$34,000,000	$11,970,000	$24,696,000	$36,666,000

In late 2019, a marketing research firm estimated industry volume for commercial and residential vinyl flooring for 2020 at 800,000 rolls. Actual industry volume for 2020 was 700,000 rolls.

Required

Compute the sales-mix variance and the sales-quantity variance by type of vinyl flooring and in total. (Compute all variances in terms of contribution margins.)
Compute the market-share variance and the market-size variance.
What insights do the variances calculated in requirements 1 and 2 provide about Payne Company’s performance in 2020?

Solution

1. Actual sales-mix percentage:

$\begin{array}{rcl} Commercial & = & 25,200 \div 84,000 = 0.30, or 30% \\ Residential & = & 58,800 \div 84,000 = 0.70 or 70% \end{array}$

Budgeted sales-mix percentage:

$\begin{array}{rcl} Commercial & = & 20,000 \div 80,000 = 0.25, or 25 % \\ Residential & = & 60,000 \div 80,000 = 0.75 or 75 % \end{array}$

Budgeted contribution margin per unit:

$\begin{array}{rcl} Commercial & = & $ 10,000,000 \div 20,000 units = $ 500 per unit \\ Residential & = & $ 24,000,000 \div 60,000 units = $ 400 per unit \end{array}$

The table depicts actual units of all products sold times the quantity actual sales-mix percentage minus budgeted sales-mix percentage times budgeted contribution margin per unit equals sales-mix variance. The details of the table are as follows:

1. Commercial

• Actual units of all products sold: 84,000 units

Times

• The quantity actual sales-mix percentage minus budgeted sales-mix percentage: 0.30 minus 0.25

Times

• Budgeted contribution margin per unit: 500 dollars per unit

Equals

• Sales-mix variance: 2,100,000 dollars F

2. Residential

• Actual units of all products sold: 84,000 units

Times

• The quantity actual sales-mix percentage minus budgeted sales-mix percentage: 0.70 minus 0.75

Times

• Budgeted contribution margin per unit: 400 dollars per unit

Equals

• Sales-mix variance: 1,680,000 dollars U

3. Total sales-mix variance: 420,000 dollars F

The table depicts the quantity actual units of all products sold minus budgeted units of all products sold times the budgeted sales-mix percentage times budgeted contribution margin per unit equals sales-quantity variance. The details of the table are as follows:

1. Commercial

• The quantity actual units of all products sold minus budgeted units of all products sold: 84,000 units minus 80,000 units

Times

• Budgeted sales-mix percentages: 0.25

Times

• Budgeted contribution margin per unit: 500 dollars per unit

Equals

• Sales-mix variance: 500,000 dollars F

2. Residential

• The quantity actual units of all products sold minus budgeted units of all products sold: 84,000 units minus 80,000 units

Times

• Budgeted sales-mix percentages: 0.75

Times

• Budgeted contribution margin per unit: 400 dollars per unit

Equals

• Sales-mix variance: 1,200,000 dollars F

3. Total sales-quantity variance: 1,700,000 dollars U

2. $\begin{array}{l} Actual market share = 84,000 \div 700,000 = 0.12, or 12% \\ Budgeted market share = 80,000 \div 800,000 units = 0.10, or 10 % \end{array}$

$\begin{array}{l} \begin{matrix} Budgeted contribution margin \\ per composite unit \\ of budgeted mix \end{matrix} & = & $ 34,000,000 \div 80,000 units = $ 425 per unit \end{array}$

Budgeted contribution margin per composite unit of budgeted mix can also be calculated as follows:

The table depicts calculations for budgeted contribution margin per composite unit of budgeted mix. The details of the table are as follows:

1. Commercial, 500 dollars per unit times 0.25: 125 dollars

2. Residential, 400 dollars per unit times 0.75: 300 dollars

3. Budgeted contribution margin per composite unit: 425 dollars

$\begin{array}{l} \begin{matrix} Market - share \\ variance \end{matrix} & = & \begin{array}{l} \begin{matrix} Actual \\ market size \\ in units \end{matrix} & \times & (\begin{matrix} \begin{matrix} Actual \\ market \\ share \end{matrix} & - & \begin{matrix} Budgeted \\ market \\ share \end{matrix} \end{matrix}) & \times & \begin{matrix} Budgeted \\ contribution margin \\ per composite unit \\ for budgeted mix \end{matrix} \end{array} \\ = & 700,000 units \times (0. 12 - 0. 10) \times $ 425 per unit \\ = & $ 5,950,000 F \end{array}$

$\begin{array}{l} \begin{matrix} Market - size \\ variance \end{matrix} & = & \begin{array}{l} (\begin{matrix} \begin{matrix} Actual \\ market size \\ in units \end{matrix} & - & \begin{matrix} Budgeted \\ market size \\ in units \end{matrix} \end{matrix}) & \times & \begin{matrix} Budgeted \\ market \\ share \end{matrix} & \times & \begin{matrix} Budgeted \\ contribution margin \\ per composite unit \\ for budgeted mix \end{matrix} \end{array} \\ = & (700,000 units - 800,000 units) \times 0. 10 \times $425 per unit \\ = & $ 4,250,000 U \end{array}$

Note that the algebraic sum of the market-share variance and the market-size variance is equal to the sales-quantity variance: $$ 5,950,000 F + $ 4,250,000 U = $ 1,700,000 F.$

3. Both the total sales-mix variance and the total sales-quantity variance are favorable. The favorable sales-mix variance occurred because the actual mix was composed of more of the higher-margin commercial vinyl flooring. The favorable total sales-quantity variance occurred because the actual total quantity of rolls sold exceeded the budgeted amount.
The company’s large favorable market-share variance is due to a 12% actual market share compared with a 10% budgeted market share. The market-size variance is unfavorable because the actual market size was 100,000 rolls less than the budgeted market size. Payne’s performance in 2020 is very good. Although overall market size declined, the company sold more units than budgeted and gained market share.