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14-23

(30 min.) Variance analysis, working backward.

1, and 2. Solution Exhibit 14-23 presents the sales-volume, sales-quantity, and sales-mix variances for the Plain and Chic wine glasses and in total for Jinwa Corporation in June 2003. The steps to fill in the numbers in Solution Exhibit 14-23 follow:

Step 1:  

Consider the static budget column (Column 3):

Static budget total contribution margin$5,600

Budgeted units of all glasses to be sold  2,000

Budgeted contribution margin per unit of Plain $2

Budgeted contribution margin per unit of Chic $6

Suppose that the budgeted sales-mix percentage of Plain is y.  Then the budgeted sales-mix percentage of Chic is (1 – y).  Hence,

(2,000y $2) + (2,000 (1 – y) $6) = $5,600

4000y + 12,000 – 12,000y = 5,600

8,000y = 6,400

y = 0.8 or 80%

1 – y = 1 – 0.8 = 0.2 or 20%

Jinwa's budgeted sales mix is 80% of Plain and 20% of Chic.  We can then fill in all the numbers in Column 3.

Step 2:

Next, consider Column 2 of Solution Exhibit 14-23.

The total of Column 2 in Panel C is $4,200 (the static budget total contribution margin of $5,600––the total sales-quantity variance of $1,400 U which was given in the problem).

We need to find the actual units sold of all glasses, which we denote by q.  From Column 2, we know that

(q 0.8 $2) + (q 0.2 $6)=$4,200

$1.6q + $1.2q= $4,200

$2.8q= $4,200

q    =  1,500 units

Hence, the total quantity of all glasses sold is 1,500 units.  This computation allows us to fill in all the numbers in Column 2.

Step 3:

Next, consider Column 1 of Solution Exhibit 14-23.  We know actual units sold of all glasses (1,500 units), the actual sales-mix percentage (given in the problem information as Plain, 60%; Chic, 40%), and the budgeted unit contribution margin of each product (Plain, $2; Chic, $6).  We can therefore determine all the numbers in Column 1.

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