(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:
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.
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
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.
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.