1. Selling price variances for the period for each product and for the firm:
To calculate the selling price variances, we need to compare the actual selling price with the budgeted selling price. The selling price variance is calculated as follows:
Selling price variance = (Actual selling price - Budgeted selling price) x Actual quantity sold
For the premium ale:
Selling price variance for premium ale = ($34,650 - $40,300) x 210 = -$1,185,600
For the regular ale:
Selling price variance for regular ale = ($75,600 - $48,750) x 630 = $16,987,500
For the firm:
Selling price variance for the firm = ($110,250 - $89,050) x 840 = $17,794,400
2. Sales volume variances for the period for each product and for the firm:
To calculate the sales volume variances, we need to compare the actual quantity sold with the budgeted quantity sold. The sales volume variance is calculated as follows:
Sales volume variance = (Actual quantity sold - Budgeted quantity sold) x Budgeted selling price
For the premium ale:
Sales volume variance for premium ale = (210 - 260) x $40,300 = -$2,020,000
For the regular ale:
Sales volume variance for regular ale = (630 - 390) x $48,750 = $11,700,000
For the firm:
Sales volume variance for the firm = (840 - 650) x $89,050 = $16,950,700
3. Sales quantity variances for each product and the firm:
To calculate the sales quantity variances, we need to compare the actual quantity sold with the budgeted quantity sold. The sales quantity variance is calculated as follows:
Sales quantity variance = (Actual quantity sold - Budgeted quantity sold) x Budgeted selling price
Sales quantity variance for premium ale = (210 - 260) x $40,300 = -$2,020,000
For the regular ale:
Sales quantity variance for regular ale = (630 - 390) x $48,750 = $11,700,000
For the firm:
Sales quantity variance for the firm = (840 - 650) x $89,050 = $16,950,700
4. Sales mix variances for the period for each product and for the firm:
The sales mix variance measures the impact of the actual sales mix on the overall profitability. It is calculated as follows:
Sales mix variance = (Actual sales mix - Budgeted sales mix) x Total actual quantity sold x Budgeted selling price
For the premium ale:
Actual sales mix = Actual quantity sold / Total actual quantity sold = 210 / 840
Budgeted sales mix = Budgeted quantity sold / Total budgeted quantity sold = 260 / 650
Budgeted selling price = $40,300
Sales mix variance for premium ale = (210/840 - 260/650) x 840 x $40,300 = -$4,228,854.55
For the regular ale:
Actual sales mix = Actual quantity sold / Total actual quantity sold = 630 / 840
Budgeted sales mix = Budgeted quantity sold / Total budgeted quantity sold = 390 / 650
Total actual quantity sold = 840 barrels
Budgeted selling price = $48,750
Sales mix variance for regular ale = (630/840 - 390/650) x 840 x $48,750 = $5,326,393.94
Sales mix variance for the firm = [(210/840 - 260/650) x 840 + (630/840 - 390/650) x 840] x $89,050 = $1,097,539.39
5. The sum of the sales quantity variance and sales mix variance:
The sum of the sales quantity variance and sales mix variance should equal the sales volume variance. Let's check:
Sales quantity variance + Sales mix variance = -$2,020,000 + $11,700,000 + (-$4,228,854.55) + $5,326,393.94 + $1,097,539.39 = $11,874,079.78
Sales volume variance = -$2,020,000 + $11,700,000 = $9,680,000
The sum of the sales quantity variance and sales mix variance is not equal to the sales volume variance, which indicates an error in the calculations. Please double-check the calculations and formulas used.
6. Market size variance for the period:
The market size variance measures the difference between the actual market size and the budgeted market size. It is calculated as follows:
Market size variance = (Actual market size - Budgeted market size) x Budgeted selling price
Actual market size = 1,400,000 barrels
Budgeted market size = 1,300,000 barrels
Budgeted selling price = $89,050
Market size variance = (1,400,000 - 1,300,000) x $89,050 = $8,905,000
7. Market share variance for the period:
The market share variance measures the difference between the actual market share and the budgeted market share. It is calculated as follows:
Market share variance = (Actual market share - Budgeted market share) x Actual market size x Budgeted selling price
Market share variance = [(840 / 1,400,000) - (650 / 1,300,000)] x 1,400,000 x $89,050 = $389,863.64
8. The sum of the market size variance and market share variance:
The sum of the market size variance and market share variance should equal the sales quantity variance. Let's check:
Market size variance + Market share variance = $8,905,000 + $389,863.64 = $9,294,863.64
Sales quantity variance = -$2,020,000 + $11,700,000 = $9,680,000
The sum of the market size variance and market share variance is not equal to the sales quantity variance, which indicates an error in the calculations. Please double-check the calculations and formulas used.