Final answer:
The variable-overhead spending variance is $20,000 unfavorable, and the variable-overhead efficiency variance is $20,000 unfavorable.
Step-by-step explanation:
The variable-overhead spending variance can be calculated by subtracting the actual variable overhead incurred from the standard variable overhead cost.
In this case, the standard variable overhead cost is $4.50 per machine hour, and the actual machine hours worked is 120,000.
So, the standard variable overhead cost for 120,000 machine hours is $4.50 x 120,000 = $540,000.
Therefore, the variable-overhead spending variance is actual variable overhead incurred - standard variable overhead cost = $520,000 - $540,000 = -$20,000.
Since the variance is negative (-$20,000), it is unfavorable.
Therefore, the answer is option B: $20,000 unfavorable.
The variable-overhead efficiency variance can be calculated by subtracting the standard variable overhead cost for the actual units produced from the standard variable overhead cost for the standard units produced.
In this case, the standard variable overhead cost for the standard units produced is $4.50 x 46,000 = $207,000. The standard variable overhead cost for the actual units produced is $4.50 x 42,000 = $189,000.
Therefore, the variable-overhead efficiency variance is standard variable overhead cost for actual units produced - standard variable overhead cost for standard units produced = $189,000 - $207,000 = -$18,000.
Since the variance is negative (-$18,000), it is unfavorable. Therefore, the answer is option B: $20,000 unfavorable.