The Company uses standard costing. The company makes and sells a single product

Question

The Company uses standard costing. The company makes and sells a single product called a Roff. The following data are for the month of August:

• Actual cost of direct material purchased and used: $110,792
• Material price variance: $10,072 unfavorable
• Total materials variance: $24,872 unfavorable
• Standard cost per pound of material: $4
• Standard cost per direct labor-hour: $7
• Actual direct labor-hours: 10,340 hours
• Labor efficiency variance: $2,800 favorable
• Standard number of direct labor-hours per unit of Roff: 3 hours
• Total labor variance: $2,370 unfavorable

The total number of units of Roff produced during August was:
3180, 3380, 3580 or 3400 (answer choices)

Explanation / Answer

Partially Solved for want of time: Direct materials price variance (MPV) formula: [Materials Price Variance = (Actual quantity purchased × Actual price) - (Actual quantity purchased × Standard price)] ie MPV= $10,072U = 10072 = $110,792 - (ACt Qty*$4) So Actual Qty = (110792-10072)/4 = 25,180 Lbs ..........(A) Actual cost of direct material purchased and used: $110,792 So Actual Cost per Lb of Mat = 110792/25180 = $4.40 .......(B) Materials quantity variance (MQV) Formula: [Materials quantity variance = (Actual quantity used × Standard price) - (Standard quantity allowed × Standard Price)] ie MQV = (25180*$4) - (Std QTy*$4) = $100,720 -Std Qty*$4 Total materials variance (TMV)= $24,872 unfavorable=24872 = MPV+MQV ie 24872 = 10072+100720-4*Std Qty So Std QTy = (10072+100720 - 24872)/4 = 21,480Lbs ..............(C) Formula of labor efficiency variance (LEV) : [Labor efficiency variance = (Actual hours worked × Standard rate) - (Standard hours allowed × Standard rate)] ie LEV =2800F = -2800 = (10340*$7) - (Std Hrs*$7) So Std Hrs = (10340*7 + 2800)/7 = 10,740Hrs ............(D) So Std Units = Std Hrs/Std hr pu = 10740/3 = 3580 units................(E) Direct Labor Rate Variance (DLRV) Formula: [Labor rate variance = (Actual hours worked × Actual rate) - (Actual hours worked × Standard rate)] ie DLRV = (10340*Act Rate) - (10340*$7) Total labor variance (TLV)= $2,370U = -2370 = LEV+DLRV = -2800 + (10340*Act Rate) - (10340*$7) So Actual Rate per Lab Hr = (2800-2370+10340*7)/10340 = $7.04 ...(F) [Labor rate variance = (Actual hours worked × Actual rate) - (Actual hours worked × Standard rate)] ie DLRV = 10340*7.04 - 10340*7 = $413.60 Also Actual Units*Act Hr pu = Acual Hrs = 10340

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