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Mackinaw Inc. processes a base chemical into plastic. Standard costs and actual costs for direct materials, direct labor, and factory overhead incurred for the manufacture of 40,000 units of product were as follows:

\textbf{Standard Costs and Actual Costs}
\begin{tabular}{lll}
\hline
& \textbf{Standard Costs} & \textbf{Actual Costs} \\
\hline
Direct materials & 120,000 lb. at [tex]$\$[/tex] 3.20[tex]$ & 118,500 lb. at $[/tex]\[tex]$ 3.25$[/tex] \\
Direct labor & 12,000 hrs. at [tex]$\$[/tex] 24.40[tex]$ & $[/tex]\[tex]$ \square$[/tex] \\
Factory overhead & Rates per direct labor hr., based on 100\% of normal capacity of 15,000 direct labor hrs.: & \\
& Variable cost, [tex]$\$[/tex] 8.00[tex]$ & $[/tex]\[tex]$ 91,200$[/tex] variable cost \\
& Fixed cost, [tex]$\$[/tex] 10.00[tex]$ & $[/tex]\[tex]$ 150,000$[/tex] fixed cost \\
\end{tabular}

Each unit requires 0.3 hours of direct labor.

\textbf{Required:}
a. Determine the direct materials price variance, direct materials quantity variance, and total direct materials cost variance. Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number.

b. Determine the direct labor rate variance, direct labor time variance, and total direct labor cost variance. Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number.

Direct labor rate variance:
[tex]$\$[/tex][tex]$ $[/tex]\square[tex]$ Unfavorable $[/tex]\checkmark$

Sagot :

GinnyAnsweridn
Let's break down the problem step-by-step to find the required variances:

### a. Direct Materials Variance Calculation

1. Direct Materials Price Variance:
- Formula: [tex]\((\text{Actual cost per lb} - \text{Standard cost per lb}) \times \text{Actual quantity}\)[/tex]
- Calculation: [tex]\((\$3.25 - \$3.20) \times 118,500 \text{ lb}\)[/tex]
- Result: [tex]\( \$0.05 \times 118,500 = \$5,925 \)[/tex] (Unfavorable)

2. Direct Materials Quantity Variance:
- Formula: [tex]\((\text{Actual quantity} - \text{Standard quantity}) \times \text{Standard cost per lb}\)[/tex]
- Calculation: [tex]\((118,500 \text{ lb} - 120,000 \text{ lb}) \times \$3.20\)[/tex]
- Result: [tex]\(-1,500 \text{ lb} \times \$3.20 = -\$4,800 \)[/tex] (Favorable)

3. Total Direct Materials Cost Variance:
- Formula: [tex]\(\text{Materials Price Variance} + \text{Materials Quantity Variance}\)[/tex]
- Calculation: [tex]\( \$5,925 + (-\$4,800) \)[/tex]
- Result: \[tex]$1,125 \( \) (Unfavorable) ### b. Direct Labor Variance Calculation 1. Direct Labor Rate Variance: - Formula: \((\text{Actual rate per hr} - \text{Standard rate per hr}) \times \text{Actual hours}\) - Calculation: \((\$[/tex]24.40 - \[tex]$24.40) \times 12,000 \text{ hrs}\) - Result: \( \$[/tex]0 \times 12,000 = \[tex]$0 \) (No Variance) 2. Direct Labor Time Variance: - Formula: \((\text{Actual hours} - \text{Standard hours}) \times \text{Standard rate per hr}\) - Calculation: \((12,000 \text{ hrs} - 12,000 \text{ hrs}) \times \$[/tex]24.40\)
- Result: [tex]\(0 \text{ hrs} \times \$24.40 = \$0\)[/tex] (No Variance)

3. Total Direct Labor Cost Variance:
- Formula: [tex]\(\text{Labor Rate Variance} + \text{Labor Time Variance}\)[/tex]
- Calculation: [tex]\( \$0 + \$0\)[/tex]
- Result: \[tex]$0 \( \) (No Variance) ### Summary of Variances - Direct Materials Price Variance: \$[/tex]5,925 (Unfavorable)
- Direct Materials Quantity Variance: -\[tex]$4,800 (Favorable) - Total Direct Materials Cost Variance: \$[/tex]1,125 (Unfavorable)
- Direct Labor Rate Variance: \[tex]$0 (No Variance) - Direct Labor Time Variance: \$[/tex]0 (No Variance)
- Total Direct Labor Cost Variance: \$0 (No Variance)

These variances help the company understand where they have deviated from their standard costs, and can be useful in identifying areas for improvement in cost control and efficiency.
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