Problem 4 - Accounting

Question

The following data relate to the direct materials cost for the production of 2,000 automobile tires: Actual: 54,600 lbs. at \(1.80 \)98,280 Standard: 53,400 lbs. at \(1.85 \)98,790 a. Determine the price variance, quantity variance, and total direct materials cost variance. b. To whom should the variances be reported for analysis and control?

Step-by-Step Solution

Answer

a. Price Variance: $-2,730; Quantity Variance: $2,220; Total Cost Variance: $-510. b. Report to the production manager and cost accountant.

Step 1: Understand the Variances

There are three types of variances to calculate: 1. **Price Variance**: Measures the difference between the actual cost of materials and the expected (standard) cost of materials per unit. 2. **Quantity Variance**: Measures the deviation of the actual quantity of materials used from the standard quantity allowed for actual production levels. 3. **Total Direct Materials Cost Variance**: The sum of the price and quantity variances to measure overall cost discrepancies.

Step 2: Calculate the Price Variance

The price variance is calculated using the formula: \[ \text{Price Variance} = (\text{Actual Price per Unit} - \text{Standard Price per Unit}) \times \text{Actual Quantity} \]Given:- Actual Price: \(1.80- Standard Price: \)1.85- Actual Quantity: 54,600 lbsPlug in the values:\[ (1.80 - 1.85) \times 54,600 = -0.05 \times 54,600 = -2,730 \]The price variance is $-2,730, indicating a savings since the actual price was lower than the standard price.

Step 3: Calculate the Quantity Variance

The quantity variance is calculated using the formula: \[ \text{Quantity Variance} = (\text{Actual Quantity} - \text{Standard Quantity}) \times \text{Standard Price per Unit} \]Given:- Actual Quantity: 54,600 lbs- Standard Quantity: 53,400 lbs- Standard Price: \(1.85Plug in the values:\[ (54,600 - 53,400) \times 1.85 = 1,200 \times 1.85 = 2,220 \]The quantity variance is \)2,220, indicating an excess usage since more materials were used than the standard.

Step 4: Calculate the Total Direct Materials Cost Variance

The total direct materials cost variance is the sum of the price variance and the quantity variance: \[ \text{Total Direct Materials Cost Variance} = \text{Price Variance} + \text{Quantity Variance} \]Given:- Price Variance: \(-2,730- Quantity Variance: \)2,220Plug in the values:\[ -2,730 + 2,220 = -510 \]The total direct materials cost variance is $-510, indicating an overall favorable variance as the costs were lower than expected.

Step 5: Reporting the Variances

Variances should be reported to management personnel such as the production manager and the cost accountant. Their role involves analyzing the reasons for variances and implementing control measures to address any inefficiencies or cost savings.

Key Concepts

Price Variance

Price variance is an important metric for businesses. It tells us whether the actual cost of materials per unit is higher or lower than the standard (expected) cost. To calculate it, we need three pieces of information:

• Actual Price per Unit: This is how much you truly paid for one unit of material.
• Standard Price per Unit: This is how much you expected to pay as per your budget or plan.
• Actual Quantity: The total volume of materials you used during production.

You calculate the price variance using this formula: \[\text{Price Variance} = (\text{Actual Price per Unit} - \text{Standard Price per Unit}) \times \text{Actual Quantity}\]In our example, the actual price was \(1.80, the standard price was \)1.85, and the actual quantity was 54,600 lbs. Plug these into the formula:\[(1.80 - 1.85) \times 54,600 = -2,730\]This shows a favorable price variance of -$2,730 because the actual price was lower than the standard price. A negative value here indicates savings.
If the number was positive, it would mean spending more than expected on materials.

Quantity Variance

Quantity variance focuses on the efficiency or inefficiency of material usage during production. This variance shows whether you used more or fewer materials than the standard quantity allowed. Here's what you'll need:

• Actual Quantity: The real amount of materials used in production.
• Standard Quantity: The amount that would have been used if production went exactly as planned.
• Standard Price per Unit: How much each unit was supposed to cost as per standards.

To find the quantity variance, use the formula:\[\text{Quantity Variance} = (\text{Actual Quantity} - \text{Standard Quantity}) \times \text{Standard Price per Unit}\]In this exercise, the actual quantity is 54,600 lbs, the standard quantity is 53,400 lbs, and the standard price is $1.85. Calculating gives us:\[(54,600 - 53,400) \times 1.85 = 2,220\]This is an unfavorable variance of 2,220, indicating that excess material was used beyond the standard allowance. A higher than standard usage suggests inefficiencies in production.
The goal is to minimize this variance to ensure efficient material use.

Variance Analysis

Variance analysis involves looking at both price and quantity variances to understand the overall cost performance. It's a key tool for managing production costs and ensuring efficiency. The total direct materials cost variance allows companies to see if they spent more or less than what was initially planned.The total variance is computed by adding the price and quantity variances:\[\text{Total Direct Materials Cost Variance} = \text{Price Variance} + \text{Quantity Variance}\]In this context:

• Price Variance: -\(2,730
• Quantity Variance: \)2,220

Plugging in these numbers gives:\[-2,730 + 2,220 = -510\]This total variance of -\(510 is a favorable result, indicating that overall production costs were \)510 less than expected.
It's crucial for managers and cost accountants to review these variances thoroughly. Understanding the reasons behind each variance helps in identifying cost-saving opportunities and areas that require efficiency improvements. Continuous monitoring and reporting help keep a company's production process aligned with its financial goals.