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Sagot :
Alright, let's work through the exercise step-by-step to calculate the material price variance (MPV) and material usage variance (MUV) for August.
### 1. Data Provided:
1. Budgeted production: 23,000 units
2. Actual production: 24,075 units
3. Standard cost per pound of direct material: $1.00
4. Actual cost per pound of direct material: $0.90
5. Pounds of raw material used: 267,500 pounds
6. Standard amount of raw material required per unit: 9 pounds
### 2. Material Price Variance (MPV):
The Material Price Variance is calculated using the formula:
[tex]\[ MPV = (Standard \ Cost \ per \ Pound - Actual \ Cost \ per \ Pound) \times Pounds \ Used \][/tex]
Substituting the given values:
[tex]\[ MPV = (1.00 - 0.90) \times 267,500 \][/tex]
[tex]\[ MPV = 0.10 \times 267,500 \][/tex]
[tex]\[ MPV = 26,750 \][/tex]
Since the actual cost per pound is less than the standard cost per pound, the variance is favorable.
Thus, the Material Price Variance (MPV) is \( 26,750 \) and the effect is "F" (favorable).
### 3. Material Usage Variance (MUV):
The Material Usage Variance is calculated using the formula:
[tex]\[ MUV = (Standard \ Pounds \ Required - Actual \ Pounds \ Used) \times Standard \ Cost \ Per \ Pound \][/tex]
First, we need to compute the standard pounds required for the actual production:
[tex]\[ Standard \ Pounds \ Required = Actual \ Production \times Standard \ Pounds \ Per \ Unit \][/tex]
[tex]\[ Standard \ Pounds \ Required = 24,075 \times 9 \][/tex]
[tex]\[ Standard \ Pounds \ Required = 216,675 \][/tex]
Now we can find the MUV:
[tex]\[ MUV = (216,675 - 267,500) \times 1.00 \][/tex]
[tex]\[ MUV = (-50,825) \times 1.00 \][/tex]
[tex]\[ MUV = -50,825 \][/tex]
Since the actual pounds used exceed the standard pounds required, the variance is unfavorable.
Thus, the Material Usage Variance (MUV) is \( -50,825 \) and the effect is "U" (unfavorable).
### Final Results:
[tex]\[ \begin{array}{|l|c|c|} \hline \text{Material Price Variance} & 26,750 & \text{F} \\ \hline \text{Material Usage Variance} & -50,825 & \text{U} \\ \hline \end{array} \][/tex]
So, the Material Price Variance is [tex]\( 26,750 \)[/tex] (Favorable) and the Material Usage Variance is [tex]\( -50,825 \)[/tex] (Unfavorable).
### 1. Data Provided:
1. Budgeted production: 23,000 units
2. Actual production: 24,075 units
3. Standard cost per pound of direct material: $1.00
4. Actual cost per pound of direct material: $0.90
5. Pounds of raw material used: 267,500 pounds
6. Standard amount of raw material required per unit: 9 pounds
### 2. Material Price Variance (MPV):
The Material Price Variance is calculated using the formula:
[tex]\[ MPV = (Standard \ Cost \ per \ Pound - Actual \ Cost \ per \ Pound) \times Pounds \ Used \][/tex]
Substituting the given values:
[tex]\[ MPV = (1.00 - 0.90) \times 267,500 \][/tex]
[tex]\[ MPV = 0.10 \times 267,500 \][/tex]
[tex]\[ MPV = 26,750 \][/tex]
Since the actual cost per pound is less than the standard cost per pound, the variance is favorable.
Thus, the Material Price Variance (MPV) is \( 26,750 \) and the effect is "F" (favorable).
### 3. Material Usage Variance (MUV):
The Material Usage Variance is calculated using the formula:
[tex]\[ MUV = (Standard \ Pounds \ Required - Actual \ Pounds \ Used) \times Standard \ Cost \ Per \ Pound \][/tex]
First, we need to compute the standard pounds required for the actual production:
[tex]\[ Standard \ Pounds \ Required = Actual \ Production \times Standard \ Pounds \ Per \ Unit \][/tex]
[tex]\[ Standard \ Pounds \ Required = 24,075 \times 9 \][/tex]
[tex]\[ Standard \ Pounds \ Required = 216,675 \][/tex]
Now we can find the MUV:
[tex]\[ MUV = (216,675 - 267,500) \times 1.00 \][/tex]
[tex]\[ MUV = (-50,825) \times 1.00 \][/tex]
[tex]\[ MUV = -50,825 \][/tex]
Since the actual pounds used exceed the standard pounds required, the variance is unfavorable.
Thus, the Material Usage Variance (MUV) is \( -50,825 \) and the effect is "U" (unfavorable).
### Final Results:
[tex]\[ \begin{array}{|l|c|c|} \hline \text{Material Price Variance} & 26,750 & \text{F} \\ \hline \text{Material Usage Variance} & -50,825 & \text{U} \\ \hline \end{array} \][/tex]
So, the Material Price Variance is [tex]\( 26,750 \)[/tex] (Favorable) and the Material Usage Variance is [tex]\( -50,825 \)[/tex] (Unfavorable).
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