Answer :
Sure! Let's solve for the unknown variables step-by-step using the given data:
### Row 1:
- THC (Total Fixed Costs): [tex]$6,000 - TVA (Total Variable Costs): $[/tex]7,600
- Unit VC (Variable Cost per Unit): [tex]$6.50 - Selling Price per Unit: $[/tex]14
- Total Revenue: ?
- Level of Output: 266.67 units
- Net Income: [tex]$4,000 - Contribution Margin Ratio (CR): 53.57% - Unit Contribution Margin (Unit CM): $[/tex]7.50
First, let's find the Total Revenue for Row 1:
[tex]\[ \text{Total Revenue} = \text{Selling Price} \times \text{Level of Output} \][/tex]
[tex]\[ \text{Total Revenue} = 14 \times 266.67 \][/tex]
[tex]\[ \text{Total Revenue} \approx 3733.38 \][/tex]
So, the Total Revenue for Row 1 is approximately [tex]$3,733.38. ### Row 2: - THC: $[/tex]2,100
- TVA: ?
- Unit VC: [tex]$6 - Selling Price per Unit: $[/tex]13
- Total Revenue: [tex]$21,000 - Level of Output: ? - Net Income: ? - CR: ? - Unit CM: ? First, let's find the Level of Output for Row 2: \[ \text{Level of Output} = \frac{\text{Total Revenue}}{\text{Selling Price}} \] \[ \text{Level of Output} = \frac{21,000}{13} \] \[ \text{Level of Output} \approx 1,615.38 \] Next, let's find the Total Variable Costs (TVA) for Row 2: \[ \text{TVA} = \text{Unit VC} \times \text{Level of Output} \] \[ \text{TVA} = 6 \times 1,615.38 \] \[ \text{TVA} \approx 9,692.31 \] Now, let's find the Net Income for Row 2: \[ \text{Net Income} = \text{Total Revenue} - \text{TVA} - \text{THC} \] \[ \text{Net Income} = 21,000 - 9,692.31 - 2,100 \] \[ \text{Net Income} \approx 9,207.69 \] ### Row 3: - THC: ? - TVA: ? - Unit VC: ? - Selling Price per Unit: $[/tex]70
- Total Revenue: [tex]$72,000 - Level of Output: ? - Net Income: $[/tex]12,500
- CR: 36%
- Unit CM: ?
First, let's find the Level of Output for Row 3:
[tex]\[ \text{Level of Output} = \frac{\text{Total Revenue}}{\text{Selling Price}} \][/tex]
[tex]\[ \text{Level of Output} = \frac{72,000}{70} \][/tex]
[tex]\[ \text{Level of Output} = 1,028.57 \][/tex]
Using the Contribution Margin Ratio (CR), we can find the Unit CM:
[tex]\[ \text{CR} = \frac{\text{Total CM}}{\text{Total Revenue}} = \frac{36}{100} = 0.36 \][/tex]
[tex]\[ \text{Total CM} = \text{CR} \times \text{Total Revenue} \][/tex]
[tex]\[ \text{Total CM} = 0.36 \times 72,000 = 25,920 \][/tex]
[tex]\[ \text{Unit CM} = \frac{\text{Total CM}}{\text{Level of Output}} \][/tex]
[tex]\[ \text{Unit CM} = \frac{25,920}{1,028.57} \approx 25.2 \][/tex]
Next, let's find THC for Row 3. We know:
[tex]\[ \text{Net Income} = \text{Total Revenue} - \text{Total Variable Costs} - \text{THC} \][/tex]
Total Variable Costs (TVA) can be calculated as:
[tex]\[ \text{TVA} = \text{Level of Output} \times \text{Unit VC} \][/tex]
We can simplify:
[tex]\[ \text{Net Income} = \text{Total Revenue} - (\text{Unit VC} \times \text{Level of Output}) - \text{THC} \][/tex]
Rearranging for THC:
[tex]\[ \text{THC} = \text{Total Revenue} - \text{TVA} - \text{Net Income} \][/tex]
We know:
[tex]\[ \text{Net Income} = 12,500 \][/tex]
[tex]\[ \text{Total Revenue} = 72,000 \][/tex]
Let's assume Level of Output multiplied by Unit VC can be replaced by Total Variable Costs which is solved for THC to find exact calculated value.
### Row 4:
- THC: [tex]$16,000 - TVA: $[/tex]41,000
- Unit VC: ?
- Selling Price per Unit: ?
- Total Revenue: [tex]$82,500 - Level of Output: 1,600 units - Net Income: ? - CR: ? - Unit CM: ? Using: \[ \text{Net Income} = \text{Total Revenue} - \text{TVA} - \text{THC} \] \[ \text{Net Income} = 82,500 - 41,000 - 16,000 = 25,500 \] Now, to recap: ### Result Table | THC | TVA | Unit VC | Selling Price | Total Rev | Level of Output | Net Income | CR | Unit CM | |-------|----------|---------|---------------|------------|-----------------|------------|-------|---------| | \$[/tex]6,000 | \[tex]$7,600 | \$[/tex]6.50 | \[tex]$14 | \$[/tex]3733.38 | 266.67 | \[tex]$4,000 | 53.57% | \$[/tex]7.50 |
| \[tex]$2,100 | \$[/tex]9,692.31 | \[tex]$6 | \$[/tex]13 | \[tex]$21,000 | 1615.38 | \$[/tex]9,207.69 | - | - |
| - | - | - | \[tex]$70 | \$[/tex]72,000 | 1,028.57 | \[tex]$12,500 | 36% | \$[/tex]25.2 |
| \[tex]$16,000 | \$[/tex]41,000 | - | - | \[tex]$82,500 | 1,600 | \$[/tex]25,500 | - | - |
### Row 1:
- THC (Total Fixed Costs): [tex]$6,000 - TVA (Total Variable Costs): $[/tex]7,600
- Unit VC (Variable Cost per Unit): [tex]$6.50 - Selling Price per Unit: $[/tex]14
- Total Revenue: ?
- Level of Output: 266.67 units
- Net Income: [tex]$4,000 - Contribution Margin Ratio (CR): 53.57% - Unit Contribution Margin (Unit CM): $[/tex]7.50
First, let's find the Total Revenue for Row 1:
[tex]\[ \text{Total Revenue} = \text{Selling Price} \times \text{Level of Output} \][/tex]
[tex]\[ \text{Total Revenue} = 14 \times 266.67 \][/tex]
[tex]\[ \text{Total Revenue} \approx 3733.38 \][/tex]
So, the Total Revenue for Row 1 is approximately [tex]$3,733.38. ### Row 2: - THC: $[/tex]2,100
- TVA: ?
- Unit VC: [tex]$6 - Selling Price per Unit: $[/tex]13
- Total Revenue: [tex]$21,000 - Level of Output: ? - Net Income: ? - CR: ? - Unit CM: ? First, let's find the Level of Output for Row 2: \[ \text{Level of Output} = \frac{\text{Total Revenue}}{\text{Selling Price}} \] \[ \text{Level of Output} = \frac{21,000}{13} \] \[ \text{Level of Output} \approx 1,615.38 \] Next, let's find the Total Variable Costs (TVA) for Row 2: \[ \text{TVA} = \text{Unit VC} \times \text{Level of Output} \] \[ \text{TVA} = 6 \times 1,615.38 \] \[ \text{TVA} \approx 9,692.31 \] Now, let's find the Net Income for Row 2: \[ \text{Net Income} = \text{Total Revenue} - \text{TVA} - \text{THC} \] \[ \text{Net Income} = 21,000 - 9,692.31 - 2,100 \] \[ \text{Net Income} \approx 9,207.69 \] ### Row 3: - THC: ? - TVA: ? - Unit VC: ? - Selling Price per Unit: $[/tex]70
- Total Revenue: [tex]$72,000 - Level of Output: ? - Net Income: $[/tex]12,500
- CR: 36%
- Unit CM: ?
First, let's find the Level of Output for Row 3:
[tex]\[ \text{Level of Output} = \frac{\text{Total Revenue}}{\text{Selling Price}} \][/tex]
[tex]\[ \text{Level of Output} = \frac{72,000}{70} \][/tex]
[tex]\[ \text{Level of Output} = 1,028.57 \][/tex]
Using the Contribution Margin Ratio (CR), we can find the Unit CM:
[tex]\[ \text{CR} = \frac{\text{Total CM}}{\text{Total Revenue}} = \frac{36}{100} = 0.36 \][/tex]
[tex]\[ \text{Total CM} = \text{CR} \times \text{Total Revenue} \][/tex]
[tex]\[ \text{Total CM} = 0.36 \times 72,000 = 25,920 \][/tex]
[tex]\[ \text{Unit CM} = \frac{\text{Total CM}}{\text{Level of Output}} \][/tex]
[tex]\[ \text{Unit CM} = \frac{25,920}{1,028.57} \approx 25.2 \][/tex]
Next, let's find THC for Row 3. We know:
[tex]\[ \text{Net Income} = \text{Total Revenue} - \text{Total Variable Costs} - \text{THC} \][/tex]
Total Variable Costs (TVA) can be calculated as:
[tex]\[ \text{TVA} = \text{Level of Output} \times \text{Unit VC} \][/tex]
We can simplify:
[tex]\[ \text{Net Income} = \text{Total Revenue} - (\text{Unit VC} \times \text{Level of Output}) - \text{THC} \][/tex]
Rearranging for THC:
[tex]\[ \text{THC} = \text{Total Revenue} - \text{TVA} - \text{Net Income} \][/tex]
We know:
[tex]\[ \text{Net Income} = 12,500 \][/tex]
[tex]\[ \text{Total Revenue} = 72,000 \][/tex]
Let's assume Level of Output multiplied by Unit VC can be replaced by Total Variable Costs which is solved for THC to find exact calculated value.
### Row 4:
- THC: [tex]$16,000 - TVA: $[/tex]41,000
- Unit VC: ?
- Selling Price per Unit: ?
- Total Revenue: [tex]$82,500 - Level of Output: 1,600 units - Net Income: ? - CR: ? - Unit CM: ? Using: \[ \text{Net Income} = \text{Total Revenue} - \text{TVA} - \text{THC} \] \[ \text{Net Income} = 82,500 - 41,000 - 16,000 = 25,500 \] Now, to recap: ### Result Table | THC | TVA | Unit VC | Selling Price | Total Rev | Level of Output | Net Income | CR | Unit CM | |-------|----------|---------|---------------|------------|-----------------|------------|-------|---------| | \$[/tex]6,000 | \[tex]$7,600 | \$[/tex]6.50 | \[tex]$14 | \$[/tex]3733.38 | 266.67 | \[tex]$4,000 | 53.57% | \$[/tex]7.50 |
| \[tex]$2,100 | \$[/tex]9,692.31 | \[tex]$6 | \$[/tex]13 | \[tex]$21,000 | 1615.38 | \$[/tex]9,207.69 | - | - |
| - | - | - | \[tex]$70 | \$[/tex]72,000 | 1,028.57 | \[tex]$12,500 | 36% | \$[/tex]25.2 |
| \[tex]$16,000 | \$[/tex]41,000 | - | - | \[tex]$82,500 | 1,600 | \$[/tex]25,500 | - | - |
