Cost Analysis
1. **State the problem:** We need to find the missing values in the table: Unit Variable Cost, Total Revenue, Level of Output, Contribution Rate (%), and Unit Contribution Margin.
2. **Given data:**
- Total Fixed Costs (TFC) = 5985
- Total Variable Costs (TVC) = 6863
- Selling Price (SP) = 10.00
- Net Income (NI) = 3498
3. **Formulas and important rules:**
- Total Revenue (TR) = Selling Price × Level of Output
- Total Costs (TC) = Total Fixed Costs + Total Variable Costs
- Net Income = Total Revenue - Total Costs
- Unit Variable Cost (UVC) = Total Variable Costs ÷ Level of Output
- Unit Contribution Margin (UCM) = Selling Price - Unit Variable Cost
- Contribution Rate (%) = (Unit Contribution Margin ÷ Selling Price) × 100
4. **Find Level of Output (Q):**
Using Net Income formula:
$$NI = TR - TC = (SP \times Q) - (TFC + TVC)$$
Rearranged:
$$3498 = 10Q - (5985 + 6863)$$
$$3498 = 10Q - 12848$$
$$10Q = 3498 + 12848 = 16346$$
$$Q = \frac{16346}{10} = 1634.6$$
5. **Calculate Total Revenue (TR):**
$$TR = SP \times Q = 10 \times 1634.6 = 16346.00$$
6. **Calculate Unit Variable Cost (UVC):**
$$UVC = \frac{TVC}{Q} = \frac{6863}{1634.6} \approx 4.20$$
7. **Calculate Unit Contribution Margin (UCM):**
$$UCM = SP - UVC = 10.00 - 4.20 = 5.80$$
8. **Calculate Contribution Rate (%):**
$$Contribution\ Rate = \frac{UCM}{SP} \times 100 = \frac{5.80}{10.00} \times 100 = 58.00\%$$
**Final answers rounded to two decimals:**
- Unit Variable Cost = 4.20
- Total Revenue = 16346.00
- Level of Output = 1634.60
- Contribution Rate = 58.00%
- Unit Contribution Margin = 5.80