1. **Problem Statement:** Calculate variable cost per unit for Production and Assembly departments using the High-Low method, determine total fixed costs, estimate total cost for given units, and analyze cost impact of 20% production increase. 2. **High-Low Method Formula:** Variable cost per unit = $\frac{\text{Cost at high activity} - \text{Cost at low activity}}{\text{High activity units} - \text{Low activity units}}$ 3. **Step 1: Identify high and low activity months for Production and Assembly:** - Production units: Low = 150 (Jan), High = 500 (Jun) - Assembly units: Low = 300 (Jan), High = 600 (Jun) 4. **Step 2: Calculate total variable cost change:** - Total cost at high (Jun) = 11,500,000 - Total cost at low (Jan) = 4,800,000 - Change in cost = 11,500,000 - 4,800,000 = 6,700,000 - Change in Production units = 500 - 150 = 350 - Change in Assembly units = 600 - 300 = 300 5. **Step 3: Variable cost per unit increase rule:** Variable costs increase by 10% for every additional 100 units in either department. 6. **Step 4: Calculate variable cost per unit for Production and Assembly:** Let $v_p$ = variable cost per unit for Production, $v_a$ = variable cost per unit for Assembly. Since variable costs increase by 10% per 100 units, the variable cost per unit is not constant but increases with units. We approximate using average units: Average Production units = $\frac{150 + 500}{2} = 325$ Average Assembly units = $\frac{300 + 600}{2} = 450$ Assuming base variable cost per unit $v_{p0}$ and $v_{a0}$ at zero units, variable cost per unit at average units: $$v_p = v_{p0} \times (1 + 0.10 \times \frac{325}{100}) = v_{p0} \times 1.325$$ $$v_a = v_{a0} \times (1 + 0.10 \times \frac{450}{100}) = v_{a0} \times 1.45$$ 7. **Step 5: Set up equations for total variable cost change:** Total variable cost change = $v_p \times 350 + v_a \times 300 = 6,700,000$ Substitute $v_p = 1.325 v_{p0}$ and $v_a = 1.45 v_{a0}$: $$1.325 v_{p0} \times 350 + 1.45 v_{a0} \times 300 = 6,700,000$$ 8. **Step 6: Use fixed costs to find $v_{p0}$ and $v_{a0}$:** Fixed costs total = 1,200,000 (Production) + 800,000 (Assembly) = 2,000,000 Total cost at low activity (Jan) = Fixed costs + Variable costs at low units Variable cost at low units: $$v_p \times 150 + v_a \times 300 = (1.325 v_{p0}) \times 150 + (1.45 v_{a0}) \times 300$$ Total cost at low = 4,800,000 So: $$2,000,000 + 1.325 v_{p0} \times 150 + 1.45 v_{a0} \times 300 = 4,800,000$$ Simplify: $$1.325 v_{p0} \times 150 + 1.45 v_{a0} \times 300 = 2,800,000$$ 9. **Step 7: Solve system of equations:** Equation 1: $$1.325 v_{p0} \times 350 + 1.45 v_{a0} \times 300 = 6,700,000$$ Equation 2: $$1.325 v_{p0} \times 150 + 1.45 v_{a0} \times 300 = 2,800,000$$ Subtract Eq2 from Eq1: $$1.325 v_{p0} (350 - 150) = 6,700,000 - 2,800,000$$ $$1.325 v_{p0} \times 200 = 3,900,000$$ $$v_{p0} = \frac{3,900,000}{1.325 \times 200} = \frac{3,900,000}{265} \approx 14,716.98$$ 10. **Step 8: Find $v_{a0}$:** From Eq2: $$1.325 \times 14,716.98 \times 150 + 1.45 v_{a0} \times 300 = 2,800,000$$ Calculate first term: $$1.325 \times 14,716.98 \times 150 \approx 2,925,000$$ So: $$2,925,000 + 1.45 v_{a0} \times 300 = 2,800,000$$ $$1.45 v_{a0} \times 300 = 2,800,000 - 2,925,000 = -125,000$$ $$v_{a0} = \frac{-125,000}{1.45 \times 300} = \frac{-125,000}{435} \approx -287.36$$ Negative variable cost is not possible, so we revise assumption: variable cost per unit increases by 10% per 100 units in total units (Production + Assembly). 11. **Step 9: Recalculate assuming combined units:** Change in total units = (350 + 300) = 650 Variable cost per unit base $v_0$: $$v_0 \times 650 \times (1 + 0.10 \times \frac{650}{100}) = 6,700,000$$ $$v_0 \times 650 \times (1 + 0.65) = 6,700,000$$ $$v_0 \times 650 \times 1.65 = 6,700,000$$ $$v_0 = \frac{6,700,000}{650 \times 1.65} = \frac{6,700,000}{1,072.5} \approx 6,245.61$$ 12. **Step 10: Calculate variable cost per unit for Production and Assembly at average units:** Production variable cost per unit: $$v_p = 6,245.61 \times (1 + 0.10 \times \frac{325}{100}) = 6,245.61 \times 1.325 = 8,273.94$$ Assembly variable cost per unit: $$v_a = 6,245.61 \times (1 + 0.10 \times \frac{450}{100}) = 6,245.61 \times 1.45 = 9,055.13$$ 13. **Step 11: Total fixed costs:** Given as 1,200,000 (Production) + 800,000 (Assembly) = 2,000,000 14. **Step 12: Estimate total cost for 375 Production units and 475 Assembly units:** Variable cost Production: $$375 \times 8,273.94 = 3,102,727.5$$ Variable cost Assembly: $$475 \times 9,055.13 = 4,299,429.25$$ Total variable cost: $$3,102,727.5 + 4,299,429.25 = 7,402,156.75$$ Total cost: $$7,402,156.75 + 2,000,000 = 9,402,156.75$$ 15. **Step 13: Impact of 20% increase in production units:** New Production units: $$375 \times 1.20 = 450$$ New Assembly units: $$475 \times 1.20 = 570$$ Variable cost Production: $$450 \times 8,273.94 = 3,723,273$$ Variable cost Assembly: $$570 \times 9,055.13 = 5,160,449.1$$ Total variable cost: $$3,723,273 + 5,160,449.1 = 8,883,722.1$$ Total cost: $$8,883,722.1 + 2,000,000 = 10,883,722.1$$ Increase in total cost: $$10,883,722.1 - 9,402,156.75 = 1,481,565.35$$ **Final Answers:** - Variable cost per unit approx: Production = 8,274, Assembly = 9,055 - Total fixed costs = 2,000,000 - Estimated total cost at 375 Production and 475 Assembly units = 9,402,157 - Total cost increase with 20% production increase = 1,481,565