exercise 5.2: the contribution margin and the pv ratio In $ Revenue 420,000 Variable costs Purchases (205,000) Freight-in (4,000) Commissions (3,000) Total variables costs (212,000) Contribution margin 208,000 Fixed costs Salaries (distribution) (60,000) Travel (3,000) Advertising (5,000) Salaries (administration) (38,000) Depreciation/amortization (40,000) Leasing (7,000) Finance costs (14,000) Total fixed costs (167,000) Profit before taxes 41,000 (1) Profit before taxes (excluding other income) is $41,000 (2) Contribution margin is $208,000 (3) PV ratio is .495 ($208,000 $420,000) exercise 5.3: the break-even point The Millers are thinking of introducing a new product line in their store. For this exercise, assume the following: Total fixed costs for the line are estimated at $15,000. Total number of units they expect to sell are 10,000, based on a market study. Total variable costs are $20,000. Unit selling price is $4.50. Based on the information, answer the following questions: Unit selling price $4.50 Unit variable costs (2.00) ($20,000 10,000 units) Unit contribution margin $2.50 What is the break-even point in units? Fixed costs $15,000 ---------- = 6,000 units Contribution margin $2.50 What is the break-even point in revenue? Number of 6,000 units $4.50 = $27,000 Should they go ahead with their plan? Yes, they should go ahead with the decision. They expect to sell 10,000 units and the break-even point is 6,000 (60% of the objective). In terms of revenue, the expected revenue based on the study is $45,000 and the revenue break-even is $27,000 (also 60% of the revenue objective). exercise 5.4: cash and profit break-even points The Millers have been approached by a supplier to sell a new product line. Based on the suppliers estimates, CompuTech could sell as many as 1,500 units. The suggested retail price for each unit is $14.50. The purchase price for each unit is $7.00. The fixed costs for that department is $6,000, which includes $1,000 for depreciation. On the basis of this information, calculate the following: Contribution margin: Revenue $21,750 (1,500 units $14.50) Variable costs (10,500) (1,500 units $ 7.00) Contribution margin $11,250 unit contribution $ 7.50 PV ratio: Contribution margin $11,250 ----------- = .517 Revenue $21,750 Revenue break-even by using the PV ratio: Fixed costs $6,000 --------- = $11,605 PV ratio .517 The break-even point will be achieved at 53.4% ($11,605 $21,750) of the revenue estimates. Cash break-even point in units and in revenue: in units Cash fixed costs ($6,000 - $1,000) $5,000 -------- = 667 units Unit contribution $7.50 in revenue Cash fixed costs ($6,000 - $1,000) $5,000 -------- = $ 9,671 PV ratio .517 Profit generated: Statement of Income (in $) Revenue 21,750 Variable costs (10,500) Contribution margin 11,250 Fixed costs (6,000) Profit 5,250 Profit break-even point in units and in revenue in units Fixed costs and profit objective ($6,000 + $5,250) $11,250 ----------- = 1,500 units Unit contribution $7.50 in revenue Fixed costs and profit objective ($6,000 + $5,250) $11,250 ---------- = $ 21,760 PV ratio .517 These calculations (with rounding) only confirm the numbers presented on the statement of income. exercise 5.5: sensitivity analysis Begin with the information in the Self-Test Exercise 5.3. If fixed costs were increased by $5,000 and variable costs and unit selling price remained unchanged, what would be the new PV ratio and breakeven point in units and in revenue? The PV ratio remains unchanged since both unit selling price or revenue and variable costs remained unchanged. The new break-even point in units is 8,000 ($20,000 $2.50) The new break-even point in revenue is $36,000 (8,000 $4.50) exercise 5.6: company-wide break-even point Contribution margin and profit before taxes: The contribution margin is $208,000 and the profit before taxes (excluding other income) is $41,000. In $ Revenue 420,000 Variable costs Purchases (cost of sales) (205,000) Freight-in (cost of sales) (4,000) Commissions (3,000) Total variables costs (212,000) Contribution margin 208,000 Fixed costs Salaries (distribution) (60,000) Travel (3,000) Advertising (5,000) Salaries (administration) (38,000) Depreciation/amortization (40,000) Leasing (7,000) Finance costs (14,000) Total fixed costs 167,000 Profit before taxes (excluding other income) 41,000 Revenue break-even point: The revenue break-even point is $337,374. $208,000 PV ratio = ----------- = .495 $420,000 $167,000 Break-even point = ----------- = $337,374 .495 Cash break-even point: Cash break-even point is $252,566. Cash fixed costs: Total fixed costs $167,000 Depreciation/amortization 40,000 Total cash fixed costs $127,000 $127,000 Cash break-even point = ----------- = $256,566 .495 exercise 5.7: product line analysis using the break-even point With the following information, calculate the break-even point in sales dollars for CompuTechs product lines A, B, and C. Revenue Product line A $ 45,000 Product line B $ 21,750 Product line C $ 35,000 Cost of sales for the three product lines is 45%, 50%, and 52% of revenue, respectively. Fixed costs are estimated at $32,000. Total revenue $101,750 Variable costs (cost of sales): Product line A (45%) $ (20,250) Product line B (50%) (10,875) Product line C (52%) (18,200) Total variable costs (49,325) Contribution margin $ 52,425 $ 52,425 PV ratio = ------------ = .515 $101,750 $32,000 Break-even point = ---------- = $62,136 .515