Cost-Volume-Profit Analysis with Step Fixed Costs
Jua Kali Manufacturers produces a single product. The following information is available for the current year: selling price per unit KES 1,000; variable cost per unit KES 600; total fixed costs KES 400,000 per year for production up to 2,000 units. If production exceeds 2,000 units, additional fixed costs of KES 200,000 are incurred (e.g., for extra shift supervision and equipment maintenance). The company's current production and sales are 1,800 units. The marketing manager proposes a 10% price reduction to increase sales volume to 2,500 units. The production manager warns that this would require the additional fixed costs. The company's target profit is KES 300,000.
1. Calculate the current break-even point in units and the margin of safety. Determine whether the company is currently meeting its target profit.
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Current break-even point: Contribution per unit = 1,000 - 600 = KES 400. Fixed costs = KES 400,000 (since 1,800 units < 2,000). Break-even units = 400,000 / 400 = 1,000 units.
Margin of safety: Current sales = 1,800 units. Margin of safety in units = 1,800 - 1,000 = 800 units. Margin of safety ratio = 800 / 1,800 = 44.44%.
Target profit check: Current profit = (1,800 × 400) - 400,000 = 720,000 - 400,000 = KES 320,000. Target profit is KES 300,000, so the company is exceeding the target by KES 20,000. Thus, it is meeting the target profit.
2. Evaluate the marketing manager's proposal. Calculate the new break-even point and profit at 2,500 units under the proposal. Advise whether the proposal should be accepted, considering the target profit.
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Proposal analysis: New selling price = 1,000 × 90% = KES 900. New contribution per unit = 900 - 600 = KES 300. New sales volume = 2,500 units, which exceeds 2,000, so fixed costs = 400,000 + 200,000 = KES 600,000.
New break-even point: Break-even units = 600,000 / 300 = 2,000 units. However, at 2,000 units, fixed costs are only 400,000 (since the step is for >2,000). So we must check break-even within the first range: at 2,000 units, contribution = 2,000 × 300 = 600,000, which covers fixed costs of 400,000, giving profit 200,000. So break-even is actually lower than 2,000? Let's compute: For volumes up to 2,000, fixed costs = 400,000. Break-even = 400,000/300 = 1,333.33 units. Since 1,333 < 2,000, this is valid. So break-even is 1,334 units (rounded up). But wait, at 2,500 units, fixed costs are 600,000. The break-even in that range would be 600,000/300=2,000 units, but at 2,000 units fixed costs are 400,000, so the break-even in the second range must be above 2,000. Actually, at 2,001 units, fixed costs jump. So the break-even point is the volume where total contribution equals total fixed costs. For volumes >2,000, fixed costs=600,000, so break-even = 2,000 units, but that's exactly at the threshold. At 2,000 units, fixed costs are 400,000, so profit is 200,000. At 2,001 units, contribution = 2,001×300=600,300, fixed costs=600,000, profit=300. So break-even is just above 2,000. Precisely, break-even = 600,000/300 = 2,000 units, but since at 2,000 fixed costs are 400,000, the actual break-even is 2,000 units? No, because at 2,000 units, contribution is 600,000, fixed costs 400,000, profit 200,000. So break-even is lower. The break-even point is the volume where profit=0. For V<=2000: profit = 300V - 400,000. Set to 0: V=1,333.33. For V>2000: profit = 300V - 600,000. Set to 0: V=2,000. But 2,000 is not >2000, so the break-even in the second range is not attainable because at 2,000 fixed costs are still 400,000. Actually, the profit function is discontinuous: at V=2000, profit=200,000; at V=2001, profit=300. So there is no break-even point above 2,000 because profit jumps from 200,000 to 300. The company is always profitable above 1,333 units. So the break-even point is 1,334 units. However, the step fixed cost creates a discontinuity, but the break-even remains at 1,334 units. But we must ensure that at 1,334 units, fixed costs are 400,000, which they are. So break-even = 1,334 units.
Profit at 2,500 units: Contribution = 2,500 × 300 = 750,000. Fixed costs = 600,000. Profit = 150,000.
Advice: Under the proposal, profit at 2,500 units is KES 150,000, which is below the target profit of KES 300,000 and also below the current profit of KES 320,000. Therefore, the proposal should be rejected. The price reduction erodes contribution margin, and the additional fixed costs further reduce profitability. The company would need to sell more than 2,500 units to achieve the target profit. To find the required volume for target profit of 300,000 under proposal: (600,000+300,000)/300 = 3,000 units. Since 3,000 > 2,500, the proposal is not viable. Management should consider alternative strategies such as cost reduction or increasing sales without price reduction.