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Set up the revenue side first: 20 users times (15 GB at $1 each) gets you $300 in usage revenue.
Break down the problem into revenue and cost components, calculate each separately, then subtract costs from revenue to find profit. Show your work step-by-step and state any assumptions clearly.
Pro tip: After calculating, briefly discuss how profit would change if key variables (e.g., usage, pricing) shift, showing business acumen. This demonstrates you think beyond the arithmetic.
List all provided numbers: number of subscribers (20), fixed cost ($400), variable cost per user ($5), price per GB ($1), and average usage per user (15 GB).
Compute total revenue by multiplying the number of subscribers, average usage per user, and price per GB: 20 * 15 * $1 = $300.
Compute total variable cost (20 * $5 = $100) and add fixed cost ($400) to get total costs: $500.
Subtract total costs from total revenue: $300 - $500 = -$200. The monthly profit is -$200 (a loss).
Explain that the company is operating at a loss and suggest potential actions, such as increasing price, reducing costs, or growing the subscriber base.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Plugged in 40 users: revenue becomes 40 times $15 = $600, costs are $400 + 40 times $5 = $600.
First, clarify the break-even definition and the cost structure (fixed vs. variable). Then, calculate the contribution margin per subscriber and determine the break-even subscriber count, comparing it to 40. Finally, state whether break-even is reached and discuss assumptions and sensitivity.
Pro tip: Always state your assumptions explicitly and note that the answer depends on the cost structure; this shows you think like a data scientist who understands business context.
Ask whether break-even means covering total costs (fixed + variable) or just variable costs, and identify which costs are fixed vs. variable.
Compute revenue per subscriber minus variable cost per subscriber to get the contribution margin that goes toward covering fixed costs.
Divide total fixed costs by the contribution margin per subscriber to find the minimum number of subscribers needed to break even.
If the break-even count is ≤ 40, then doubling to 40 reaches break-even; otherwise, it does not.
Highlight key assumptions (e.g., constant variable cost per subscriber, no economies of scale) and how changes could affect the conclusion.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Define the break-even condition by setting total revenue equal to total cost, then solve for the proportion of paid users. Use a simple equation with p as the fraction of paid users, and clearly state any assumptions (e.g., no other costs).
Pro tip: After solving, mention that this is a simplified model and that real-world factors like customer acquisition cost, churn, and economies of scale would affect the break-even point. This shows business acumen beyond the math.
Let p be the fraction of paid users, so (1-p) is the fraction of free users. Assume no other costs or revenues, and that each user is either free or paid.
Total revenue = 54p. Total cost = 1*(1-p) + 5p = 1 + 4p. Break-even when revenue equals cost: 54p = 1 + 4p.
Subtract 4p from both sides: 50p = 1, so p = 1/50 = 0.02 or 2%.
2% of users need to be on the paid tier. Verify: with 100 users, 2 paid generate $108 revenue, costs: 98 free * $1 + 2 paid * $5 = $108, break-even.
Mention that this is a simplified model; in reality, fixed costs, variable costs, and other revenue streams would change the break-even point.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.