Subscription Price Cut with Fixed Costs
A small online course platform currently charges $30 per month and has 1,500 subscribers. Its monthly fixed cost is $18,000, and each subscriber costs $12 per month in hosting and payment processing. The founders are considering a promotional price of $24 per month. Their market test suggests that a 40% price cut from $30 to $24 would raise the subscriber count by 40%, to 2,100. Before deciding, they want to know whether the promotion improves monthly profit, how many subscribers would be needed at $24 to match the current profit, and whether the decision changes if fixed costs are expected to rise to $21,000 next month. The founders care about short-run profit but also want to avoid a promotion that only breaks even on a per-subscriber basis. They ask you to evaluate the proposal using only the data above.
1. Calculate current monthly profit and projected monthly profit at $24, then state whether the promotion should be approved if the goal is to maximize short-run profit.
Read the worked answer
Current price: contribution per subscriber = $30 - $12 = $18. Total contribution = 1,500 × $18 = $27,000. Monthly profit = $27,000 - $18,000 = $9,000.
At $24: contribution per subscriber = $24 - $12 = $12. Total contribution = 2,100 × $12 = $25,200. Monthly profit = $25,200 - $18,000 = $7,200.
The promotion lowers monthly profit by $1,800. It is still profitable in absolute terms because 2,100 subscribers exceed the $24 break-even count of $18,000 / $12 = 1,500, but it does not maximize short-run profit. On the stated goal, reject the promotion unless non-financial benefits are assigned a value.
2. At $24, what subscriber count would be required to match the current $9,000 monthly profit? Express the required increase over 1,500 as a percentage, and compare it with the 40% increase assumed by the market test.
Read the worked answer
Target profit = current $9,000. Required total contribution at $24 = fixed cost + target profit = $18,000 + $9,000 = $27,000. Required subscribers = $27,000 / $12 = 2,250.
Required increase = 2,250 - 1,500 = 750 subscribers. Percentage increase = 750 / 1,500 = 50%.
The market test assumes a 40% increase, which yields 1,500 × 1.40 = 2,100 subscribers. That is 150 subscribers short of the 2,250 needed to match current profit. The test therefore understates the lift required.
3. If fixed costs rise to $21,000, does the $24 price still cover total costs at 2,100 subscribers? What is the minimum number of subscribers at $24 to avoid a monthly loss?
Read the worked answer
At 2,100 subscribers and fixed cost $21,000: total contribution = $25,200, so profit = $25,200 - $21,000 = $4,200. The price still covers total costs at that volume.
Minimum subscribers to avoid a loss = $21,000 / $12 = 1,750. At 1,750 subscribers, contribution equals fixed cost and profit is zero.
For comparison, keeping the $30 price at 1,500 subscribers gives contribution $27,000 and profit $27,000 - $21,000 = $6,000. The $24 promotion still lowers profit by $1,800 relative to the current price. The higher fixed cost changes the break-even volume, not the ranking of the two prices at the stated volumes.