Question

There are 2 different catalogs sent to customers. One of the catalogs costs 50 cents to make and is 50 pages long. The conversion rate for the catalog is 5% and each customer brings in 315 dollars. The second catalog costs 95 cents to make, is 100 pages long and each customer brings in 300 dollars from it. The profit margin is 30%. What should the conversion rate for the second catalog be to make at least the same amount of profit as the first one.

Answer 1

We can assume without any loss of generality that 100 catalogs of both the 1^st and the 2^nd type are made.

In case of the 1^st catalog, the cost is 100 * $ 0.50 = $ 50. The conversion rate is 5 % so that the number of customers that the 1^st catalog brings in is 5. Hence, the revenue generated is 5 * $ 315 = $ 1575 so that the profit is $ 1575 - $ 50 = $ 1525.

Let the conversion rate for the 2^nd catalog be x %.

In case of the 2^nd catalog, the cost is 100 * $ 0.95 = $ 95. The conversion rate is x % so that the number of customers that the 2^nd catalog brings in is x. Hence, the revenue generated is x * $ 300 = $ 300x so that the profit is $ 300x-95.

If the second catalog is to make at least the same amount of profit as the first one, then 300x-95 ≥ 1525 or, 300x ≥ 1525+95 or, 300x ≥ 1620 so that x ≥ 1620/300 i.e. x ≥ 5.4.

Thus, the conversion rate for the second catalog should be at least 5.4 % to make at least the same amount of profit as the first one.