The conversion rate of the second catalog need to be a minimum of 5.4% in order to make the same amount of profit as the first catalog.
Conversion costs are the manufacturing expenses needed to transform raw resources into finished goods.
To calculate the value of ending inventory, which is then recorded in the balance sheet, cost accounting uses the concept.
Looking at the 1st catalog, the cost of production = 100 * $ 0.50
= $ 50.
This mean that the rate of conversion is 5 %.
Hence, the number of customers that the 1st catalog brings in is 5.
Therefore, the revenue generated is computed at:
5 * $ 315
= $ 1575, and
Profit is (Revenue less cost)
= $ 1575 - $ 50
= $ 1525.
Assuming that the conversion rate for the 2nd catalog is y%
Hence, for the second catalog, the cost is
100 * $ 0.95
= $ 95.
The conversion rate is y % so that the number of customers that the 2nd catalog brings in is y.
Therefore, the revenue generated is y * $ 300
= $ 300y; therefore,
The profit is $ 300y-95.
From the above, we can state mathematically that if the 2nd catalog will make the same amount of profit like the first, at the very least, then:
our function should be stated as follows:
300y - 95 ≥ 1525; that is
300y ≥ 1525+95; that is
300y ≥ 1620; hence
y ≥ 5.4
QED
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