I continue the example from the previous post about your potential business. How do you find out if the price is set correctly and how many books he needs to sell in a month to make this business profitable?

First, you need to decide whether you will invest your money or borrow it from the bank. The cost of the loan over the next year and the sum of interest from the bank deposit can calculate from the formula:

A = B * ( 1 + r/n )n – B

In this formula, “r” is the interest rate on the loan or deposits during the month, and “n” is the number of months. The symbol “B” is the amount given or borrowed from the bank. Since the deposit has an annual interest rate of 6%, so “r” is 0.5% per month. In contrast, the annual interest rate on a loan is 12%, so “r”=1% per month.

From this formula, we calculated the value of interest on the deposits A=740 PLN and the value of interest on the loan for the bank A=1521 PLN. This means that if Nowak decides to invest his money, even if he gets his 12,000 PLN back in a year, he will be 740 PLN behind compared to if he put his money in the bank today. When he takes a loan, he’ll come out even worse off. He will then lose PLN 1521, which he will have to compensate from the company’s profits. You can see that he will incur a higher cost by taking the loan, but something for something – his savings will earn interest in the bank and he will feel more secure. The actual cost of the loan is the difference of these amounts, or PLN 781.

And what about inflation? It turns out that he should actually earn not 12,000 PLN, but 8% more (for simplicity), or 12960 PLN. Inflation always complicates the situation. For simplicity in this example I will omit it, but you can already see that it is not an amount to be ignored in real conditions.

To calculate the number of books you need to sell, you should go back to elementary school math. With its help, you will determine 2 functions, one of which will illustrate the costs and the other the revenues of the bookstore. The intersection of these functions will determine the number of books you need to sell for you to start coming out ahead.

The monthly cost function for the first year of operation will be built from two types of costs:

- fixed, i.e. Kowalska’s salary of 4819 PLN, rent of premises of 2000 PLN, financial service fee of 500 PLN and other costs – 2000 PLN, as well as fixed return of invested capital (if it was his money) or repayment of the bank loan with interest – 1061.7 PLN in the case of savings ((12000 + 740)/12) and 1126.8 ((12000 + 1521)/12) PLN in the case of the bank loan,
- variable, and therefore dependent on the number of books sold, purchased at the wholesaler at an average of PLN 20 each.

The monthly cost function will therefore have the formula:

- in the case of investing your savings, y = 20 * x + 10380.7,
- and in the case of taking a bank loan y = 20 * x + 10445.8.

The monthly revenue function will depend only on the income from the sale of books, so it will have the form y = 50 * x. In all formulas, “x” means the number of books that guarantees that the business begins to be profitable for you. The symbol “y” will then determine the amount of revenue necessary for this purpose.

And this is where a repeat of elementary school will come in handy. After solving two systems of equations, you will find out how many books you need to sell in a month to start making a profit. If you take a bank loan, the number of books is 346, and if you invest your own money, it will be 349. The value of monthly income in the first case is 17,300, and in the second case – 17,450 PLN.