Non-linear effects

Since 2017, the percentage rate of flat-rate expenses has been increased from 40% to 60% of the total income. The monthly limit (420 euros) has been cancelled and the annual limit of the sum of flat-rate expenses is increased from 5 040 euros to 20 000 euros. The changes in the flat-rate expenses are a consequence of the adoption of the law no. 341/2016 Coll., which amended the law no. 595/2003 Coll. on income tax as amended (hereinafter only "income tax act").

Calculate:
a) the minimum total income at which the ceiling of 20 000 EUR on flat-rate expenses is applied
b) what is the real percentage rate of flat-rate expenses at a total income of 40 000 EUR
c) what is the real percentage rate of flat-rate expenses at the maximum possible total income (i.e. 49 790 EUR, the exceeding of which makes the taxpayer a VAT payer and he cannot apply flat-rate expenses)?

Final Answer:

a =  33333.33 EUR
b =  50 %
c =  40.1687 %

Step-by-step explanation:

$$\begin{gathered} r=60\%=\frac{60}{100}=\frac{3}{5}=0.6 \\ r\cdot x=20000 \\ 0.6\cdot x=20000 \\ 0.6x=20000 \\ x=\frac{20000}{0.6}=33333.33333341 \\ x=\frac{100000}{3}\doteq 33333.333333 \\ a=x=33333.3333=33333.33\text{EUR} \end{gathered}$$

$b=100\cdot \frac{20000}{40000}=\frac{100\cdot 20000}{40000}=\frac{2000000}{40000}=50\%$

$c=100\cdot \frac{20000}{49790}=\frac{100\cdot 20000}{49790}=\frac{2000000}{49790}=40.1687\%$

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