【笔记】增值税计算笔记

设
进价为$\alpha$元
出价为$\alpha \tau$元
增值税率为$r$

$$\begin{gathered} \because \{\begin{array}{rl}进项税& =\frac{\alpha }{1+r}\times r\\ 销项税& =\frac{\alpha \tau }{1+r}\times r\\ 增值税& =销项税-进项税\end{array} \\ \begin{array}{rl}\therefore 增值税& =\alpha \times \left(\tau -1\right)\times \frac{r}{1+r}\end{array} \end{gathered}$$

$$\begin{gathered} \because 收入=出价-进价-增值税 \\ \therefore 收入=\frac{\left(\tau -1\right)}{1+r}\times \alpha \end{gathered}$$

当$\tau =1$时即按进货价出售，增值税为0，收入也为0。
当$\tau =1.2$时即进价加价20%出售。