Calculating discount not working

The method of increasing a value $V$ by $p\%$ is actually adding $V\times\frac p{100}$: $$V_\text{new} = V + V\times\frac p{100} = V\times\left(1 + \frac p{100}\right)$$ For $p=15$ you have a nice multiplier $$\left(1 + \frac p{100}\right) = 1 + 0.15 = 1.15$$

Remember, however, that '1.p' is a shortcut or mnemonic, not a method. It wouldn't even work for $p$ greater than 99, say for $+120\%$. And it certainly won't work for $p <0$.

For decreasing you need to apply the method, which is: $$V_\text{new}=V - V\times\frac p{100} = V\times\left(1 - \frac p{100}\right)$$ so for 15-percent decrement you get: $$V_\text{new}=V - V\times\frac {15}{100} = V\times(1 - 0.15) = V\times 0.85$$

EDIT

To answer your main question directly, forget percentages. Suppose you need to rise a value from 100 to 125. The new value is $$125 = 100\times\frac 54=100\times(1+\tfrac 14) $$ hence an increase by 25%. Now, if you want to reduce it back to 100, you get $$100=125\times \frac 45=120\times(1-\tfrac 15)$$ which is 20% decrease. Why was it 1/4 before, and 1/5 now? Because the same difference $\pm 25$ was taken relative to 100 in the former case and to 125 in the latter one. When we added a fourth part, we got five fourths of the initial value, so we needed to take away one of those five, i.e. a fifth part to get back.

And here you have the difference in percentages: 1/4=25%, while 1/5=20%.

So, a division like $value/1.p$ reduces the value by p% of the resulting value, not of the original one.

The reason that your suggested formula doesn't work is that "increase by $k$%" and "decrease by $k$%" do not undo one another like $+5$ and $-5$ or $\times 2$ and $\div 2$ do (we would say that they are not inverses).

For example $100$ increased by $50\%$ is $150$. However, $150$ decreased by $50\%$ is 75.

Therefore, if we want to decrease a number by a percentage, we can't just attempt to do the opposite operation of increasing by that percentage.

What you did is the right answer to a different problem. The general method, "multiply by $1+$ change" is a good one when used properly.

To increase a number by $15\%$ you multiply by $$ 1 + 0.15 = 1.15. $$ To decrease a number by $15\%$ you multiply by $$ 1 - 0.15 = 0.85. $$ But to undo a $15\%$ increase you have to "unmultiply" by $1.15$. So you divide by $1.15$. Since $$ \frac{1}{1.15} = 0.86956521739 \approx 0.87 = 1 - 0.13, $$ to undo a $15\%$ increase you make a $13\%$ decrease.