Ask Me Help Desk - Calculate year ago sales from current sales and percent change

Start with the formula for percentage change from one year to the next. If we let $x_0$ be the initial value, and $x_1$ be the value one year later, then the change in sales expressed as a percent of the initial value is then:

$ p =\ \frac {\Delta x} {x_0} \times 100 \ =\ \frac {x_1 - x_0} {x_0} \times 100 $

So if you know the percent change p and the value for $x_1$ you can rearrange this to get:

$ x_0 = \frac {x_1}{(1 + \frac p {100})} $

For example: if $x_1=1000$ and $p = 33.3%$ then

$ x_0 = \frac {1000}{(1 + \frac {33.3} {100})} = \frac {1000}{1.333} = 750 $

You can check this by substituting this value for $x_0$ back into the first equation and see if it agrees:

$ p = \frac {x_1 - x_0} {x_0} \times 100 = \frac {1000-750} {750} \times 100 = 33.3% $