Calculating Spend from Revenue and ROI

Question

I'm trying to figure out what the formula would be to generate the Spend if I know the Revenue and the Return on Investment.

Here is the formula on how to calculate the ROI: (Revenue - Spend) / Spend

And here is an example using the formula above:

Spend:      $100
Revenue:    $300
Profit:     $200
ROI:        200%

So with the formula and example above, how do I generate Spend if I have the Revenue and ROI?

Answer 1

Let $S = Spend$

Let $R = Revenue$

Let $R_i = ROI$

You know $R_i = (R-S)/S$

Now, $SR_i = R-S$

$S(R_i+1) = R$

$S = \frac{R}{(1+R_i)}$