Reversing a Calculator Formula - Help Needed

[Ckot]

I have a simple excel formula that tells me the return (ROI) of a stock investment based on the share sell price (column B). I'd like to reverse engineer things and input the ROI (column C) so it tells me the price to sell at for that target ROI. Stuck on this bad. Had to zip the excel so it would attach. Promise no spam/malware. Just basic spreadsheet with a few basic math formulas

 

[stapel]

I have a simple excel formula that tells me the return (ROI) of a stock investment based on the share sell price (column B). I'd like to reverse engineer things and input the ROI (column C) so it tells me the price to sell at for that target ROI. Stuck on this bad. Had to zip the excel so it would attach. Promise no spam/malware. Just basic spreadsheet with a few basic math formulas

I'm sorry, but nobody at all web-savvy is going to download and open an unknown ZIP file.

Please reply with the formula you are wanting to "reverse", along with a clear listing of your thoughts and efforts so far. Thank you!

 

[Ckot]

Pic instead

OK, thank you. The image below shows the basic formulas, used in sequence to obtain ROI.


I'm been trying to reverse engineer this, where I can input the desired ROI of say, 10%. And then obtain the result of what share price to sell at.

 

[Ckot]

My Thinking

When putting all the separate small formulas together, I get
.10 = ((E-(C+(((A*X)-C)*.33)))/(C+(((A*X)-C)*.33)))

.10 being the target ROI
X being the target share sell price

I just can't figure out the formula with 2 instances of X

 

[stapel]

OK, thank you. The image below shows the basic formulas, used in sequence to obtain ROI.
View attachment 8080

I'm been trying to reverse engineer this, where I can input the desired ROI of say, 10%. And then obtain the result of what share price to sell at.

The formulation for "I" ends up having three variables (being the inputs A, B, and D). There is no way to pick a value for "I" and then be able somehow to find "the" values for A, B, and C. There would be infinitely-many solutions.

What, exactly, is this exercise asking you to do? What, specifically, do the instructions say? Thank you!

 

[HallsofIvy]

When putting all the separate small formulas together, I get
.10 = ((E-(C+(((A*X)-C)*.33)))/(C+(((A*X)-C)*.33)))

.10 being the target ROI
X being the target share sell price

I just can't figure out the formula with 2 instances of X

Then put them together.
\(\displaystyle .10= \frac{E-(C+ 0.33(AX- C))}{C+ 0.33(AX- C)}= \frac{E- 0.33AX- 0.67C}{0.33AX- 0.67C}\)
Multiply on both sides by the denominator 0.33AX- 0.67C:
\(\displaystyle .10(0.33AX- 0.67C)= 0.033AX- 0.067C= E- 0.33AX- 0.67C\)

Add 0.33Ax+ 0.067C to both sides:
\(\displaystyle 0.363AX= 0.603C\)

Finally, divide both sides by 0.363A:
\(\displaystyle X= 1.6611\frac{C}{A}\).