Finance Question? What kind of equation am I looking for?

abovetheclouds

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Mar 1, 2022
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I may be in the wrong sub-forum, if so please move to where it belongs. I don't know precisely what kind of math I'm trying to figure out here. Thanks! Hopefully what I'm saying below makes sense to you despite seeming kind of complicated to me. I included abbreviations for the variables, use them if they help share an answer or discard them if they are confusing or unhelpful.

Let's say I am trying to purchase a skyscraper. I will be forced to make a Down Payment (DP) of 20% of my Offer Price (OP). I will need to make an Initial Investment (II) into the skyscraper because it is really dated. However, once I make the Initial Investment, the skyscraper will be worth the Market Value (MV). I can then recover a Refinance Total (RT) equal to 90% of Market Value (MV).

The Offer Price can be anything I want but the Market Value, Initial Investment and the fact that the Refinance Total equals 90% of MV cannot change. What I am trying to solve for is the Offer Price (OP) that makes the Refinance Total minus (Initial Investment + Offer Price) equal the Down Payment.

I am confused with the problem because the Down Payment changes in response to adjustments to the Offer Price. And because I have the Offer Price, which I'm trying to solve for, situated on both sides of the equation.

If it helps, let's make the following values available for any response I might get:
Offer Price (OP) = ??
Initial Investment (II) = $1,000,000
Market Value (MV) = $20,000,000
Refinance Total (RT) = .9MV = $18,000,000
Down Payment (DP) = .2(OP)

How do I solve this so that the Offer Price results in (Refinance Total minus (Initial Investment + Offer Price)) equal to the Down Payment or (20% of Offer Price)?
 
How do I solve this so that the Offer Price results in (Refinance Total minus (Initial Investment + Offer Price)) equal to the Down Payment or (20% of Offer Price)?
Translate what you want into a math equation:
[math] RT-(II + OP)=DP\\ RT-II-OP=DP\\ OP=RT-II-DP \\ OP=.9MV-II-.2OP \\ \boxed{OP=\frac{.9MV-II}{1.2}}[/math]
 
That seems to be it! Thanks a lot. I had the formula right except I was putting it over .2 not 1.2 so I thought I was way off based on the numbers I was getting. Thanks again.
 
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