I need to create a formula to solve a problem involving loan to value ratio (LTV) on a property and total funds (TF) available. Applying 80% LTV on £100 000 property price (PP) means, bank gives £80,000 and purchaser puts down £20 000 cash deposit (CD). However CD is limited by total funds (TF) available, i.e. purchaser's cash savings. CD cannot be greater than TF.

TF, LTV and PP are variable.

The problem is a little more tricky for me than it seems .

What I actually need is, given any value for TF and, LTV being between 0% and 100% what is the maximum purchase price of a property (PP).

If i'm given a mortgage with an LTV of 100% then i know that PP can be any value

If I'm given a mortgage with an LTV of 0% ie no mortgage then PP = TF = CD.