Math question

[Brendan Blake]

Say I have this example

Rental Property: $100,000

Loan Amount: $75,000

Loan Rate: 5%

Years: 30 Year Amortized

Monthly Payment amount: $402.62

LTV ratio: 75%

My money is being put to work in two ways, 1) creating a pos cash flow 2) building equity in an asset. Obviously cash on cash return is decently easy to calculate but I find the equity return to be harder to calculate. Say that the property appreciates 1%, how do I calculate the return on the mortgage payoff, obviously less future interest is needed to be paid because the bank now owe less of it and since there is an appreciation in the home my equity I'm building is then worth more.

Any formula that would delve into this would be appreciated.

[Dion DePaoli]

The equity is only realized upon liquidation or if you tap in to it through a refinance. Appreciation applied can be a fairly linear approach. Simply use a make sense number, like you have listed of 1%.

In the model simply make an assumption of sale somewhere in the future. Then determine what the principal balance would be at the time of sale. In order to do that, simply calculate what principal would have been paid during the term of the loan and subtract it from the original balance. If you use excel, it has a built in formula for Cumulative Principal, that is what I will put here, although you can use a financial calculator or short hand math as well. But this will be pretty simple for you to work with.

=CUMPRINC([Rate],[nPer],[PV],[Start Period],[ End Period],[Type])

Defined:
Rate = 5% (divided the rate by 12 annual payments so '5%/12')*
nPer = 360 (amortization)*
PV = $75,000 (original loan amount)
Start Period = 1
End Period = 12
Type = 0 (payment made at beginning of period)

** - these ideas just need to match. If you use years, then you don't have to break interest into monthly periods, so no divide by 12. That only be a calculation for each year at a time so you could not find 1.5 years only 1 and 2, etc.

So in your example, at the end of year 1 (periods 1 through 12), you will have paid $1,163.14 in principal. So the balance due will be $73,893.48. If you sold the home for $100,000 and we estimate closing costs to be 10% (round number) then you take the difference between the net proceeds from sale and the balance. ($90,000 minus $73,893.48) you will get the gain on sale of $16,106.52.

To factor in appreciation, simply multiply the appreciation number to the original purchase price and add that together to make your sale price. So instead of the sale price of $100k, you sell for $101k.

"....calculate the return on the mortgage payoff, obviously less future interest is needed to be paid because the bank now owe less of it and since there is an appreciation in the home my equity I'm building is then worth more."

There is really no 'return' on a mortgage payoff. You just pay the balance. The idea of interest is not really coming into play here since interest is paid with principal as a function of amortization. Assuming this is a fixed rate mortgage your payment remains the same through the life of the loan. The amount of that payment that is allocated to reduce principal grows from period 1 through period 360 and interest goes down.

I feel like to some degree the interest idea you have in your head is confusing you. You solve for the amount of principal paid, the interest paid does not affect what is owed in the future. It is just what it is.

What order of operations you put these in will not matter much. So you can find the principal paid then find the appreciation and then sale proceeds, etc. Looking at any amortization schedule, you can also simply add the principal payments up for each period or some of them have a cumulative principal column.

In your example, the original $25k in equity would not be realized for 7 years if you are selling the property. In year 7 you would net $25,584.77, using all the assumptions herein.