# What return are you getting on your money from paying down a mortgage on a rental property?

If you bought a \$200,000 rental home with 20% down, what is the return on investment you're earning over the full 30 year period from paying down the loan using the rental income?

We will assume the property does NOT change in value at all over the 30 years since I'll attribute that return to appreciation.

Also, ignore any tax benefits or consequences.

Assume that the entire mortgage payment and all expenses of the property are exactly covered by the tenant's rent payment and not included in this particular calculation.

I don't think it is relevant, but the interest rate you're paying on the loan is 4.5% fixed for 30 years.

• You mentioned tenant, are you asking how to calculate ROI for a rental property? – littleadv Nov 20 '15 at 5:28
• No. Specifically just the ROI from paying down the mortgage. I can calculate Cash on Cash Return from the cash flow. – James Orr Nov 20 '15 at 5:29
• So.... paying down the mortgage changes the invested cash amount in the cash-on-cash calculation. Which you already know how to do. So, what's exactly not clear to you? – littleadv Nov 20 '15 at 5:31
• Let me rephrase to clarify: if I bought a rental property with a 30 year mortgage and put \$40,000 down. Assuming I am exactly break-even on income and expenses for the rental. Further assuming the property does not go up in value at all. And finally, assuming I have no tax benefits. What is the return I've earned on my \$40,000 when the mortgage is paid off in 30 years? – James Orr Nov 20 '15 at 5:39
• If your expenses are covered by the income exactly, as you have said to assume, then you are basically starting with a \$40K asset (your starting equity), and ending with a \$200K asset (a paid for home, at the same value since you have said to ignore any appreciation). So, to determine what you have earned on the \$40K you leveraged 5x, wouldn't it be a matter of computing a CAGR that gets you from \$40K to \$200K in 30 years? The result would be a nominal return, not a real return. (p.s. non real-estate investments leveraged 5x might also produce impressive returns, or as dreadful losses.) – Chris W. Rea Nov 20 '15 at 5:53

This is a great question, considering that all of your expenses including PITA, Maintenance, etc. are paid by a tenant, your cash flow is \$0. Most people would stop and assume your investment is not performing and your only chance at making money is through appreciation. Your question eliminates appreciation so here are the returns you would get on your investment. The math will probably surprise many that you are actually earning a return on your money.

Annual Return = [((Future Value)/(Initial Investment))^((Periods per Year)/(Number of Periods) -1]*100 %

5.51% = [(\$200,000/\$40,000)^(12/360)-1]*100 %

As Chris Rea commented:

The subtlety that some would miss is that while "income covers expenses exactly", embedded in the "expenses" is actually a repayment of the loan principal (and technically, that's not an "expense") so not all of the income is "lost" covering the "expenses". That repayment of principal portion of the rental income constitutes the return on the original capital invested.

• The subtlety that some would miss is that while "income covers expenses exactly", embedded in the "expenses" is actually a repayment of the loan principal (and technically, that's not an "expense") so not all of the income is "lost" covering the "expenses". That repayment of principal portion of the rental income constitutes the return on the original capital invested. – Chris W. Rea Nov 20 '15 at 13:55

There are a few ways to look at this question.

• What is the return on equity? At any given time? Or averaged over the course of 30 years?
• What is the return on paying down the mortgage?
• What is the internal rate of return if the owner never sells?

Assumptions.
Per the original post's assumptions, this answer:

• Ignores income taxes, property taxes, insurance, property management costs, depreciation, maintenance, changes in rental value, and property appreciation.
• Ignores pre-payment penalties, and opportunities for refinancing.
• Assumes that after taxes and maintenance, the net revenue is enough to cover the initial principal and interest payment, and remains at that level regardless of any financial engineering.
• Assumes a 20% initial equity, with no other out-of-pocket initial costs.
• Assumes a fixed-rate 4.5% APR level-payment mortgage amortized over 360 months.
• 4.5% APR corresponds to 4.594 % APY.
• The first month's \$ 810.70 principal and interest payment consists of \$ 600 of interest, and \$ 210.70 of principal.

In other words, if the owner paid the mortgage on its original schedule, the deal could boil down to a \$ 40,000 up-front payment, in exchange for \$ 200,000 of equity after 30 years. Or the deal could boil down to a \$ 40,000 up-front payment, in exchange for a \$ 810.70 monthly payment starting in 30 years.

While the owner is paying down the mortgage, the return on equity is the principal payment divided by the equity. The principal payment is the net rent minus non-financing costs and interest, so it is actually a profit.

The initial return on equity is 6.321 % APR, or 6.507 % APY. This is calculated by dividing the \$ 210.70 monthly principal payment by the initial \$ 40,000 equity, and converting from monthly return to annual return.

After 30 years, the return on equity is 4.864 % APR, or 4.974 % APY. This is calculated by dividing the \$ 810.70 monthly cash flow (which is no longer reduced by mortgage payments) by the \$ 200,000 equity after 30 years, and converting from monthly return to annual return.

The cap rate is the same as the return on equity in the absence of debt. In this example, 4.864 % APR, or 4.974 % APY.

The return on equity declines from 6.507 % APY initially to 4.974 % APY after 30 years. This is because the cap rate exceeds the note rate (4.974 % APY vs. 4.594 % APY), and the leverage decreases from 5x to 1x.

The weighted average compound annual growth rate of the equity during the 30 years is 5.511 % APY. Per the original poster's answer, this is computed by taking the 30th root of the 5-fold increase in equity. Because the owner made no extra principal payments (besides those already discussed), the relevant amounts are the initial \$ 40,000 owner payment and the final \$ 200,000 owner equity. 5.511 % APY corresponds to a 5.377 % APR.

The internal rate of return if the owner never sells can be computed by treating the deal as a \$ 40,000 up-front payment, in exchange for an \$ 810.70 monthly payment starting in 30 years. The internal rate of return (IRR) is not a very useful number, because it assumes that you can somehow reinvest the eventual dividends at the same rate. In this example, the IRR is 5.172 % APR, or 5.296  % APY. In this example, the IRR is calculated by (iteratively) finding an interest rate for which (initial investment) * (1 + IRR) ^ (number periods before dividends start) = (periodic dividend) / (IRR - growth rate of dividend). For example:

\$ 40,000 * (1.004309687)^360 = \$ 810.70 / (0.004309687 - 0) = \$ 188,111

I then converted the 0.431 % monthly IRR to an annual IRR.

The deal can be thought of as a return on equity, plus a return on paying down the mortgage.

When computing the return from paying down the mortgage, the initial equity is irrelevant. It does not matter whether you start with a \$ 160,000 mortgage on a \$ 160,000 property, a \$ 160,000 mortgage on a \$ 200,000 property, or a \$ 160,000 mortgage on a \$ 1,000,000 property. All that matters is the note rate on the mortgage, which is the applicable compound interest rate.

The return on paying down the mortgage equals the note rate of the mortgage. For a 4.5% note rate, this works out to a 4.594% annual percentage yield (APY).

You can confirm this by looking at your amortization schedule. Suppose you have a \$ 160,000 mortgage with a fixed 4.5% APR note rate for 360 months. Your monthly payment is \$ 810.70. In the first month, \$ 600 goes toward interest, and \$ 210.70 reduces the principal. In other words, the \$ 210.70 principal payment eliminated the need for a \$ 810.70 payment 30 years later. Notice that:

```. \$ 210.70 * (1 + 0.045 / 12)^360 = \$ 210.70 * (1.00375)^360 = \$ 210.70 * 3.8477 = \$ 810.71```

which is within rounding error of \$ 810.70. The interest rate is 3/8 % per month, which is an APR of 4.5%, and an APY of 4.594 %.

• – James Orr Nov 20 '15 at 8:13
• Going back and reading your answer again Jasper, I find it exceptionally well thought out and detailed. Thank you again for updating it. – James Orr Nov 21 '15 at 5:31

As Chris pointed out:

If your expenses are covered by the income exactly, as you have said to assume, then you are basically starting with a \$40K asset (your starting equity), and ending with a \$200K asset (a paid for home, at the same value since you have said to ignore any appreciation). So, to determine what you have earned on the \$40K you leveraged 5x, wouldn't it be a matter of computing a CAGR that gets you from \$40K to \$200K in 30 years? The result would be a nominal return, not a real return.

So, if I set up the problem correctly, it should be:

`\$40,000 * (1 + Return)^30 = \$200,000`

Then solve for Return. It works out to be about 5.51% or so.