# How to calculate PV of annuities for a home loan

I am trying to model investing in residential real estate vs investing fully in stock. I have a corpus of say 1M in S&P500. I also receive monthly income which will be used to either invest in this real estate or stock

Scenario 1: I buy a house and put it up on rent and sell it after 20 years. There will be mortgage that i will have to pay which will be offset by the rental income every month.For the first 15 years mortgage > rental income and then opposite. This delta will be funded with my monthly income, remaining will be invested in S&P500. How do i calculate the PV of these 2 annuities? What should be the discount factor- should it be wacc or opportunity cost of s&p500?

The alternate scenario is: I fully remain invested in S&P500. and the monthly income also remains in S&500. How do i compute PV of the monthly income? do i discount it with S&P rate or risk free rate or opportunity cost of scenario 1?

## 2 Answers

For the real estate scenario:

Calculate net cash flow by subtracting mortgage payments from rental income monthly. When the mortgage payment exceeds rental income, use your monthly income to cover the difference. Compute the PV of this stream using a rate representing your investment cost—like a weighted average cost of capital (WACC) considering borrowing costs and opportunity costs.

Invest the remaining funds in S&P500. Compute the PV of this investment stream using the opportunity cost, i.e., the expected return from S&P500.

For the scenario entirely invested in S&P500:

Compute the PV of monthly income invested in S&P500 using the expected return from S&P500 as the discount rate.

For real estate, use WACC for mortgage and income coverage, and S&P500's expected return for invested funds. For S&P500 scenario, employ the S&P500's expected return for discounting the income. Remember, these calculations rely on future projections and rates of return, which can vary. Consider risk, inflation, and other factors affecting money's future value.

• Thanks. One way to model wacc is to take how much downpayment ill do and discount that with S&P returns, and the remaining loan with interest rate of the loan. Is this correct? How do i factor in opportunity costs? FOr the scenario entirely invested in S&500: Here im confused - do i factor in S&P500 returns, or S&P500 and inflation. Also, its counterintuitive that im penalizing S&P500 investment with my income with a higher discount rate. That would skew the output towards debt based strategy as the dcf will be lower Commented Dec 20, 2023 at 21:22

There are a few things to consider even before comparing the rental to alternative investments:

• Can you cash-flow the mortgage payments, insurance, and taxes if the house goes unrented for 6 months (i.e. can you keep from getting foreclosed on)?
• Do you even want to be a part-time landlord?

If you are comfortable with that risk and want to compare the rental to the S&P 500, then using the expected return of the S&P 500 as the discount rate will tell you that. If the NPV of all cash flows (including the upfront cost, rental income, maintenance, taxes, sale value, etc.) is positive, then it's expected (but not guaranteed) to be more profitable. I would also take into account the fact that the S&P is truly passive, while real estate is not. You could add some cash flow to "pay yourself" for the time required to manage the investment to account for that. Or you could use a slightly higher discount rate that the expected S&P return. There's not really a "right" answer for intangible considerations like those.

This assumes that real estate and the S&P 500 are equally risky, which may not be the case, but if the efficient use of risk is not your main concern, then using the S&P return as a discount rate is appropriate for a pure return comparison.

• Fair callourts. I want to start by purely tangible considerations, and then add in time cost. One way im thinking is to add cost of hiring an agent. That is equivalent of time value for me. How do i model efficient use of risk if i had to? Can you point me to some examples Commented Dec 20, 2023 at 21:24
• Even with an agent you will have some personal time invested, but sure, you could add in property management cost. By "efficient use of risk" I mean even if the returns for a rental are higher, there may be more risk so you have higher potential downside risk than, say the S&P 500. There's no practical way to measure the "risk" of a single rental. Commented Dec 20, 2023 at 22:03