## Monday, July 16, 2018

### Interest Rates and Real Estate Pricing

Real estate investors are facing rising interest rates. Below is a graph with the 1-month forward LIBOR curve:

As demonstrated above, 1-month LIBOR, a benchmark rate commonly used in setting total interest rates for real estate loans, is currently at ~2.1%, which is just about equal to the 52 week high, and is expected to increase to about ~2.8% a year from now. The 52 week low, for comparison, is 1.2%. Let's create an example to see how rising interest rates affect real estate pricing.

### Which Valuation Metrics You Use Matter

The first important point here is that interest rates only impact certain return / valuation metrics. Unlevered metrics, almost definitionally, will not be impacted by changes in interest rates, insomuch as things like the purchase price and forecasted exit price are not impacted by interest rates (a big assumption, but necessary for our example). However, levered metrics (levered IRR, equity multiple, total profit to equity holders, etc...) are impacted by interest rates in 2 ways:

1. The size of loan that can be obtained
2. The cost of borrowing, i.e. the cost of debt, i.e. the cost of capital, i.e. the profit from operating cash flows received over the project

### Loan Sizing

Lenders often utilize debt service coverage ratio (DSCR) as a way to size the loan they are willing to issue a borrower for a particular property. DSCR is defined as (Adjusted Stabilized NOI / Total Loan Payment).

Adjusted Stabilized NOI = Stabilized NOI - (typically) a capex reserve

Total Loan Payment = Total Payment (both interest and principal) based on a given loan size (this is what we're trying to solve for)

A lender might set the ratio at 1.20x, which implies the ANOI must be 20% more than the total payment. The lender will have a interest rate and number of amortization periods that they will base the total payment off of. Again, total payment is a function of loan size, but we're trying to solve for the loan size, so it seems like we're stuck. Fortunately, we actually do know the biggest payment amount that we can afford which will then allow us to back into a loan size.

The max payment, based on a 1.20x DSCR, is then equal to our ANOI / 1.20. The example in our Excel sheet has a stabilized ANOI of \$975k. ANOI of \$975k would imply a total payment of \$812,500. Note that our total payment is a composed of an interest payment (derived from the interest rate the lender sets for the DSCR test) and an amortization payment (based on the amortization periods the lender sets for the test). Since we have interest rate, amortization periods and total payment amount, we can then back into the loan size.

For our Excel example, I've assumed the lender is applying a 30-year amortization period to the DSCR test. The interest rate used for the DSCR test is where it becomes applicable to our discussion on interest rates. In one case, I've assumed the lender is using the 52 week low 1-month LIBOR  rate of 1.2% plus a made-up spread of 4.0% for a total rate of  5.2%. In another case, I've used next year's projected 2.8% 1-month LIBOR rate plus the same made-up spread of 4.0% for a total rate of 6.8%.

Plugging these 2 cases into the PV calculation on Excel (=-PV(monthly interest rate, number of amo periods in months, the total payment amount) yields:

Total loan size of \$12.3 million in case 1 with the 5.2% total interest rate

and

Total loan size of \$10.4 million in case 2 with a 6.8% total interest rate.

As we see here, the loan size a lender is willing to provide changes drastically with the interest rate that is used in the test. Of course, there are several overly simplistic assumptions built in here for demonstration purposes (lender keeps the same spread in the interest rate, DSCR is the only loan sizing tool, etc...), but the main point / takeaway is that there is less cushion between NOI and debt service which will make lenders more conservative with loan sizing.

The amount of debt in a project will have a big impact on the project's cost of capital. Less debt = higher cost of capital, which hurts levered return metrics.

### Net Cash Flow

Simplistically, net cash flow is (NOI - Cost of Debt). Definitionally, if Cost of Debt increases (higher interest rate), then net cash flow will decrease.

### Excel Example Explained

In our Excel example, let's assume there is an investor looking at acquiring a hypothetical property. This investor needs to acheive a 15% levered IRR to make it an attractive investment for its risk level. The first set of levered cash flows, the 1.20% LIBOR cash flows, suggest a 15% levered IRR can be achieved at a \$16.4 million purchase price.

In the next scenario, 2.80% LIBOR cash flows, all assumptions are the same. The only change is the loan amount and debt service payments. This scenario suggests that to achieve the same 15% levered IRR, the investor can now only pay \$15.2 million.

Of course, this brings up the question of whether or not it's realistic to assume the same exit price as the first scenario. If the increase in interest rates have made this buyer only able to acquire this property for \$1.2 million less than before, isn't it reasonable to expect that the exit buyer is also only able to buy at a lower purchase price?

The third scenario, 2.80% LIBOR and 7.00% exit cap rate cash flows, demonstrates what happens if we take all the assumptions from the above example, but adjust our exit price expectations to reflect this rising interest rate environment. As we can see, the hypothetical investor's purchase price must now be \$14.5 million to achieve the 15% levered IRR.

The increase in LIBOR from its recent extreme low to its projected 2019 level has adversely affected the value of this hypothetical asset by almost \$2 million, about 12% of its value. Of course we've made many simplifying assumptions for this demonstration. For example, higher / rising interest rates tend to imply higher inflation which would imply rents growing faster and NOI growing faster.

But also keep in mind that this recent increase in interest rates is occurring at the tail-end of the longest commercial real estate bull market in history. Are investors really going to underwrite higher rent growth than they have in the past? Do investors really believe we're in a more inflationary environment now than in the past couple of years? I tend to think not.