April 21, 2024

by Stephen Stofka

This week’s letter is about the cash flows we receive from a house and whether we can use those cash flows to help us determine an appropriate price range for a house. While we might not think of a house as a business, the owner is a landlord. Like any business, a house has similar metrics: an initial investment, loans, cash flows, continuing expenses and investment, “sweat equity,” capitalization and profits.

A house offers similar features to a coupon bond with one important difference – the mortgage. When we buy a coupon bond, we pay for the bond outright. The bond pays a series of payments called coupons over the life of the bond, then pays back the principal amount at the end of the bond’s term. What is the coupon we receive from a house? The housing service which is valued at what we could expect to rent the house for. Each year we discount that coupon by the opportunity cost of what that money could earn. As a benchmark rate, I will use the 40-year average rate of 5.5% that a 30-year Treasury bond (FRED Series DGS30) has paid.

As I noted last week, average owner equivalent rent has grown 3.7% each year for the past thirty years. Urban areas drive the growth of housing rents, and the highest growth occurs in the most competitive cities that offer employment and urban amenities. For several decades the city average of owner equivalent rents has been 8 – 15% higher than the median household income in the country as a whole (FRED graph). Incomes are much lower in rural areas and so are the rents and the taxes. Some rural areas offer a picturesque natural setting and recreational opportunities, but the lackluster job market does not attract young families.

Consider a house that might rent for $2000 a month, or $24000 a year. In thirty years, that annual rent will be $68,833, the result of a 3.7% increase in housing rents each year. Using the 30-year Treasury yield of 5.5%, today’s net present value of those rising cash flows from the house is $537,673. I will leave the calculation in the notes along with the address of an online calculator so you can do this yourself. These are long-term averages that can vary by decade. In 2014 the fair market rent for a 2-BR apartment in the Denver metro area rose 20%, according to HUD. Rental prices can respond quickly and dramatically to population migration and underinvestment in multi-family housing.

An investment in a house is partially funded with a mortgage whose principal and interest payments remain stable for the term of the mortgage. Although interest rates are above recent averages, they are about half of what a borrower might pay on a car loan or a margin loan from a broker. Interest on car loans can vary from 6% to 25%, according to Bankrate.com. Vanguard would charge 11% to 14% on a margin loan to buy stock. These are shorter term loans yet charge higher interest rates. Implicit guarantees of mortgages by the federal government give a homeowner the same interest rate on long-term debt as Apple, the second most valuable company in the world. In 2014, Apple paid a rate of 4.45% on its 30-year bonds. The average 30-year mortgage rate (MORTGAGE30US) at that time was 4.36%.

While government support introduces distortions to the housing market, residential investment and strong population growth do not fit a free-market model because land in a dense urban area is not a commodity like farm or ranch lands. Before the Federal Housing Administration was created in 1934, creditors often required a down payment of up to 40% even from those with good income and credit, according to a history published by the Richmond Fed. In the late 19^th century, twelve percent of mortgages were underwritten by building and loan associations of the mortgage holders themselves. During stressful economic times, these associations would go bankrupt, leaving homeowners with deficient claims to their property. In all developed countries today, national government policies support home ownership.

Let us say a homeowner buys a home for almost $600,000 as in the example above. After thirty years, the owner will have received the net present value of the purchase price and will have a home that will be worth $2 million (calculation in the notes). However, this does not represent a windfall for the owner. A replacement home will also contain its cash flows for the past thirty years so that similar homes in that area will sell at a similar price. What the owner discovers is that their home’s value is priced like a share in a community resource. They can capture the capital gain in their home while they are alive by buying a home in a different community with a lower-priced resource pool, a strategy often employed by retired folks.

So, future cash flows are capitalized into the price of a house. The homeowner’s profit comes from any spread between the growth in house prices and the growth in market rentals over three decades of ownership. For some people, the true profit is the piece of mind that comes from ownership in a house that is mortgage free. Economic factors and changing tastes can slow the growth of home prices in an area. Crime may have increased; the quality of schools may have declined. Homeowners in these areas can feel trapped because they can not leverage the smaller equity in their home to buy a home in a more expensive area.

While the principal and interest on a mortgage remain stable during the term of the mortgage, taxes, repairs and insurance do not. Next week I will look at property taxes, the annual dues we pay to the county where our property is located.

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Photo by Kara Eads on Unsplash

This online calculator allows you to specify the number of cash flows but you need to input each cash flow.

Excel requires less work so you can calculate 30 years of cash flows based on a 3.7% increase in housing rents and an opportunity cost of 5.5% each year. Microsoft has an example of using NPV. In case you do not use Excel often for this kind of work, here are some instructions. In an empty spreadsheet:
In cell A1 enter 1.037. That is the annual growth of housing rents at 3.7%.
In cell B1, enter .055, the interest rate you could earn investing the purchase price of the house in a Treasury bond.
In cell A2, enter 24000, an estimate of the current rental value of the home.
In cell A3, enter the formula “=A2*A$1” without the quotes.
With the caret, grab the right lower corner of cell A3 and drag it down to include cell A31. This will copy the formula to the cells A4:A31.
In cell C1, enter “=NPV(B1, A2:A31)” without the quotes. That is the Net present value.
You can change the starting annual rent in cell A2, vary the discount rate in cell B1, or the growth of housing costs in cell A1. You can select and copy cells A1:C31, then go to cell E31 and paste in the cells. Now you have a side-by-side comparison.

Calculation of future home price: The Case-Shiller national home price index (CSUSHPINSA) has risen an average of 4.25% for the past 35 years.