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The Math Behind Purchasing a Home: Part II

Updated: Dec 15, 2020

The sequel that nobody, not even me, expected. This post will compare the profitability of purchasing a home and renting one over 5, 10, and 15-year periods. This exciting sequel follows the first post, The Math Behind Purchasing a Home, which can be found on the homepage under Posts. This discussion topic uses the Home Buying Calculator, which can be found on the Downloads page.


For a new reader or for a refresher, head to the first post and take a look at the Mortgage Data tab in the Home Buying Calculator to see the total cost of homeownership. This is an important read, as we are assuming the same down payment, rate, mortgage amount, etc. for this discussion.


Overview

Making a bold assumption that you read the initial post on this topic, remember that owning a home comes with additional costs including mortgage insurance, HOA fees, taxes, homeowner's insurance, etc.


We're going to find out how those costs add up over time, the homeowner's return on sale at different intervals, and if renting a home and investing would have resulted in a better return on investment than buying a home. Just like the first article, we're using data from 1991 to 2019, all of which is found online. The Home Price data and the S&P 500 data have been indexed to 100 at 1991, so the value growth of each can be easily compared


Index Values

The not-blurry-at-all table above shows the values that the S&P 500 and Home Price Indices reach during 5-year intervals. Both indices are indexed to 100 in 1991 (Home Price Index is slightly higher since it was close enough to 100 in 1991). These are the values that we will be comparing to over time. The above table essentially shows that the S&P 500 had a 91% increase from 1991 to 1996, a 194% return between 1991 and 2001, and so on.


Home Ownership Costs

The Home Buying Calculator shows that the all-in mortgage payment would be about $1,243/month for the scenario defined in the initial post. For our purposes, this means that the homeowner would have paid the following in costs at the given time intervals. Keep in mind, this does not include broker's fees, third-party fees, or other fees of the like.

Year 5: $74,000

Year 10: $149,000

Year 15: $224,000


Rental Costs

The table above shows the cost of renting annual, assuming a 3% annual rent increase, industry standard. For our purposes, this means the renter would have paid the following amounts in total rent:

Year 5: $79,000

Year 10: $171,000

Year 15: $227,000


5-Year Return

Year 5 shows the S&P reached an index of 191 while home prices reached an index of 116. The renter would see their S&P 500 investment of $40,000 increase to $77,600. After five years of renting, the renter would have paid about $79,000 in rent, per the table below.


At year five, the investor would have put forth a total of $119,000 between rent payments and investment in an S&P 500 index fund, resulting in a $42,000 loss. Let's take a look at how the homeowner would have fared over in Year 5.


In 5 years of making an all-in housing payment, the homeowner would have made $74,000 in housing payments, a total of $114,000 including the $40,000 down payment. At Year 5, the homeowner's index reached 116, indicating that the home value would have been worth $232,000 upon sale. The Amortization Schedule in the Home Buying Calculator shows that the mortgage balance would be about $143,000, indicating that the homeowner would pocket about $90,000 after sale, resulting in, a loss of $24,000 after accounting for the homeowner's all-in housing payment. Let's see how the renter and homeowner fare after 10 years.


10-Year Return

At Year 10 the S&P 500 shows a value of 294 while the Home Price index reached 153. In real dollars, the renter's initial investment of $40,000 into an S&P 500 index fund would be worth $117,000 while the homeowner's home would reach a value of $306,000. There's no need to continue the narrative, below are bullet points of the homeowner's and renter's theoretical return on their investments.


Renter's Rundown

Initial S&P Investment: $40,000

Total Rent Paid at Year 10: $171,000

Total Paid in 10 Years: $211,000

S&P Index Value at Year 10: $117,000

Total Gain or Loss: $94,000 Loss


Homeowner's Rundown

Downpayment: $40,000

Total Home Payments at Year 10: $149,000

Total Paid in 10 Years: $189,000

Mortgage Balance at Year 10: $122,000

Total Ownership Costs at Year 10: $311,000

Home Value at Year 10: $306,000

Total Gain or Loss: $5,000 Loss


15-Year Return

At Year 15 the S&P 500 shows a value of 364 while the Home Price index reached 222. In real dollars, the renter's initial investment of $40,000 into an S&P 500 index fund would be worth $145,000 while the homeowner's home would reach a value of $444,000. Below is the rundown.


Renter's Rundown

Initial S&P Investment: $40,000

Total Rent Paid at Year 15: $227,000

Total Paid in 15 Years: $267,000

S&P Index Value at Year 15: $145,000

Total Gain or Loss: $122,000 Loss


Homeowner's Rundown

Downpayment: $40,000

Total Home Payments at Year 15: $224,000

Total Paid in 15 Years: $264,000

Mortgage Balance at Year 15: $98,000

Total Ownership costs at Year 15: $362,000

Home Value at Year 15: $444,000

Total Gain or Loss: $82,000


Conclusion

TFC isn't much for advice, but buying a home is a solid investment for anyone that an afford a significant downpayment of at least 20%. Renting is a great tool to build one's liquidity in order to purchase a home, but the data show that buying a home using a significant downpayment is a strong way to build one's net worth. This is driven by the homeowner locking in a payment based on the home's value at purchase, rather than the renter continually having to pay market-value rent for their home, reflected by the 3% increase in annual rent. Further, as evidenced by the decreasing mortgage balance, the homeowner buys back a bit of equity with every mortgage payment, which continually increases their ownership and return on their investment.


Sources

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