Maria aims to purchase a house for $200, 000. Because she has financial assets of $300,000, one of her options is to buy the house for all cash. Alternatively, she can obtain a mortgage of $180,000 for 15 years at 4% and zero fees. Maria has excess disposable income of $2,000 a month which would more than cover the payment on a mortgage.
How does she make the choice? The method I would use is to calculate her net worth at the end of her expected period in the house, or at the mortgage payoff date. whichever comes first. I will assume the mortgage payoff period of 15years. The calculation of future net worth would be done twice, once on the assumption that Maria purchases with all cash, and once on the assumption that she borrows 90% of the price.
I've developed a spreadsheet to make the calculations manageable; interested readers can download the Future Net Worth spreadsheet to their computers.
Advertisem*nt
In the all-cash purchase, future net worth after 15 years is the sum of the future value of Marie's $2000 of excess income, invested monthly to earn 4%, or $492,181; plus the future value of the $100,000 of financial assets left after buying the house for cash, or $182,030; plus the future value of the house at an assumed appreciation rate of 3%, or $313,486. The three items sum to a total net worth of $987,697.
If Maria finances the purchase with a $180,000 mortgage at 4%, her excess income is reduced from $2,000 to $669 because of the mortgage payment, but her financial assets are reduced only by $20,000 to $280,000. The future values are $164, 526, $509,684 and $313,486, which sum to $987, 697. The future net worth is the same in both cases because I assumed that Maria's financial assets earned the same return as the rate she paid on the mortgage.
The relationship between the mortgage rate and the investment rate is the major factor determining whether or not it makes sense to pay all cash. If Maria earns only 2% on investments while paying 4% on a mortgage, financing the purchase with a mortgage would result in a future net worth of only $831, 558. She should pay all cash. On the other hand If she earned 8% on investments, her net worth would be $1,470,772, so she should finance the purchase.
But there is a small proviso. Mortgage interest paid is deductible whereas interest earned is taxable. If Maria is in the 28% tax bracket, taking account of the mortgage interest deduction would increase the future net worth in the case where she borrows by $20,000 -$25, 000. My spreadsheet allows the user to specify any tax bracket desired.
Advertisem*nt
And there is a major proviso that is much more likely to be overlooked. I have assumed that when the purchaser pays all cash, she allocates to monthly savings an amount equal to the monthly mortgage payment that she would have made had she borrowed. In the borrowing case, she is required to pay $1331 a month on the mortgage, leaving $669 for investment. In the all cash purchase, the obligatory payment is gone and she must invest $2,000 a month voluntarily.
This is critically important. If Maria spends all her disposable income in the two cases, her future net worth in the borrowing case would be twice as large as in the all cash purchase case, the 8% investment rate notwithstanding. It reminds us, once again, that the forced saving feature of the long-term fully amortizing mortgage serves many consumers well.
For more information on how to make educated decisions about home financing, or to shop for a mortgage in an open and unbiased environment, visit my website The Mortgage Professor
Support HuffPost
Our 2024 Coverage Needs You
Your Loyalty Means The World To Us
At HuffPost, we believe that everyone needs high-quality journalism, but we understand that not everyone can afford to pay for expensive news subscriptions. That is why we are committed to providing deeply reported, carefully fact-checked news that is freely accessible to everyone.
Whether you come to HuffPost for updates on the 2024 presidential race, hard-hitting investigations into critical issues facing our country today, or trending stories that make you laugh, we appreciate you. The truth is, news costs money to produce, and we are proud that we have never put our stories behind an expensive paywall.
Would you join us to help keep our stories free for all? Your contribution of as little as $2 will go a long way.
As Americans head to the polls in 2024, the very future of our country is at stake. At HuffPost, we believe that a free press is critical to creating well-informed voters. That's why our journalism is free for everyone, even though other newsrooms retreat behind expensive paywalls.
Our journalists will continue to cover the twists and turns during this historic presidential election. With your help, we'll bring you hard-hitting investigations, well-researched analysis and timely takes you can't find elsewhere. Reporting in this current political climate is a responsibility we do not take lightly, and we thank you for your support.
Contribute as little as $2 to keep our news free for all.
Dear HuffPost Reader
Thank you for your past contribution to HuffPost. We are sincerely grateful for readers like you who help us ensure that we can keep our journalism free for everyone.
The stakes are high this year, and our 2024 coverage could use continued support. Would you consider becoming a regular HuffPost contributor?
Dear HuffPost Reader
Thank you for your past contribution to HuffPost. We are sincerely grateful for readers like you who help us ensure that we can keep our journalism free for everyone.
The stakes are high this year, and our 2024 coverage could use continued support. If circ*mstances have changed since you last contributed, we hope you’ll consider contributing to HuffPost once more.
Already contributed? Log in to hide these messages.
