How to calculate the real cost of buying a home

What’s the cost of buying a home?

Yes, this is a trick question.

The obvious answer is the price you pay for it. If you find a house you like and pay $400,000 cash to buy it, the cost is the price, $400,000. Long-term, buying for cash will probably work out well. The value of the house is likely to appreciate with inflation. The eventual sale will likely be a tax-free event.

While you’re living in the house, you’ll enjoy another benefit. It’s what economists call “imputed income.” That’s the invisible, tax-free benefit of shelter you’d otherwise have to pay for with after-tax income.

Sweet.

But simplicity becomes complex when you finance the purchase of your home, and that’s what most of us do. According to the National Association of Realtors, 87% of all homebuyers finance their homes.

When you sit down to sign that enormous stack of documents, one will tell you how many dollars you will be paying over the life of the mortgage. Borrow $300,000 for 30 years at 3.25% — the rate available before Russia invaded Ukraine — and you’ll be repaying $470,023. Borrow it at 6%, as many did long ago, and you’ll be repaying a whopping $647,515.

That’s pretty intimidating. It’s also why many homeowners are in a rush to pay off their mortgage. “Think of all the money I’ll save,” they say.

In fact, the true savings from prepayment will probably be smaller.

How can that be? The answer is what financial types call “the time value of money.” A dollar coming our way in 2040 isn’t as valuable to us as a dollar in our bank account this week.

And yep, there’s this thing called inflation.

So how do you calculate the true cost of buying your home?

You’ll need a financial calculator to do the specifics for your own house. Meanwhile, let me show you how it would work with some calculations for a typical home cost in Texas. According to a recent report from the Texas Real Estate Research Center at Texas A&M University, median home prices in our major urban areas ranged upward from $300,000.

• San Antonio was the least expensive at $303,000.
• Houston followed at $309,100 and Fort Worth at $319,600.
• Dallas came in at $383,100.
• Austin led with a stunning $453,600.

As I write this, a qualified buyer with a good credit score and a 20% down payment could snag a mortgage rate as low as 3.75 %. (This doesn’t count any payments of points that raise the effective interest rate.)

So what’s the true cost of a $300,000 or $400,000 home?

If you buy a home for $300,000 with a $60,000 down payment, you’ll be borrowing $240,000 and have a monthly payment of $1,111.48, repaying $400,132.80 over 30 years. If inflation matched the interest rate, the present value of all those payments would be exactly the amount you borrowed, $240,000.

But what if the inflation rate is a good deal higher?

If inflation ran at the trailing 7% rate, for instance, you’d be paying back $167,063.86 in current value, not $240,000. In effect, the true cost of your house would be $227,063.86 (the $60,000 down payment plus the $167,063.86 present value of the amount you would repay).

Now let’s do the same exercise with a $400,000 house. With a down payment of $80,000, you would need a $320,000 mortgage with a monthly payment of $1,481.97. Over 30 years, you’d pay $533,509.20. But the present value of those payments after 7% inflation is $222,751.31, not $320,000. Again, the effect is to reduce the cost of buying your home to the down payment plus the present value of your mortgage, a total of $302,751.31.

In both cases, you’re buying the house at an effective discount of nearly 25%.

How well this actually works out depends on one thing. It’s the difference between the interest rate on the mortgage and the inflation rate you experience. If inflation runs hot, you’ll make out big time.

Yes, it’s a gamble. But it’s the gamble that built middle-class net worth for decades after World War II.

This isn’t new finance magic. It has been this way whenever the rate of inflation is greater than the interest rate on mortgages. It’s not a sure thing, but it’s looking like a pretty good bet.

Does this mean home prices aren’t high?

No. It only means that daring homebuyers may not be quite as crazy as many seem to think.

Scott Burns is the personal finance columnist for The Dallas Morning News.