You're still tripping up. Forget about houses. Say I buy 100% of the stock in a business for $60k. The business then borrows $240k. When profit comes in, some of it goes to the bank who owns the debt (giving the debt value), and some of it goes to me - the owner of the equity (giving the equity value). So both debt and equity are valuable - they are claims on the business's cash flows.
Now suppose someone wants to buy the business. I still have $60k worth of equity (100%). Do you think they can buy the entire business (claims on ALL of it's cash flow) for $60k? Of course not. They'd have to pay off the debt AND buy the equity. That number is $300k - the enterprise value.
Market cap is defined as the value of the outstanding equity (share price x number of shares). Period. The value of the company can be, and often is, much greater because most companies choose debt as part of their capital structure.
Startup tech companies like Instagram rarely do that. Nobody lends us money, so we're stuck with equity. So for Instagram, Market Cap (if there is such a beast for private companies) IS the enterprise value. For the NY Times, market cap is but a percentage of the enterprise value. So it turns out the headline of this article is actually quite incorrect. The NY Times, in any way you can measure, is clearly worth more than $1B.
Look, I totally get the debt part of the valuation, and what enterprise value is. I also completely understand that enterprise value is an important measure of valuation. All I'm saying is that using market cap to indicate the value of the company is not that misleading either. Enterprise value is just one way to value a business, there are others. It's not precise science.
So in your latest example, and also throughout the thread, you're confusing (or using interchangeably) the concrete sale price and a fuzzy intrinsic value. Why would the buyer of your business pay $300K upfront? All other things being equal, the sale price of the business would still be $60k, and they can be paying off debt for the next 15 years for all I know. The conventional media-reported value of the business would still be $60K, and it won't be very misleading.
In addition, not all debt is created equal. A company like Google can probably easily get, say 1B of super cheap debt on favorable terms, while something like Barnes & Noble would barely get the same 1B at much higher interest rates and repayment schedules. It's still 1B in enterprise value, but it's clearly not the same debt.
You also mentioned cash flows. So to continue with your example, if your business is actually losing money hand over fist, and has negative cash flow on top of $240K of debt, what do you think its value would be? Would it be equal to your simple enterprise value formula? What if the same business is growing at 100% per quarter with super high operating margins? Enterprise value can be just as misleading.
To make Times worth about a billion dollars (it's market cap), you need to believe that that $700M+ of debt is totally worthless to the debt holders. That isn't some fuzzy detail. It's a fundamental concept that the author of this article ignores (or doesn't understand).
Not totally worthless, but most likely not worth the full $700M. They have $2.2B in Plant/Property/Equipment on their balance sheet. Then they have $500M+ of goodwill and intangibles. And only $500M of equity, which is constantly declining quarter after quarter. One stupid move, and the equity is easily wiped out, leaving debtholders with goodwill and a bunch of newspaper printing equipment.
Further sticking with houses, if the officially appraised value of that house drops 40% since the said mortgage was issued, and comp sales in that neighborhood are 50% lower, the house's real value is nowhere near $500K, no matter what the formula says.
You'd still owe $300K in mortgage, and be out $200K of cash, but that doesn't mean the house is worth $500K.
But no one is going to spend $200k for a $300k mortgage if the house's value is significantly less than $500k. The price you would be willing to pay is basically the house's value minus the outstanding mortgage.
Well, it could decline in value after you buy it. The point is that having debt of $N doesn't always mean the value of the house is automatically adjusted by $N. Value is in the eye of beholder, or buyer in this case.