You're missing the nuance of the question. If Airbnb is worth 1.5 million before selling 10% for 150k then after the sale they are still worth 1.5M they were valued at before the sale, but also have an additional 150k in the bank which should add another 150k to their valuation.
(ergo the pre/post money valuation thing linked above)
But wait - You're leaving out the company's loss of 10% of its equity as part of the investment transaction.
The company's equity was worth $1500K before the investment.
After the investment, the company had $1350K of equity left because it sold 10% of itself, and it no longer owned that chunk of equity.
However, it had $150K of cash that its equity investor paid for 10% of the company's equity. So $1350K of remaining equity + $150K cash = $1500K company value. Same as pre-investment valuation.
It looks like the company's total value didn't change, it just traded 10% of its value for cash. Which is the point of selling equity - cash allows a company to pay for people and things. Equity doesn't.
But wait - You're leaving out the company's loss of 10% of its equity as part of the investment transaction.
A "company" can't lose equity it never owned any to begin with. The equity was transferred from one party (usually the founders) to another entity in exchange for cash.
After the investment, the company had $1350K of equity left because it sold 10% of itself, and it no longer owned that chunk of equity.
