So the way interest rates factor into cashflow analysis is in the opportunity cost
to the investor of investing in a particular asset. That is, if interest rates rise, that means I can probably find greater yields elsewhere, which for a stock means I should increase my discount rate.
https://seekingalpha.com/article/137623-how-interest-rates-i...
> First, assume that our opinion of future free cash flow doesn’t change so as to isolate the effect that the discount rate will have on value. You can think of the discount rate as the opportunity cost of investing in Stock A over Stock B or Investment C. If interest rates rise, so too should our discount rate since we would have more opportunities to do more with our money elsewhere. And since discount rates and present values are inversely related, value will decline, all else equal, as the result of a rise in interest rates.
https://www.graduatetutor.com/corporate-finance-tutoring/cas...
> The first way in which interest rates factor into a DCF model is through the discount rate. The discount rate captures the rate at which the value of money declines. Prevailing interest rates are a big factor in opportunity cost. And opportunity cost is an ingredient of the discount rate.
https://www.investopedia.com/terms/d/dcf.asp
> Calculating the DCF involves three basic steps. One, forecast the expected cash flows from the investment. Two, select a discount rate, typically based on the cost of financing the investment or the opportunity cost presented by alternative investments. Three, discount the forecasted cash flows back to the present day, using a financial calculator, a spreadsheet, or a manual calculation.
So DCF analysis doesn't actually say anything about company's actual future cashflows. It's about the value of those cashflows to the investor when weighing the value of that stock versus other types of investments.
Bringing us back to the topic at hand, that means higher interest rates should depress stock prices because of the increased opportunity cost versus investing in other assets.