First, to value future dividends, an investor must discount them back to the present; as higher interest rates make a given future dividend less valuable in today's dollars, higher interest rates reduce the value of a share of stock.
For example, according to the New York Fed's Survey of Consumer Expectations, in May 2022, US households were expecting an inflation rate of 4.8 % three years from now. Before picking up strongly at the end of 2020, this figure stood at slightly above 3 % for some years.