Interest rates and their effect on stock market

Every now and then we hear about RBI planning to raise interest rates to tame inflation. How does interest rate tame inflation may be little complex if we go into the detail but from a broader perspective a token raise in interest rate tightens the money supply in the market. Now there will be lesser money and the same amount of goods available (in the short run) in the market. The buying power of money increases. This is valid for a short run only. On long runs, producers find ways to tackle; they will either decrease the production or will move to some other rewarding business. Both the steps will bring up the prices.

But how does interest rate affect stock market? For businesses interest rate is the cost of money or funding. If rates increase, they will have to pay more for the money. This will (again short run) bring down corporations margin, thus free cash flow, thus the net profit per share. Since the cash generating power of corporations comes down, the price people would want to pay for the stocks will be less. The market in general comes down.