Can cost of equity be negative?

In theory it can, but in practice a negative cost of equity means something is wrong with the inputs. Shareholders take the most risk in a company, so they need a positive return. A negative result is a signal to recheck beta, growth or the stock price.

CAPM produces a negative number only when beta is strongly negative. With a 5% risk-free rate and a 5% equity risk premium, beta would need to fall below -1. A beta of -1.2 gives 5% minus 6%, or -1%. A short or noisy regression is the usual cause.

The dividend growth model goes negative when dividends are expected to shrink faster than the yield, such as a 3% yield with dividends falling 5% a year. That points to a broken forecast. Check the inputs in the cost of equity calculator and the notes on beta and the dividend discount model.