Cost of Equity and Dividend payments

Question #25 on CFAI EOC questions, Reading 30 has a problem where a company pays a dividend out from earnings and it lowers thier cost of capital for equity. They calculate the cost of equity droping from 10% to 9% but I can’t seem to figure out how they got this number. How does paying a dividend reduce the cost of equity?

last passage says: Skylark’s competitors that pay a benefit… from a 100 basis point reduction …regardless of cap. structure. I assume Skylark’s cost of equity… will decline by same amount if it initiates a dividend."