$1.$ Simba, Inc. is planning a capital investment of $5$ million $$.$ The firm$$s last year net income was $7\mathrm{.}5$ million $$.$ Simba shows a debt to equity ratio of $40\%$ which is considered to be optimal. There are $2$ million of shares outstanding with a market price of $30$ $$.$ a$)$ If Simba follows the residual dividend policy, calculate the firm$$s dividend per share. b$)$ Calculate the dividend yield in the previous case. c$)$ If the firm wants to provide a $5\%$ dividend yield, calculate the pay$-$out