The investment banking firm of Einstein & Company will use a dividend valuation model to appraise the shares of the Modern Physics Corporation. Dividends $(D_1)$ at the end of the current year will be $$1\mathrm{.}65.$ The growth rate $(g)$ is $11$ percent and the discount rate $(K_e)$ is $14$ percent.

a$.$ What should be the price of the stock to the public?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places.

Price of the stock

b$.$ If there is a $3$ percent total underwriting spread on the stock, how much will the issuing corporation receive?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places.

Net price to the corporation

c$.$ If the issuing corporation requires a net price of $$53\mathrm{.}50($proceeds to the corporation$)$ and there is a $3$ percent underwriting spread, what should be the price of the stock to the public?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places.

Necessary public price