Top hedge fund manager Sally Buffit believes that a stock with the same market risk as the S&P $500$ will sell at year$-$end at a price of $$57.$ The stock will pay a dividend at year$-$end of $$2\mathrm{.}00.$ Assume that risk$-$free Treasury securities currently offer an interest rate of $1\mathrm{.}8\%.$

$2\mathrm{.}5$

points

Average rates of return on Treasury bills, government bonds, and common stocks, $1900-2020($figures in percent per year$)$ are as follows.

$\backslash$table$[[,\backslash$table$[[$Average Annual$],[$Rate of$],[$Peturn$]],\backslash$table$[[$Average Premium $($Extra$],[$return versus Treasury$]]],[$Portfolio$,(\%),$bills$)(\%)],[$Treasury bills,$3\mathrm{.}7,1\mathrm{.}7],[$Treasury bonds,$5\mathrm{.}4,7\mathrm{.}7]]$

a$.$ What is the discount rate on the stock?

Note: Enter your answer as a percent rounded to $2$ decimal places.

b$.$ What price should she be willing to pay for the stock today?

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

$\backslash$table$[[$a$.$ Discount rate,,$\%$