Problem $11-5$ Risk Premiums and Discount Rates $($LO$1)$

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 $$53.$ The stock will pay a dividend at year$-$end of $$2\mathrm{.}30.$ Assume that risk$-$free Treasury securities currently offer an interest rate of $2\mathrm{.}3\%.$

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

$\backslash$table$[[$Portfolio$,\backslash$table$[[$Average Annual Rate$],[$of Return $(\%)]],\backslash$table$[[$Average Premium $($Extra$],[$return versus Treasury$],[$bills$)(\%)]]],[$Treasury bills,$3\mathrm{.}7,],[$Treasury bonds,$5\mathrm{.}4,1\mathrm{.}7],[$Common stocks,$11\mathrm{.}5,7\mathrm{.}7]]$

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,$],[$b$.$ Stock price,$]]$