Richmond Rent$-$A$-$Car is about to go public. The investment banking firm of Tinkers, Evers & Chance is attempting to price the issue.

The car rental industry generally trades at a $25$ percent discount below the P$/$E ratio on the Standard & Poor's $500$ Stock Index.

Assume that the index currently has a P$/$E ratio of $25.$ The firm can be compared to the car rental industry as follows:

$\backslash$table$[[,$Richmond,Car Rental Industry$],[$Growth rate in earnings per share,$15\%,10\%$

Richmond Rent$-$A$-$Car is about to go public. The investment banking firm of Tinkers, Evers & Chance is attempting to price the issue.

The car rental industry generally trades at a $25$ percent discount below the P$/$E ratio on the Standard & Poor's $500$ Stock Index.

Assume that the index currently has a P$/$E ratio of $25.$ The firm can be compared to the car rental industry as follows:

$10$ points

Assume, in assessing the initial P$/$E ratio, the investment banker will first determine the appropriate industry P$/$E based on the Standard & Poor's $500$ Index. Then a $0\mathrm{.}50$ point will be added to the P$/$E ratio for each case in which Richmond Rent$-$A$-$Car is superior to the industry norm, and a $0\mathrm{.}50$ point will be deducted for an inferior comparison.

On this basis, what should the initial P$/$E be for the firm?

Note: Round your answer to $1$ decimal place.

Answer is complete but not entirely correct.

Initial P$/$E ratio

$19\mathrm{.}6$