$[25$ points$]$

Suppose, as in case EV$2,$ you are given earnings information about a security ABC

that experiences growth. Assume that earnings growth is $3\%,$ that the risk free rate

is $2\%,$ and that the required risk premium is $6\mathrm{.}5\%.$ Also assume that ABC has a

payout ratio of $80\%.$ As in EV$2,$ we assume that the "true" price at the end of

the $1-$year horizon is determined by the Gordon Growth model $($corrected for the

payout ratio$)$ applied to the sum of the earnings during the year.

In addition to the actual earnings from the last year, you have also received estimates

for the earnings by your analyst for this year:

You know that there are five outcomes for your analyst's estimates: he gets it right

$(50\%$ chance$),$ he gets it wrong by $\backslash$pm $1$ cent $(20\%$ chance for each direction$),$ or he

gets it wrong by $\backslash$pm $2$ cents $(5\%$ chance for each direction$).$

$($a$)$ What is your best guess of the fair price for this security?

$($b$)$ Suppose you want to avoid all losses, assume that there are no commissions.

Based on the information provided to you thus far, devise and carefully describe

a strategy that allows you to profit risk$-$lessly from buying$/$selling the security.