A share of stock is expected to sell for $100 and pay a dividend of $2 at the year's end

Answer :

calculation of Expected Return of the stock using CAPm (Capital Asset Pricing Model)

CAPM = Rf + beta of stock (Rm-Rf)

CAPM = 0.04 + 1.27 (Expected Risk Premium)

CAPM = 0.04 + 1.27 * 0.15

CAPM = 0.2305

CAPM = 23.05%

CAPM = Expected Return

Rf = Risk Free Return

Rm - Rf = Expected Risk Premium on the market

Now,

Return of Stock = Capital Gain yield + Dividend Yield

0.2305 = ( Price at the end - Price today / Price today * 100 ) + Dividend / Price today

0.2305 = (100 - Po) / P0 * 100 + 2 / Po

0.2305 = 100 - P0 + 2 / P0

0.2305 * Po = 100 - Po + 2

0.2305 Po + Po = 102

1.2305 Po = 102

Po = 82.89

So, the Fair Price Today = 82.89

Note : Price at the End = Expected Price = 100

Dividend = 2