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

Finance

A share of stock is expected to sell for $100 and pay a dividend of $2 at the year's end. What is the fair price of the stock today if its beta is 1.27? Assume that the risk free rate is 0.04 and the expected risk premium on the market is 0.15 %.

 

Round your answer to 4 decimal places . For example , if your answer is 3.205 %, then please write down 0.0321 .

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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

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