A stock is expected to pay a year-end dividend of $8 and then to sell at...

A stock is expected to pay a year-end dividend of $8 and then to sell at a price of $109. The risk-free interest rate is 4%, the expected market return is 12% and the stock has a beta of 0.8. What is the stock price today?

Multiple Choice

$102.99.

$98.73.

$105.98.

$109.00.

Solutions

Expert Solution

Solution:
	Answer is 3rd option $105.98

Working Notes:

	The stock price today (P0) = D1/(1+Ke) + P1/(1+Ke)

	Cost of equity Ke = rf + (rm - rf ) x B	using SML
	Ke = 4% + (12%-4%) x0.8
	ke= 4% + 6.4%
	Ke = 10.4%


	The stock price today (P0) = D1/(1+Ke) + P1/(1+Ke)
	P0 = 8/(1.104) + 109/(1.104)
	P0=7.246376 + 98.73188
	P0 = 105.97826
	P0 = 105.98

	The stock price today (P0) =$105.98


Notes:	Today's stock price is the present value of all the future cash flows, in our cash at year end we get dividend and then future price of stock at year end which is discounted by cost of equity to get today's stock price that is in other word the present value of future dividend & stock price.



Please feel free to ask if anything about above solution in comment section of the question.

jeff jeffy answered 1 year ago

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