A company is presently enjoying a relatively high growth because of a surge in t

Question

A company is presently enjoying a relatively high growth because of a surge in the demand for its new product management expects earnings and dividends to grow at a rate of 29% for the next two years 18.60% in three years and four and after which competition will probably reduce the growth rate in earnings and dividends to constant growth growth rate of 5.95% of the company's last Dividend was $1.00 it's beta is 1.75 the market risk premium is 10.60% and the risk-free rate is 5% what is the current Price of the common stock A company is presently enjoying a relatively high growth because of a surge in the demand for its new product management expects earnings and dividends to grow at a rate of 29% for the next two years 18.60% in three years and four and after which competition will probably reduce the growth rate in earnings and dividends to constant growth growth rate of 5.95% of the company's last Dividend was $1.00 it's beta is 1.75 the market risk premium is 10.60% and the risk-free rate is 5% what is the current Price of the common stock

Explanation / Answer

Price of common stock is $ 10.23

Working:

Step-1:Calculation of cost of Equity As per Capital Asset Pricing Model, Required rate of return = Risk Free rate + Beta *market risk premium = 5.00% + 1.75 * 10.60% = 23.55% Step-2:Calculation of Present Value of four years dividend Year Dividend Discount factor @ 23.55% Present Value 1 $        1.29      0.8094 $       1.04 2 $        1.66      0.6551 $       1.09 3 $        1.97      0.5302 $       1.05 4 $        2.34      0.4292 $       1.00 Total $       4.19 Working: Year Last years dividend Growth rate Current Years dividend 1 $       1.00 29.00% $        1.29 2 $       1.29 29.00% $        1.66 3 $       1.66 18.60% $        1.97 4 $       1.97 18.60% $        2.34 Step-3:Calculation of terminal value of dividend Terminal Value of dividend = D4*(1+g)/(Ke-g) Where, = 2.34*(1+0.0595)/(0.2355-0.0595) D4 $       2.34 = $    14.09 g 5.95% Ke 23.55% Step-4:Calculation of present value of terminal value Present Value of terminal value of dividend = $      14.09 x      0.4292 = $        6.05 Step-5:Calculation of present value of all dividends Present Value of all dividend = $       4.19 + $        6.05 = $    10.23 As per dividend discount model, price of stock is the present value of all dividends. Thus, Price of Common Stock is $    10.23

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