Question

- Computech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Computech to begin paying dividends, beginning with a dividend of $0.50 coming 3 years from today. The dividend should grow rapidly - at a rate of 35% per year - during Years 4 and 5, but after Year 5, growth should be a constant 7% per year. If the required return on Computech is 14%, what is the value of the stock today?

- You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $2.25 a share at the end of the year (D₁ = $2.25) and has a beta of 0.9. The risk-free rate is 5.4%, and the market risk premium is 4%. Justus currently sells for $41.00 a share, and its dividend is expected to grow at some constant rate, g. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years?

Answer 1

Answer : 1) Calculation of Stock Price :

Value of Stock Today = Present Value of Dividend and horizon Value

Year	Dividend / Horizon Value	PVF @14%	Present Value of Dividend /Horizon Value
1	0	0.877192982	0
2	0	0.769467528	0
3	0.5	0.674971516	0.337485758
4	0.675 (0.50 * 1.35)	0.592080277	0.399654187
5	0.91125 (0.675 * 1.35)	0.519368664	0.473274695
5 (Horizon Value)	13.92910714 (Working Note)	0.519368664	7.234341773
		Current Stock Price	8.444756413 or 8.44

Working Note :

Calculation of Horizon Value = [Dividend in Year 5 * (1 + growth rate)] / (Required Return - Growth rate)

= [0.91125 * 1.07] / (0.14 - 0.07)

= 13.92910714

Value of the stock today is $8.44

Answer : 2 )

Calculation of Growth rate :

Current Price = Expected Dividend / (Cost of Equity - growth rate)

Cost of Equity = Risk free rate + (Beta * Market Risk Premium)

= 5.4% + (0. 9 * 4%)

= 9% or 0.09

41 = 2.25 / (0.09 - g)

0.09 - g = 2.25 / 41

0.09 - g = 0.05487804878

==> g = 0.09 - 0.05487804878

= 0.03512195122 or 3.512195122%

Stock price at the end of 3 years = Current price * (1 + growth rate)^3

= 41 * (1.03512195122)^3

= 41 * 1.10910983275

= 45.4735031427 or 45.47