Question

NONCONSTANT GROWTH 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 21% per year-during Years 4 and 5; but after Year 5, growth should be a constant 8% per year. If the required return on Computech is 12%, what is the value of the stock today? Round your answer to the nearest cent. Do not round your intermediate calculations

Answer 1

g₁ = growth rate in year 4 and 5 = 0.21 , g₂ = growth rate after year 5, Ke = required return = 0.12

D3 (Dividend in Year 3) = $0.50

D4 (Dividend in Year 4) = D3 x (1 + g₁) = $0.50 x (1 + 0.21) = $0.605

D5 (Dividend in Year 5) = D4 x (1 + g₁) = $0.605 x (1 + 0.21) = $0.73205

P5 (Price at the end of year 5) = D5 x (1 + g₂) / (Ke - g₂) = $0.73205 x (1 + 0.08) / (0.12 - 0.08) = $19.76535

Value of stock today is the present value of the above cash flows -

Value of stock today

Particulars	Year	PVIF@12%	Amount	Present value
D3	3	0.7117802478	$0.50	$0.36
D4	4	0.63551807839	$0.605	$0.38
D5	5	0.5674268557	$0.73205	$0.42
P5	5	0.5674268557	$19.76535	$11.21
Value of stock today				$12.37