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 $1.50 coming 3 years from today. The dividend should grow rapidly-at a rate of 33% 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 12%, what is the value of the stock today? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Step-1, Dividend per share for Years 3,4 and 5

Dividend in Year 3 (D3) = $1.50 per share

Dividend in Year 4 (D4) = $1.9950 [$1.50 x 133%]

Dividend in Year 5 (D5) = $2.6534 [$1.9950 x 133%]

Step-2, Calculation of Stock Price in Year 5 (P5)

Dividend Growth Rate (g) = 5% per year

Required Rate of Return (Ke) = 12%

Stock Price in Year 5 = D5(1 + g) / (Ke – g)

= $2.6534(1 + 0.07) / (0.12 – 0.07)

= $2.8391 / 0.05

= $56.78 per share

Step-3, Value of the stock today

The value of the stock today is the aggregate of present value of future dividends and Stock Price in Year 5

Year	Cash flow ($)	Present Value factor at 12%	Present Value of cash flows ($)
3	1.5000	0.71178	1.07
4	1.9950	0.63552	1.26
5	2.6534	0.56743	1.51
5	56.78	0.56743	32.22
TOTAL			36.06

“Therefore, the value of the stock today would be $36.06 per share”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.