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 $1.25 coming 3 years from today. The dividend should grow rapidly - at a rate of 42% per year - during Years 4 and 5, but after Year 5, growth should be a constant 4% 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) = $1.25

Dividend in Year 4 (D4) = $1.7750 [$1.25 x 142%]

Dividend in Year 5 (D5) = $2.5205 [$1.7750 x 142%]

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

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

= $2.5205(1 + 0.04) / (0.12 – 0.04)

= $2.6213 / 0.08

= $32.77

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 ($)	Present Value Factor (PVF) at 12.00%	Present Value of cash flows ($) [Cash flows x PVF]
3	1.2500	0.71178	0.89
4	1.7750	0.63552	1.13
5	2.5205	0.56743	1.43
5	32.77	0.56743	18.59
TOTAL			22.04

Therefore, the value of the stock today is $22.04

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.