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 41% per year - during Years 4 and 5, but after Year 5, growth should be a constant 5% per year. If the required return on Computech is 16%, what is the value of the stock today? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

The question can be solved by using Gordon's Growth Model.
As per Gordon's Growth Model,
P0 = D1 / (r - g) ... when growth rate is constant till perpetuity
Where,
P0 = Price of the stock today i.e. at Year 0
D1 = Dividend paid a year from now
r = Cost of Capital / Reqd Rate of Return
g = growth rate

As per the question,
D3 = $1.5
Growth rates for Year 4 and 5 = 41% per year
Growth rate after Year 5 till perpetuity = 5% per year
r = 16%
There is no dividend in the first two years

Step 1: To find the Horizon Value i.e. P5

As per Gordon's formula,
Terminal/Horizon Value i.e. P5 = D6 / (r - g)
For finding D6, we'll also need values of D4 and D5.
D4 = D3 + g for Year 4 = 1.5 + 41% = 2.115
D5 = D4 + g for Year 5 = 2.115 + 41% = 2.982

Hence, D6 = D5 + g for Year 6 = 2.982 + 5% ... (Since growth rate after Year 5 reduces to 5%)
D6 = 3.13

Therefore, P5 = 3.13 / (16 - 5) = 3.13 / 11%
Therefore, P5 = $28.45

Now, in the next step, this Horizon Value needs to be brought to Year0 along with dividends for other 3 years.

Step 2: Find the Stock Price today i.e. P0

P0 = [D3 / (1+r)^3] + [D4 / (1+r)^4] + [D5 / (1+r)^5] + [P5 / (1+r)^5]
P0 = (1.5 / 1.16^3) + (2.115 / 1.16^4) + (2.982 / 1.16^5) + (28.45 / 1.16^5)

P0 = 0.961 + 1.168 + 1.42 + 13.55
Therefore, P0 = 17.09

Therefore, value of the stock today is $17.09
Note: The answer may be $17 or $17.10 in your textbook cause of rounding up difference

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