Investments
please solve all sub question as they are all related
The given Problem can be solved by using the Gordon's Growth
Model.
As per this Model,
Value of Share = D1 / (Ke - g)
Where,
D1 = Dividend at the end of Year 1
Ke = Cost of Capital
g = growth rate
Firm C's current net income = $2 millions
Net Income is expected to grow by 1% during the next 4 years
Therefore, Net Income after 4 years = 2 * 101% =
$2.02millions
Therefore EPS = $2.02millions / 0.5million shares =
$4.04
Retention Ratio = 65%
Therefore, D4 = 4.04 * (1- 0.65) = 4.04 * 0.35 = $1.414
a. Computation of the intrinsic value of Stock
now
As the company isn't paying any dividend at the end of Year 1, we
cannot directly apply Gordon's formula.
We'll instead apply the formula for Year 7 dividend (when the
growth is constant) and calculate Intrinsic Value at the end of
Year 6 and then discount it to Year 0.
D7 = D6 + g
= D5 + 9.5% + 0
= (D4 + 11.5%) + 9.5% + 0
= (1.414 + 11.5%) + 9.5% + 0
= (1.58 + 9.5%) + 0
= 1.73 + 0
Therefore, D7 = 1.73
Therefore, P6 = D7 / (Ke - g)
P6 = 1.73 / (8% - 0%)
Therefore, P6 = $21.625
Therefore, P0 = P6 / (1 + ke)^6
= 21.625 / (1.08)^6
= $13.63
Therefore, intrinsic value of the stock now = $13.63
b. Computation of the intrinsic value of Stock at the end of Year
2
Like Year 1, there is no dividend to be paid at the end of Year 3.
Therefore, Gordon's Model cannot be directly applied for Year 2
price either. Therefore, we will apply the same technique as
sub-question a. However, we already have the answer for Year 0 from
sub-question a, we can just drag that to Year 2 using the Cost of
Capital, instead of repeating the entire process.
Therefore P2 = P0 * (1 + ke)^2
= 13.63 * (1.08)^2
= $15.90
Therefore, intrinsic value of the stock at the end of Year
2 = $15.90
c. Computation of the intrinsic value of Stock at the end
of Year 8
Here, we can apply Gordon's model,
Therefore, P8 = D9 / (Ke - g)
D9 = D8 = D7 = $1.73, g = 0%
Therefore, P8 = 1.73 / (8% - 0%)
Therefore, P8 = $21.625
Therefore, intrinsic value of the stock at the end of
Year 8 = $21.625
d. Computation of the intrinsic value of Stock at the end
of Year 14
Here, D15 = D14 + g = 1.73 + 5% = $1.82 ...(Dividends from Year 7
to 14 will be constant)
g = 5%
Therefore, by Gordon's Model,
P14 = D15 / (Ke - g)
= 1.82 / (8% - 5%)
= 1.82 / 3%
= $60.67
Therefore, intrinsic value of the stock at the end of Year
8 = $60.67
Investments please solve all sub question as they are all related Question 3/ Firm C is...
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