Question

Investments

please solve all sub question as they are all related

Question 3/ Firm C is planning its first dividend in 4 years from now. Firm C retention ratio is 65%. Firm C current net income is $2millions with 500,000 shares outstanding. The net income is expected to grow by 1% during the next 4 years. The dividends are expected to grow during year 5 by 11.5% and during year 6 by 9.5%. From year 6 to year 14 they is no expected growth in dividends. However starting from year 15 there will be a constant dividend growth rate of 5% forever. The required rate of return on the stocks is 8%. a/ Compute the intrinsic value of the stock now? (Show your steps) b/ Compute the intrinsic value of the stock at the end of year 2? (Show your steps) c/ Compute the intrinsic value of the stock at the end of year 8? (Show your steps) d/ Compute the intrinsic value of the stock at the end of year 14? (Show your steps)

Answer 1

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