Question

Adams and Collin Enterprises expect earnings and dividends to grow at a rate of 25% for the next 4 years, after the growth rate in earnings and dividends will fall to 3%. The company's last dividend was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk- free rate is 3.00%. What is the current price of the common stock?
3. What is the intrinsic price of this company's stock?

4. If the stock is currently priced at $40.00, given your answer to Question 3, would you purchase this security?

Answer 1

Answer:

the intrinsic value of the stock is 42.97

If the stock is priced at 40 dollars it would be a good idea to purchase the share as will provide a better yield than the cost of capital of 9.6%

Explanation:

First, we solve for the cost of equity using the CAPM:

$Ke= r_f + \beta (r_m-r_f)$

risk free = 0.03

market rate = 0.09

premium market = (market rate - risk free) = 0.055

beta(non diversifiable risk) = 1.2

$Ke= 0.03 + 1.2 (0.055)$

Ke = 0.09600

Now we solve for the intrinsic price using the gordon model

with multi-stage growth:

First, we calcualte the future dividends

grow rate Dividends

0                1.25

1 0.25       1.5625

2 0.25       1.953125

3 0.25       2.44140625

4 0.25       3.051757813

4 0.03     3.143310547

Now in the last year, we calcualte using the gordon model or constant grow:

$\frac{3.143310547}{0.096-0.03} = Intrinsic \: Value$

32.7128182

Now we calculate and add together the present value of each of this future cash flow to determnate the intrinsic  value ofthe share:

$\frac{Principal}{(1 + rate)^{time} } = PV$

Present Value

1 1.5625 / (1+0.096)^1     =  1.425638686

2 1.953125 / (1+0.096)^2 = 1.625956531

and so on, giving the following values:

3 1.854421226

4 2.114987712

present value of the future dividends at 3% 22.67126448

Finally we add them and get:

42.97160726