Question

Question 6 Bonus

1. Please show me the Gordon Growth Model formula. (Just copy it done. P,-?, 0.1 point) 2. As we mentioned, g not only governs the growth of d, g also tells us how P changes along the time. Please rewrite Pin terms of P, and g. (0.2 point) 3. Now, according to 1. and 2., we know 2 ways to express P. Equate them and derive d, in terms of P. 9, and r. (0.5 point) 4. Following 3., substitute all the subscript 1 with a subscript t. (0.2 point) 5. Bonus: Please elaborate your finding in 3. and 4. Does it tell us anything about how a company decides its payout policy? (0.4 point) Now let's try to derive something really cool. On slide 22, you will see a bizarre conclusion that if a company pays out dividends according to the Gordon Growth Model, it is indifferent for investors to sell the stock at any point of time. Let's show it using our algebra. A Substitute d, with the 6. Bonus: We know that if you plan to sell the stock after 1 year, P = equation you find in 3. (0.3 point) 2. Substitute di and 7. Bonus: We know that if you plan to sell the stock after 2 years, P = 1.+ dy to find the end solution. (0.3 point) 8. Bonus: What do you see according to you answers in 6. and 7.? (0.5 point)

Answer 1

1.
Gordon Growth Model states that
P0=D1/(r-g)

2.
P1=D2/(1+g)
P1=D1*(1+g)/(r-g)
=>P1=P0*(1+g)
=>P0=P1/(1+g)

3.
D1=P0*(r-g)
D1=P1*(r-g)/(1+g)

4.
Dt=Pt*(r-g)/(1+g)

6.
P0=(P1*(r-g)/(1+g)+P1)/(1+r)=P1/(1+g)