Question

Question Number 4

1. Please show me the Gordon Growth Model formula. (Just copy it done. Po=?, 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 Po in terms of P and g. (0.2 point) 3. Now, according to 1. and 2., we know 2 ways to express Po. 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 6. Bonus: We know that if you plan to sell the stock after 1 year, Po 4 Substitute di with the 1+r equation you find in 3. (0.3 point) 7. Bonus: We know that if you plan to sell the stock after 2 years, Po = . Substitute di and d2 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)