Question

Question 5 Bonus

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

Nature of Firm	Relationship	Optimum Dividend Payout	Optimum Retention Ratio
Growing Company	Cost of Equity (Ke) < Rate of Return (r)	0%	100%
Normal Company	Cost of Equity (Ke) = Rate of Return (r)	Indifferent	Indifferent
Declining Company	Cost of Equity (Ke) > Rate of Return (r)	100%	0%

By using the growth model, a company can decide as to how much of its earnings it should retain and payout as dividend.

Retaining earnings means that the company could use these retained earnings for reinvestment if the market conditions are favorable and there is scope for growth.

Similarly, if profits are distributed as dividends, company will have less funds with it for reinvestment purpose for new projects or for infusion in current projects for growth.

In the above table, we need to observe that when the company is growing, meaning thereby that its return on investments (r) is greater than its cost of capital (Ke), the company should retain and reinvest its earnings in order to optimize its share price in line with growth.

And vice-versa, if the company is declining, meaning thereby that its return on investments (r) is less than its cost of capital (Ke), the company should payout its earnings to compensate its investors.

Under normal circumstances, whether paying or retaining its earnings is clearly at the company's discretion because it does not effects the share price at all.

For any query or clarification, please leave a comment.