The stock of Nogro Corporation is currently selling for $10 per share. Earnings per share in the coming year are expected to be $2. The company has a policy of paying out 50% of its earnings each year in dividends. The rest is retained and invested in projects that earn a 20% rate of return per year. This situation is expected to continue indefinitely.

a. Assuming the current market price of the stock reflects its intrinsic value as computed using the constant-growth DDM, what rate of return do Nogro's investors require?
b. By how much does its value exceed what it would be if all earnings were paid as dividends and nothing were reinvested?
c If Nogro were to cut its dividend payout ratio to 25%, what would happen to its stock price? What if Nogro eliminated the dividend?

a) required rate of return = 10%

b)Also, if there is no growth then Return on Equity will be equal to the Required rate of return. Hence there won't be any change.

c) a cut in the dividend payout to 25% will have no effect  or impact and as such the stock price will remain the same.

A complete elimination of dividend will not affect the stock price as well.

Explanation:

The question is in three parts and will be answered accordingly

a) The Required Rate of Return = (The Dividend Expected for the next year/ Current Price of Stock) + the Growth rate

First, we calculate the Dividend expected per share for the next year

=earnings per share x Dividends pay out ratio

=$2 /$10 = 20%

Secondly, we now calculate the return on equity as follows

= Expected Earnings Per share / Current Selling price

= $2 x (1-50%) = 10%

The third is to calculate the Growth rate =

Return on Equity x (1 - Dividend payout ratio)

= 20% x (1-50%) = 10%

Using this with the formula of required rate of return

= ($1 /$10) +10% = 20%

b) First the assumption is that all earnings were paid as dividend with no reinvestment and in this scenario, the lack of reinvestment will mean no growth. Also, if there is no growth then Return on Equity will be equal to the Required rate of return. Hence there won't be any change.

c) Because the Return on Equity is equal to required rate of return, it means a cut in the dividend payout to 25% will have no effect  or impact and as such the stock price will remain the same.

A complete elimination of dividend will not affect the stock price as well.