Stock A is expected to have net income of $3 per share by the end of the coming year

Stock B:

Constant Dividend = $6

Share Price = $40

Since there is no growth in dividends, as per perpetuity formula,

Share Price = Constant Dividend / Cost of Equity

40 = 6 / Cost of Equity

Cost of Equity = 6 / 40 = 15%

Cost of Equity of Stock B is 15%.

Since both stock A and B are equally risky, both are expected to trade at same cost of equity. Thus,

Cost of Equity of Stock A = 15%

a)

Net Income of Stock A = $3

Payout Ratio of Stock A = 70%

Return on Equity of Stock A = 20%

Reinvestment Ratio of Stock A = 1 - Payout Ratio

Reinvestment Ratio of Stock A = 1 - 70% = 30%

Stable Growth Rate of Stock A = Reinvestment Rate * Return on Equity

Stable Growth Rate of Stock A = 30% * 20% = 6%

The stable growth rate of stock A i.e. g = 6%.

Expected Dividends = Net Income * Payout Ratio

Expected Dividends = 3 * 70% = $2.1

It is expected that stock A would pay a dividend of $2.1 per share.

As per Gordan's Constant Growth Model,

Fair Price of Stock A = Expected Dividends / (Cost of Equity - Stable Growth Rate)

Fair Price of Stock A = 2.1 / (15% - 6%)

Fair Price of Stock A = $23.333

Fair Price of Stock A should be $23.333 today

b)

If there is no growth, it would mean that there is no reinvestment and

Expected Dividends = Net Income

Expected Dividends = $3

As per perpetuity formula,

Fair Price of Stock A = Expected Dividends / Cost of Equity

Fair Price of Stock A = 3 / 15% = $20

Fair Price of Stock A should be $20 if there are no growth opportunities.

Present Value of Growth Opportunities = Fair Value of Stock with Growth - Fair Value without Growth

Present Value of Growth Opportunities = 23.333 - 20 = $3.333

Present Value of Growth Opportunities would be $3.333.