Question

Web Cites Research projects a rate of return of 10% on new projects. Management plans to plow back 20% of all earnings into the firm. Earnings this year will be $3 per share, and investors expect a rate of return of 5% on stocks facing the same risks as Web Cites.

a. What is the sustainable growth rate? (Enter your answer as a whole percent.)

b. What is the stock price? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. What is the present value of growth opportunities (PVGO)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

d. What is the P/E ratio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

e. What would the price and P/E ratio be if the firm paid out all earnings as dividends? (Round your answers to 2 decimal places.)

Answer 1

Rate of Return = 10%

Retained Earnings = 20%

Earnings (Current Year) = 3

Cost of Equity = 5%

A. Sustainable Growth Rate =  ROE x (1 - dividend-payout ratio)

Dividend Payout ratio = 1 - Retained Earings = 1 - 0.2 = 0.8

Sustainable Growth Rate =  ROE x (1 - dividend-payout ratio) = 10% * (1-0.8) = 2%

B. Stock Price =

According to Gordon Growth Model

Price of Stock = Dividend Next Year/(Cost of Equity-Growth rate)

Growth rate is calculated in Part A.

Earnings this Year = 3 dollars

Earnings Next Year = 3 * (1+0.02) = 3.06

Out of this, Dividend will be 80%, 3.06*0.8 = 2.448

Price of Stock = 2.448/(0.05-0.02) = 2.448/0.03 = 81.60

C. Present Value of Growth Opportunities = Stock Price - Earnings/Cost of Equity

= 81.60 - 3/0.05 = 21.60

D. P/E Ratio = Price/Earnings = 81.60/3 = 27.2

E. Price & P/E ratio if firm pays all earnings as dividend =

Current Year Dividend = 3

Next Year Dividend = 3*(1+0.02) = 3.06

Price = Dividend Next Year/(Cost of Equity-Growth rate)

Price = 3.06/(0.05-0.02) = 102

P/E Ratio = 102/3 = 34

Please comment, in case you need more help. Thank You.