Question

 

the​ investor's required rate of return is 14 ​percent

the expected level of earnings at the end of this year (E 1) is $6​,

the retention ratio is 40 percent,

the return on equity (ROE​) is 16 percent​ (that is, it can earn 16 percent on reinvested​ earnings), and

similar shares of stock sell at multiples of 7.895 times earnings per share.

Q:

Determine the expected growth rate for dividends.

Determine the price earnings ratio (P​/E 1)

What is the stock price using the​ P/E ratio valuation​ method?

What is the stock price using the dividend discount​ model?

What would happen to the ​P/E ratio (P​/E 1) and stock price if the firm could earn 21 percent on reinvested earnings ​(ROE​)?

What does this tell you about the relationship between the rate the firm can earn on reinvested earnings and ​P/E​ ratios?

Answer 1

1. expected growth rate for dividends.
   • where b is the retention ratio
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2. price earnings ratio (P​/E 1)
   • First we calculated the price using here b is retention ratio, r is required rate of return and g is growth rate calculated above
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3. Stock price using the​ P/E ratio valuation​ method:
   • We need to multiply the market P/E by E₁
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4. stock price using the dividend discount​ model:
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5. ​P/E ratio (P​/E 1) and stock price if the firm could earn 21 percent ROE​:
   • expected growth rate for dividends.
     • where b is the retention ratio
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6. The relationship between the rate the firm can earn on reinvested earnings and ​P/E​ ratios is the as ROE increases, growath rate increases and price increases and therefore P/E ratio also increases