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(Common stock​ valuation)  Assume the​ following: bullet  the​ investor's required rate of return is 14 ​percent,...

(Common stock​ valuation)  Assume the​ following: bullet  the​ investor's required rate of return is 14 ​percent, bullet  the expected level of earnings at the end of this year ​(Upper E 1​) is ​$6​, bullet  the retention ratio is 40 ​percent, bullet  the return on equity ​(ROE​) is 16 percent​ (that is, it can earn 16 percent on reinvested​ earnings), and bullet  similar shares of stock sell at multiples of 7.895 times earnings per share. ​Questions: a.  Determine the expected growth rate for dividends. b.  Determine the price earnings ratio ​(P​/Upper E 1​). c.  What is the stock price using the​ P/E ratio valuation​ method? d.  What is the stock price using the dividend discount​ model? e.  What would happen to the ​P/E ratio ​(P​/Upper E 1​) and stock price if the firm could earn 21 percent on reinvested earnings ​(ROE​)? f.  What does this tell you about the relationship between the rate the firm can earn on reinvested earnings and ​P/E​ ratios?

Solutions

Expert Solution

Given
Required Rate of Return (Ke) 14%
Upper E 1​ $6
Retention Ratio 40%
RoE% 16%
PE multiple of similar stock 7.895
Calculated
Expected Dividend (D1) $3.60
(1-Retention Ratio)* Upper E 1 ((1-40%)*6)
Expected growth rate for dividends (g) 6.4%
(Retention Ratio*RoE%) (40%*16%)
Determine Price earnings ratio ​(P​/Upper E 1​) 7.89
(D1/(Ke-g))/Upper E1 (3.6/(14%-6.4%))/6
Stock price using the​ P/E ratio valuation​ method $47.37
(PE of comparable * Upper E 1) (7.895*6)
Stock price using the dividend discount​ model $47.37
D1/(Ke-g) 3.6/(14%-6.4%)
What would happen to the ​P/E ratio ​(P​/Upper E 1​) and stock price if the firm could earn 21 percent on reinvested earnings ​(ROE​)
Revised Expected growth rate for dividends (g) 8.4%
(Retention Ratio*RoE%) (40%*21%)
Revised Stock price using the dividend discount​ model 64.29
D1/(Ke-g) 3.6/(14%-8.4%)
Revised Price earnings ratio ​(P​/Upper E 1​) 10.714
(D1/(Ke-g))/Upper E1 (3.6/(14%-8.4%))/6
There is a positive relation ship between the ROE and the PE ratio. As higher Roe increased the future growth rate which ultimately increase the stock intrinsic value which led to increase in the stock PE ratio

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