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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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