A. The common stockholders are the owners of a corporation, and as such, they have certain rights and privileges as described below. 1. Ownership implies control. 2. Common stockholders often have the right, called the preemptive right, to purchase any additional shares sold by the firm. B:The value of any stock is the present value of its expected dividend stream: ? ? However, some stocks have dividend growth patterns which allow them to be valued using short-cut formulas. B2:A constant growth stock is one whose dividends are expected to grow at a constant rate forever.

Many companies have dividends which are expected to grow steadily into the foreseeable future, and such companies are valued as constant growth stocks. For a constant growth stock: D1 = D0(1 + g), D2 = D1(1 + g) = D0(1 + g)2, and so on. With this regular dividend pattern, the general stock valuation model can be simplified to the following very important equation: ? = ? = ?. B3:The model is derived mathematically, and the derivation requires that rs > g. If g is greater than rs, the model gives a negative stock price.

Order nowThe model simply cannot be used unless (1) rs > g, (2) g is expected to be constant, and (3) g can reasonably be expected to continue indefinitely. Stocks may have periods of supernormal growth, where gs > rs; however, this growth rate cannot be sustained indefinitely. In the long-run, g < rs. C:The SML is used to calculate temp force’s required rate of return: rs= rRF + (rM – rRF)bTemp Force = 7% + (12% – 7%)(1. 2) = 7% + (5%)(1. 2) = 7% + 6% = 13%. D1:Temp Force is a constant growth stock, and its dividend is expected to grow at a constant rate of 6 percent per year. Expressed as a time line, we have the following setup.

Just enter 2 in your calculator; then keep multiplying by 1 + g = 1. 06 to get D1, D2, and D3: 0 1 2 3 4 | | | | | g=6% D0 = 2. 00 2. 12 2. 247 2. 382 1. 88 (Year 1) 1. 76 (Year 2) 1. 65 (Year 3) D2:Since the stock is growing at a constant rate, its value can be estimated using the constant growth model: ? = ? = ? = ? = $30. 29. D3: ? = ? = ? = ? = $32. 10. D4:The expected dividend yield in any year n is Dividend Yield = ? ,

While the expected capital gains yield is Capital Gains Yield = ? = r – ?. Total return = 13. 0% Dividend yield = $2. 12/$30. 29 = 7. 0% Capital gains yield = 6. 0% E:Constant growth model – Rearranged ?s= ?. Expected Return: ?s= $2. 12/$30. 29 + 0. 060 = 0. 070 + 0. 060 = 13%. F: 0 1 2 3 | | | | 2. 00 2. 00 2. 00 1. 77 (Year 1) 1. 57 (Year 2) 1. 39 (Year 3) . . . P0 = 15. 38 P0 = PMT/r = $2. 00/0. 13 = $15. 8. G:Temp Force is no longer a constant growth stock, so the constant growth model is not applicable. The easiest way to value such non-constant growth stocks is to set the situation up on a time line as shown below: 0 1 2 3 4 | | | | | 2. 600 3. 380 4. 394 4. 658 2. 301 (Year 1) 2. 647 (Year 2) 3. 045 (Year 3) 46. 116 (Year 4) 54. 109 P0 = $54. 109. The dividend yield in year 1 is 4. 80 percent, and the capital gains yield is 8. percent: Dividend yield = ? = 0. 0480 = 4. 8%. Capital gains yield = 13. 00% – 4. 8% = 8. 2%. After year 3, the stock becomes a constant growth stock, with g = capital gains yield = 6. 0% and dividend yield = 13. 0% – 6. 0% = 7. 0%. H:? = 85. 2%. I:Now we have this situation: 0 1 2 3 4 | | | | | 2. 00 2. 00 2. 00 2. 00 2. 12 1. 77 (Year 1) 1. 57 (Year 2) 1. 39 (Year 3) 20. 99 (Year 4) 25. 72 = ?

During year 1: Dividend Yield = ? = 0. 0778 = 7. 78%. Capital Gains Yield = 13. 00% – 7. 78% = 5. 22%. In year 4 temp force becomes a constant growth stock; hence g = capital gains yield = 6. 0% and dividend yield = 7. 0%. J:The company is earning something and paying some dividends, so it clearly has a value greater than zero. That value can be found with the constant growth formula, but where g is negative: ? = ? = ? = ? = ? = $9. 89. Since it is a constant growth stock: g = Capital Gains Yield = -6. 0%, Dividend Yield = 13. 0% – (-6. 0%) = 19. 0%. Checkpoint: Dividend Yield = ? = 0. 190 = 19. 0%.

K:Analysts often use the P/E multiple, or the P/CF multiple, to value stocks. For example, estimate the average P/E ratio of comparable firms. This is the P/E multiple. Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price. The entity value (V) is the market value of equity ( shares of stock multiplied by the price per share) plus the value of debt. Pick a measure, such as EBITDA, sales, customers, eyeballs, etc. Calculate the average entity ratio for a sample of comparable firms. For example, V/EBITDA, V/customers. Then find the entity value of the firm in question.

For example, multiply the firm’s sales by the V/sales multiple, or multiply the firm’s of customers by the V/customers ratio. The result is the total value of the firm. Subtract the firm’s debt to get the total value of equity. Divide by the number of shares to get the price per share. There are problems with market multiple analysis. (1) It is often hard to find comparable firms. (2) The average ratio for the sample of comparable firms often has a wide range. L:Using P0 = D1 / (rs – g). If estimates of g change, then the price will change. If estimates of the required return on stock change, then the stock price will change. ggg