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 Subject: Finance Category: Business and Money > Finance Asked by: baseball2-ga List Price: \$7.00 Posted: 30 Jul 2005 13:46 PDT Expires: 29 Aug 2005 13:46 PDT Question ID: 549860
 ```Could you please provide me a formula to figure the following: Details: A company paid a 1.00 per share divident yesterday. I expect the divident to grow at a 4 percent per year. I need formulas for the following: 1. What is the expectd divident in each of the 3 years. 2. If the discount rate for the stock is 12% at what price will the stock sell? 3. What is the expected stock price 3 years from now? 4/ If I buy back the stock and plan to hold i for 3 yrs, what payments will I recieve and what is the present value of the payment?```
 ```Baseball2 ? This question provides a good chance to do what we didn?t do in the previous question ? look at what happens to stock value if dividends are growing. As previously noted, the general case for figuring a stock value (it also figures a bond or loan value too) is: P0 = D1 / (r-g) P0 = today's price D1 = dividends in period 1 r = required rate of return (in decimals) g = dividend growth rate 1. D1 = \$1.00 * (1 + g)^ i where i = year (and today is year 0) Today = \$1.00 Year 1 = \$1.04 Year 2 = \$1.08 Year 3 = \$1.12 2. Today the stock will sell for P0 = D1 / (r-g) P0 = \$1.00 / (.12 - .04) = \$12.50 3. In three years, the dividend has risen to \$1.12, so the stock price will be higher: P3 = \$1.12 / (.12 - .04) = \$14.00 4. If you buy the stock and hold it for 3 years, here?s your cash flow: Year 0: -\$12.50 (to buy the stock) Year 1: \$1.04 Year 2: \$1.08 Year 3: \$1.12 + \$14 (sale price) --- The NPV factors (1 + .12)^i are as follows (as before, i = year) -- Year 0: 1 Year 1: 1/(1.12) = 0.8929 Year 2: 1/(1.12)^2 = .7972 Year 3: 1/(1.12)^3 = .7118 Discounted cash flow or net present value of the payments are: Year 0: -\$12.50 Year 1: 0.8929 * \$1.04 = \$0.93 Year 2: 0.7972 * \$1.08 = \$0.86 Year 3: 0.7118 * \$15.12 = \$10.76 NPV = -\$12.50 + \$0.93 + \$0.86 + \$10.76 = \$0.05 The present value is virtually zero. Really it is zero, when rounding errors from 8 different calculations are eliminated. Why? Your expected return of 12% is being met ? and accounted for ? in the pricing of the stock and in the dividend. So, discounting everything back at 12% gives you zero. If it gave you a bigger number, one of the elements would change ? such as the stock price being higher. Your discount rate/dividend and price/NPV of your returns are all linked so that NPV is effectively zero with a CONSTANT DISCOUNT RATE. Of course, stock and even bond prices change every day in the markets, as investors try to assess future dividends; future interest rate changes; and future stock prices. Best regards, Omnivorous-GA```