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