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 |