A. Dividends today are D0 = $1 per share.
Dividend at the end of year 1 = $1 * 1.04 = $1.04
(You?ll use 0.04 for 4 percent; 0.12 for 12%
Year 2 = (1.04) ^2 = $1.08
Year 3 = (1.04 ^3 = $1.12
B. The general model for stock pricing looks like this:
Pi = Di / (r-g)
Pi = price in period i
Di = dividends in period i
r = required rate of return (in decimals)
g = dividend growth rate
i = period, usually expressed in years
P0 = $1 / (0.12 ? 0.04) = $1 / (0.08) = ?
C. You can use the same formula to figure the stock price in year 3 ?
it?s P3. Just make sure that you adjust D0 to D3 ? as your dividends
P3 = $1.12 / (0.12 ? 0.04) = $1.12/(0.08) = ? (hint: it?s bigger!)
D. First let?s do each year?s cash flows ? and don?t forget that
you?re spending money up front (that?s negative cash flow) -- but the
other returns are positive:
Year 0: -$12.50
Year 1: $1.04
Year 2: $1.08
Year 3: $1.12 + $14.00 (that?s the answer to C, $14)
NPV factor is figured by dividing $1 worth of value by the (1 + i)^t,
where i = discount rate and t = time (in years) that has passed. For
stock bought today, t = 0 and the NPV factor is $1.
Phrased differently, $1 today is worth $1 ? but in a year it?s
depreciated by 12% and so it?s worth $1/(1.12)^1 = 0.8929.
If you?ll be doing these NPV calculations often, the smoothest way to
handle it is to set up your NPV factors in a specific line because it
simplifies complicated cash flow analyses. It also allows you to
check your NPV calculations and quickly spot errors if the number's
not declining as it seems it should.
So here are your NPV factors:
Year 0 (today): 1
Year 1: 0.8929
Year 2: 1/(1.12)^2 = 0.7972
Year 3: 1/(1.12)^3 = 0.7118
The discounted cash flow becomes:
Year 0: -$12.50
Year 1: $1.04 * 0.8929 = $0.93
Year 2: $1.08 * 0.7972 = $0.86
Year 3: $15.12 = $10.76
TOTAL DISCOUNTED CASH FLOW = $0.05
That?s not much money to make on a $12.50 investment. In fact, it?s
effectively zero ? and if we hadn?t rounded 8 different calculations
of dividends and NPV, it would be zero.
Why? It?s because the stock has been priced with future cash flows
and earnings growth in mind ? and with a 12% discount rate. Holding
the stock will become more profitable only if dividends grow faster in
the 3-year period ? or if the discount rate declines.
Let us know via a Clarification Request, if any portion of this doesn?t make sense.