a. Current price calculation:
The expected dividends for year 1 and year 2 -
D1 = $2
D2 = $4
The dividends occurring in the stable growth period of 5% after year 2
g = growth rate of dividends = 5% after year 2
k = required rate of return or cost of equity = 12%
Now we can calculate the present value of each dividend;
Present value of dividend = Dividend paid / (1+k) ^t (where t is the time period)
PV1 = $2/ 1.12 = $1.79
PV2 = $4/ (1.12) ^2 = $3.19
We can apply the stable-growth Gordon Growth Model formula to these dividends to determine their residual value in the terminal year
=D2 *(1+g) / (k-g)
= $4 * (1+5%)/ (12% - 5%) = $60.00
The present value of these stable growth period dividends (residual value) are
$60 / (1.12) ^2 = $47.83
Now add the present values of future dividends to get current stock price
P0 = $1.79 + $3.19 + $47.83
= $52.81 (rounding off to two decimal points)
The company’s stock price today is $52.81 per share.
b. Expected price calculation in a year
Price of a company’s stock is the present value of its all expected future cash flows, therefore stock price after 1 year is the sum of the present value of its all expected future cash flows after year 1
P1 = stock price after 1 year =?
D2 = dividend for year 2 = $4 per share
k = required rate of return or cost of equity = 12%
g = growth rate of dividends = 5% after year 2
The dividends occurring in the stable growth period of 5%, we then apply the stable-growth Gordon Growth Model formula to these dividends to determine their value in the terminal year
Value in the terminal year = D2 * (1+g) / (k –g) = $4 *(1+5%) / (12%- 5%) = $60.00
Now we can calculate the present value at the end of year 1 of dividend and terminal value and add the present values of future dividends and terminal value to get current stock price;
P1 = $4 / (1+12%) ^1 + $60 / (1+12%) ^1
= $3.57 +$53.57
= $57.14
Therefore stock price after 1 year will be $57.14 per share
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