Final answer:
To determine the intrinsic value of the firm's stock, first calculate the dividend for the second year, then find the present values of the second year's dividend and terminal value. Sum these present values to find that the intrinsic stock value is approximately $79.05.
Step-by-step explanation:
The question asks for the calculation of the intrinsic value of a firm's stock based on dividend growth and the required rate of return. Using the Gordon Growth Model (which is a variation of the Dividend Discount Model that assumes a constant growth rate), we can calculate the value of the stock just after the first dividend payment plus the present value of all future dividends growing at a constant rate.
First, we calculate the expected dividend for the second year:
D1 = D0 * (1 + g1) = $2.75 * (1 + 0.15) = $3.1625
Next, we find the present value of the second year's dividend:
PV1 = D1 / (1 + r) = $3.1625 / (1 + 0.07) = $2.9551
Then, we calculate the terminal value, which is the present value of all future dividends after the high growth period, using the Gordon Growth Model:
P1 = D2 / (r - g2), where D2 is the dividend in year 3. Since D1 is the dividend of year 2, D2 = D1 * (1 + g2) = $3.1625 * (1 + 0.03) = $3.2574. So, P1 = $3.2574 / (0.07 - 0.03) = $81.4350
Now, discount P1 back to today to find its present value:
PV(terminal value) = P1 / (1 + r) = $81.4350 / (1 + 0.07) = $76.0813
Finally, add up the present value of the second year's dividend and the present value of the terminal value to get the intrinsic value per share:
Intrinsic value per share = PV1 + PV(terminal value) = $2.9551 + $76.0813 = $79.0364
After rounding according to instructions, we would obtain an intrinsic value per share of approximately $79.05.