A. Finding the market price of this stock requires the use of the 2-stage dividend discount model, since the annual rate of growth in the dividend is expected to be 25% for two years and then decrease to 10%.The first step is to find the present values of the dividends to be received during the first two years and sum the results. The Year 2 dividend is 125% of the Year 1 dividend.
Present Value
End of Year Dividend PV Factor @ 16% of Dividend
1 $1.00 .862 $ .862
2 1.25 .742 .929
PV of future dividends - Years 1 and 2: $1.791
We next project the dividend for Year 3 by multiplying the Year 2 dividend ($1.25) by 1 + the growth rate for Year 3 (1.10). The Year 3 dividend is therefore projected to be $1.25 × 1.10, or $1.38.Now, we use the Constant Growth Model (Dividend Growth Model), and we pretend that Year 3 is Year 1, and so the end of Year 2 becomes Year 0. We use this model to calculate what the value of the stock will be at the end of Year 2, assuming a required rate of return of 16% and an annual growth in dividends of 10% going forward from the end of Year 2, beginning with Year 3:
P2 = d3 / (r - g)P2 = $1.38 / (.16 - .10)P2 = $23.00 This present value of $23.00 occurs at the end of Year 2, not at Year 0. Therefore, it needs to be discounted back 2 years to Year 0. We will discount it back as though it is a single sum that will be received in 2 years. The present value of $1 factor for 2 years at 16% is .743, so the present value of $23.00 two years from now is $23.00 × .743, or $17.09. This is the present value as of Year 0 of the dividends to be received beginning at the end of Year 3 and continuing indefinitely. The final step is to add together the present value of the future dividends for Years 1 and 2 ($1.79) and the present value of the dividends to be received from Year 3 to infinity ($17.09) to calculate the value today, at Year 0, for a share of this stock:$1.79 + $17.09 = $18.88$18.88 is an appropriate market price for this stock, given the projected dividends and the 16% required rate of return by investors in the stock.
B. $13.80 is the projected Year 3 dividend divided by the Year 3 growth rate.
C. $4.00 is the current annual dividend divided by the current rate of growth.
D. This is the Year 3 dividend divided by the difference between the investors' required rate of return and the growth rate, as in the Dividend Growth Model. This is only one part of the calculation needed to determine the appropriate market price for the stock.
