Dividend Growth Rate, Retention Rate, and ROE Analysis
Using Stitch's assumptions, Stitch stock is _most likely_:
Correct!
The two-stage DDM is a two-part process. In this case, you'll have one stage with the dividend growth rate at 12% for eight years, followed by the other with the dividend growth at 3% in perpetuity.
First, find the value at the turning point where the growth in earnings decreases from 12% to 3%. That time is _t_ = 8, where earnings slow to 3% but remains at that level in perpetuity.
$$\displaystyle D_8= 0.1\times 1.12^8 = 0.2476 $$
Since the dividend at _t_ = 8 is 0.25, the expected dividend for _t_ = 9 is
$$\displaystyle D_9=0.25\times 1.03 = 0.2550$$.
Now apply the PV of annuity formula.
$$\displaystyle \mbox{PV}_8=\frac{D_9}{r-g}$$
$$\displaystyle \mbox{PV}_8 = \frac{0.2550} {(0.10-0.03)} = 3.6429$$
Then find the present value at _t_ = 0.
$$\displaystyle \mbox{PV}_0=\frac{3.6429}{1.1^8} = 1.6994$$
The current value of the second portion of the dividend is 1.6994. The first portion of the dividend is calculated by growing each dividend by the fast growth rate and then discounting each dividend for the present value.
$$\displaystyle \text{PV}_1 =\frac{(0.10 \times 1.12)}{1.1^1} = 0.1018$$
$$\displaystyle \text{PV}_2 = \frac{(0.10 \times 1.12^2)}{1.1^2} = 0.1037$$
$$\displaystyle \text{PV}_3 = \frac{(0.10 \times 1.12^3)}{1.1^3} = 0.1056$$
$$\displaystyle \text{PV}_4 = \frac{(0.10 \times 1.12^4)}{1.1^4} = 0.1075$$
$$\displaystyle \text{PV}_5 = \frac{(0.10 \times 1.12^5)}{1.1^5} = 0.1094$$
$$\displaystyle \text{PV}_6 = \frac{(0.10 \times 1.12^6)}{1.1^6} = 0.1114$$
$$\displaystyle \text{PV}_7 = \frac{(0.10 \times 1.12^7)}{1.1^7} = 0.1134$$
$$\displaystyle \text{PV}_8 = \frac{(0.10 \times 1.12^8)}{1.1^8} = 0.1155$$
Sum all the present values of the dividends to determine the intrinsic value.
$$\displaystyle 1.6994 + 0.1018 + 0.1037 + 0.1056 + 0.1075$$
$$\displaystyle + 0.1094 + 0.1114 + 0.1134 + 0.1155 = 2.5677$$
The intrinsic value is about 2.57, which is significantly less than the market value of 13. The stock is therefore grossly overvalued.
Incorrect.
Since there are two distinct dividend growth rates, each needs to be calculated separately.
Incorrect.
The dividend growth phase is multi-staged, not one single stage.
overvalued.
fairly valued.
undervalued.
