Problem 7-20
Nonconstant Growth Stock Valuation
Reizenstein Technologies (RT) has just developed a solar panel capable of generating 200% more electricity than any solar panel currently on the market. As a result, RT is expected to experience a 14% annual growth rate for the next 5 years. By the end of 5 years, other firms will have developed comparable technology, and RT's growth rate will slow to 5% per year indefinitely. Stockholders require a return of 12% on RT's stock. The most recent annual dividend (D0), which was paid yesterday, was $3.30 per share.
Expected dividend yield | % |
Capital gains yield | % |
Expected total return | % |
Expected dividend yield | % |
Capital gains yield | % |
Expected total return | % |
So, to calculate the future dividend,
Last year Dividend |
D0 |
3.30 |
growth rate |
year 1 |
14% |
year 2 |
14% |
|
year 3 |
14% |
|
year 4 |
14% |
|
year 5 |
14% |
|
5+ growth indefinitely |
5% |
|
working |
||
year 1 |
D1 = 3.30*1.14 |
3.76 |
year 2 |
D2 =3.76*1.14 |
4.29 |
year 3 |
D3= 4.29*1.14 |
4.89 |
year 4 |
D4 = 4.89*1.14 |
5.57 |
year 5 |
D5 = 5.57*1.14 |
6.35 |
So,
Year |
Dividend |
year 1 |
$ 3.76 |
year 2 |
$ 4.29 |
year 3 |
$ 4.89 |
year 4 |
$ 5.57 |
year 5 |
$ 6.35 |
after 5 years , he will receive dividend at a constant growth of 5% |
so we need to find the value of stock at the end of year 5 |
which is = this year dividend* (1+ growth)/(discount rate – growth) |
next years dividend = This years dividend * (1+growth) |
dis rate |
12% |
|
value of stock at the end of year 4 |
= 6.35*(1+0.05)/(0.12-0.05) |
$95.31 |
Now to find the price of stock today, we need to calculate the present value of all these dividend .
Year |
Dividend/ stock value |
working |
Discount factor = 1/(1+r)^n |
Discounted cash Flow= Cash flow * discount value |
year 1 |
3.76 |
1/ (1+0.12)^1 |
0.89 |
3.36 |
year 2 |
4.29 |
1/ (1+0.12)^2 |
0.80 |
3.42 |
year 3 |
4.89 |
1/ (1+0.12)^3 |
0.71 |
3.48 |
year 4 |
5.57 |
1/ (1+0.12)^4 |
0.64 |
3.54 |
year 5 |
6.35 |
1/ (1+0.12)^5 |
0.57 |
3.61 |
year 5 |
95.31 |
1/ (1+0.12)^5 |
0.57 |
54.08 |
Total |
71.49 |
So the value of stock today = $71.49
Dividend yield= |
D1/P0 |
D1= 3.76
P0= 71.49
DY= 3.76/71.49 = 0.0526 or 5.26%
ii. Capital yield = Return rate - dividend yield
Return rate =12%.
Dividend yield= 5.26%
Capital Yield= 12-5.26= 6.74%
Iii. Expected return = 12%
D6= 6.35*1.04= 6.67
P5= 95.31
Dividend yield= 6.67/95.31
= 0.07 or 7%
Capital yield= 0.12-0.07= 5%
Expected return = 12%
Problem 7-20 Nonconstant Growth Stock Valuation Reizenstein Technologies (RT) has just developed a solar panel capable...
Problem 7-20 Nonconstant Growth Stock Valuation Reizenstein Technologies (RT) has just developed a solar panel capable of generating 200% more electricity than any solar panel currently on the market. As a result, RT is expected to experience a 14% annual growth rate for the next 5 years. By the end of 5 years, other firms will have developed comparable technology, and RT's growth rate will slow to 7% per year indefinitely. Stockholders require a return of 12% on RT's stock....
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