In: Finance
D0=1.00
Dividend is expected to grow at 8% for 10 years, then 5% indefinitely. R=8% for the next 4 years, R=7% for the following 3 years, then 6% indefinitely.
What is today's expected stock price?
As pe dividend discount model, current price of stock is the present value of future dividends. | ||||||||
Step-1:Calculation of present value of dividends for first 10 years | ||||||||
Year | Dividend | Discount factor | Present value | |||||
a | b | c=a*b | ||||||
1 | $ 1.08 | 0.925926 | $ 1.00 | |||||
2 | $ 1.17 | 0.857339 | $ 1.00 | |||||
3 | $ 1.26 | 0.793832 | $ 1.00 | |||||
4 | $ 1.36 | 0.73503 | $ 1.00 | |||||
5 | $ 1.47 | 0.686944 | $ 1.01 | |||||
6 | $ 1.59 | 0.642004 | $ 1.02 | |||||
7 | $ 1.71 | 0.600003 | $ 1.03 | |||||
8 | $ 1.85 | 0.566041 | $ 1.05 | |||||
9 | $ 2.00 | 0.534001 | $ 1.07 | |||||
10 | $ 2.16 | 0.503774 | $ 1.09 | |||||
Total | $ 10.26 | |||||||
Working: | ||||||||
Dividend of year: | ||||||||
1 | = | $ 1.00 | * | 1.08 | = | $ 1.08 | ||
2 | = | $ 1.08 | * | 1.08 | = | $ 1.17 | ||
3 | = | $ 1.17 | * | 1.08 | = | $ 1.26 | ||
4 | = | $ 1.26 | * | 1.08 | = | $ 1.36 | ||
5 | = | $ 1.36 | * | 1.08 | = | $ 1.47 | ||
6 | = | $ 1.47 | * | 1.08 | = | $ 1.59 | ||
7 | = | $ 1.59 | * | 1.08 | = | $ 1.71 | ||
8 | = | $ 1.71 | * | 1.08 | = | $ 1.85 | ||
9 | = | $ 1.85 | * | 1.08 | = | $ 2.00 | ||
10 | = | $ 2.00 | * | 1.08 | = | $ 2.16 | ||
Discount factor of year: | ||||||||
1 | = | 1.08^-1 | = | 0.925926 | ||||
2 | = | 1.08^-2 | = | 0.857339 | ||||
3 | = | 1.08^-3 | = | 0.793832 | ||||
4 | = | 1.08^-4 | = | 0.73503 | ||||
5 | = | 1.07^-1 | * | 1.08^-4 | = | 0.686944 | ||
6 | = | 1.07^-2 | * | 1.08^-4 | = | 0.642004 | ||
7 | = | 1.07^-3 | * | 1.08^-4 | = | 0.600003 | ||
8 | = | 1.06^-1 | * | 1.07^-3 | * | 1.08^-4 | = | 0.566041 |
9 | = | 1.06^-2 | * | 1.07^-3 | * | 1.08^-4 | = | 0.534001 |
10 | = | 1.06^-3 | * | 1.07^-3 | * | 1.08^-4 | = | 0.503774 |
Step-2:Calculation of present value of dividend after year 10 | ||||||||
Present value of dividends | = | D10*(1+g)/(Ke-g)*DF10 | Where. | |||||
= | $ 114.20 | D10 | $ 2.16 | |||||
g | 5% | |||||||
Ke | 6% | |||||||
DF10 | 0.503774 | |||||||
Step-3:Calculation of value of stock today | ||||||||
Value of stock today | = | Sum of present value of future dividends | ||||||
= | $ 10.26 | + | $ 114.20 | |||||
= | $ 124.46 |