In: Finance
Find the present value of ACME stock to an investor who has a required rate of return of 10 percent. The current dividend of $1.00 per share has been just paid out today and the dividends are expected to grow 8 percent per year for 3 years. At the end of 3 years the investor expects to sell the security for $80.
Present value of ACME stock is $ 63.00
As per dividend discount model, current share price is the present value of future dividends. | ||||||
Price at the end of year 3 represents present value of future dividends after 3rd year. | ||||||
Step-1:Present value of dividend of next 3 years | ||||||
Year | Dividend | Discount factor | Present value | |||
a | b | c=1.10^-a | d=b*c | |||
1 | $ 1.08 | 0.909091 | $ 0.98 | |||
2 | $ 1.17 | 0.826446 | $ 0.96 | |||
3 | $ 1.26 | 0.751315 | $ 0.95 | |||
Total | $ 2.89 | |||||
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 |
Step-2:Present value of selling price of stock at the end of year 3 | ||||||
Present value | = | $ 80.00 | * | (1.10^-3) | ||
= | $ 80.00 | * | 0.751315 | |||
= | $ 60.11 | |||||
Step-3:Present value of stock | ||||||
Present value of stock | = | Sum of present value of dividends | ||||
= | $ 2.89 | + | $ 60.11 | |||
= | $ 63.00 |