Question

A startup will start paying dividends at the end of year 6. The initial growth rate is 10%. This growth rate will continue until year 10. Starting from year 11, the growth rate drops to 5%. The discount rate is 20%. What should the price be at the end of year 5 if the initial dividend is $10.

Answer 1

Answer: $‭76.46

Step-by-step explanation:

The price at the end of year 5 is the sum of the present values of the dividends from year 6 to 10 and the present value of the terminal in year 10.

Year Dividends Discount factor Present value

6 10 ( 1 + 20%) 8.33

7 10 * 1.1 = 11 (1 + 20%)² 7.64

8 10 * 1.1² = 12.1 (1 + 20%)³ 7.00

9 10 * 1.1³ = 13.31 (1 + 20%)⁴ 6.42

10 10 * 1.1⁴ = 14.641 (1 + 20%)⁵ 5.88

Total 35.27

Terminal value at year 10 = Next dividend / (Discount rate - growth)

= (14.641 * 1.05) / (20% - 5%)

= $‭102.487‬

Present value = ‭102.487‬/ (1 + 20%)⁵ = $41.187

Price of stock = 41.187 + 35.27

= $‭76.46