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.

$‭76.46

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

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