youyou find a stock that just paid a diviend of $2 that is expected to grow at 30% per year for the next four years, then at a constant rate of 6%. If you require a 12% return, what should be the current price of the stock?

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amcool amcool · Answer 1 · 2021-05-19T02:42:53+02:00

Answer:

Current price of the stock is $75.91.

Explanation:

Note: See the attached file for the calculation of present values (PV) of dividends for year 1 to 4.

From the attached excel file, we have:

Previous year dividend in year 1 = Dividend just paid = $2

Total of dividends from year 1 to year 4 = $11.77371265390720

Year 4 dividend = $5.7122

Therefore, we have:

Year 5 dividend = Year 4 dividend * (100% + Constant dividend growth rate) = $5.7122 * (100% + 6%) = $6.054932

Share price at year 4 = Year 5 dividend / (Rate of return - Constant dividend growth rate) = $6.054932 / (12% - 6%) = $100.915533333333

PV of share price at year 4 = Price at year 4 / (100% + Required return)^Number of years = $100.915533333333 / (100% + 12%)^4 = $64.1336458251985

Therefore, we have:

Current price of the stock = Total of dividends from year 1 to year 4 + PV of share price at year 4 = $11.77371265390720 + $64.1336458251985 = $75.91