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A7X Corp. just paid a dividend of $2.50 per share. The dividends are expected to grow at 17 percent for the next eight years and then level off to a growth rate of 7 percent indefinitely. If the required return is 13 percent, what is the price of the stock today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Sagot :

Answer:

Price of the stock today = $82.35

Explanation:

Note: See the attached file for the calculation of present values for year 1 to 8 dividends.

From the attached excel file, we have:

Previous year dividend in year 1 = Dividend just paid = $2.50

Total of dividends from year 1 to year 8 = $23.46345631521910

Year 8 dividend = 8.77863318950395

Therefore, we have:

Year 9 dividend = Year 8 dividend * (100% + Dividend growth rate in year 9) = 8.77863318950395 * (100% + 7%) = 9.39313751276923

Price at year 8 = Year 9 dividend / (Rate of return - Perpetual dividend growth rate) = 9.39313751276923 / (13% - 7%) = $156.552291879487

PV of price at year 8 = Price at year 8 / (100% + Required return)^Number of years = $156.552291879487 / (100% + 13%)^8 = $58.88868846568915

Price of the stock today = Total of dividends from year 1 to year 8 + PV of price at year 8 = $23.46345631521910 + $58.88868846568915 = $82.35

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