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Apple Inc. just paid a dividend of $3 per share. You expect that Apple's dividend will increase at the rate of 10% per year for the next 10 years. After that, you expect that Apple Inc. will increase its dividend at the rate of 3% per year forever. The required rate of return for Apple is 20%. What is the price of Apple just after the current dividend was paid?

Sagot :

Answer:

The price of Apple just after the current dividend was paid is $26.79.

Explanation:

Note: See the attached file for the calculation of present values for year 1 to 10 dividends.

From the attached excel file, we have:

Previous year dividend in year 1 = Dividend just paid = $3

Total of dividends from year 1 to year 10 = $19.17617169980840

Year 10 dividend = $7.781227380

Therefore, we have:

Year 11 dividend = Year 10 dividend * (100% + Perpetual dividend growth rate) = $7.781227380 * (100% + 3%) = $8.0146642014

Price at year 10 = Year 11 dividend / (Rate of return - Perpetual dividend growth rate) = $8.0146642014 / (20% - 3%) = $47.1450835376471

PV of price at year 10 = Price at year 10 / (100% + Required return)^Number of years = $47.1450835376471 / (100% + 20%)^10 = $7.61419419713817

Price of Apple = Total of dividends from year 1 to year 8 + PV of price at year 10 = $19.17617169980840 + $7.61419419713817 = $26.79

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