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Quantitative Problem 3: Assume today is December 31, 2019. Imagine Works Inc. just paid a dividend of $1.35 per share at the end of 2019. The dividend is expected to grow at 18% per year for 3 years, after which time it is expected to grow at a constant rate of 5.5% annually. The company's cost of equity (rs) is 9.5%. Using the dividend growth model (allowing for nonconstant growth), what should be the price of the company's stock today (December 31, 2019)

Sagot :

Answer:

The price of the company's stock today (December 31, 2019) is $49.27.

Explanation:

Note: See the attached file for the calculation of present values (PV) for year 1 to 3 dividends.

From the attached excel file, we have:

Previous year dividend in year 1 = Dividend just paid = $1.35

Total of dividends from year 1 to year 3 = $4.71193752458119

Year 3 dividend = $2.2180932

Therefore, we have:

Year 4 dividend = Year 3 dividend * (100% + Constant dividend growth rate) = $2.2180932 * (100% + 5.5%) = $2.340088326

Share price at year 3 = Year 4 dividend / (Cost of equity - Constant dividend growth rate) = $2.340088326 / (9.5% - 5.5%) = $58.50220815

PV of share price at year 3 = Share price at year 3 / (100% + Cost of equity)^Number of years = $58.50220815 / (100% + 9.5%)^3 = $44.55843215078

Therefore, we have:

The price of the company's stock today = Total of dividends from year 1 to year 3 + PV of share price at year 3 = $4.71193752458119 + $44.55843215078 = $49.27

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