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quantitative problem 3: assume today is december 31, 2019. imagine works inc. just paid a dividend of $1.20 per share at the end of 2019. the dividend is expected to grow at 15% 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 10%. using the dividend growth model (allowing for nonconstant growth), what should be the price of the company's stock today (december 31, 2019)? do not round intermediate calculations. round your answer to the nearest cent.



Answer :

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

Previous year dividend in year 1 = Dividend just paid = $1.20

Total of dividends from year 1 to 3 = $4.71

Year 3 dividend = $2.21

Thus, we have,

Year 4 dividend = Year 3 dividend * (100% + Constant dividend growth rate) = $2.218 * (100% + 5.5%) = $2.340

Share price at year 3 = Year 4 dividend / (Cost of equity - Constant dividend growth rate) = $2.34 / (10% - 5.5%) = $58.50

So, the price of the company's stock today = Total of dividends from year 1 to year 3 + PV of share price at year 3

= $4.711 + $44.55 = $49.27

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

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