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Dividend discount model: two-stage value of a share, with the growth a price implies (illustrative company)

Tool	Dividend Discount Model
Source	Illustrative case computed by the tool with the constant-growth formula of Gordon, M. J., and Shapiro, E. (1956), "Capital Equipment Analysis: The Required Rate of Profit", Management Science, Vol. 3, No. 1, pp. 102–110. No published worked example is reproduced.
Level	Undergraduate

Problem

A share paid a dividend of 2.00 last year. The dividend is expected to grow 8 % a year for five years and 3 % a year afterwards, and an investor requires a return of 9 % a year. What are the dividends worth today, how much of the value lies beyond year 5, and what constant growth would a price of 45.00 imply?

Inputs to Enter

Dividend last year 2.00; required return 9 %; two-stage model: growth now 8 % for 5 years, long-run growth 3 %
Share price 45.00 (illustrative); Advanced: earnings 4.00 and book value 25.00 a share, ROE fade 10 years

Open the Dividend Discount Model tool (loaded with this example)

Answers

Dividends 2.1600, 2.3328, 2.5194, 2.7210, 2.9387, worth 1.9817, 1.9635, 1.9455, 1.9276, 1.9099 today: stage 1 = 9.73
Price at year 5 = 2.9387 × 1.03 / (0.09 − 0.03) = 50.45, worth 32.79 today; value per share 9.73 + 32.79 = 42.52, 77.1 % of it in the terminal stage
Same inputs: constant growth at 3 % gives 2.06 / 0.06 = 34.33; the H-model gives 38.50 against an exact straight-line sum of 39.23 (1.86 % low)
At a price of 45.00: implied growth (45 × 0.09 − 2) / (45 + 2) = 4.36 % a year for ever; implied required return 2.06 / 45 + 3 % = 7.58 %
Value at a required return of 8 % is 51.20 and at 10 % is 36.32; at long-run growth of 2 % it is 37.56 and at 4 % it is 49.45
Advanced: ROE 16 %, payout 50 %, sustainable growth 8 %; residual income value 25.00 + 8.43 = 33.43, equal to the discounted dividends of the same forecast (13.76 + 19.68); PVGO = 45.00 − 4.00 / 0.09 = 0.56

Notes

The tool's default inputs are this case; press Submit. Every figure is illustrative, so the result describes these inputs and is not a statement about any share. The numbers are the tool's own calculation, checked against closed forms, 500-year year-by-year sums and an independent numpy / scipy model (test_dividend_discount_model.php). A calculator for education and analysis, not investment advice.