Dividend Discount Model (DDM) Calculator
Using the Gordon Growth Model, estimate a stock's intrinsic value from next dividend, required return and dividend growth.
輸入資料
計算結果
重點速覽：DDM (Gordon Growth): stock value = D1 / (r - g), where D1 = next dividend, r = required return, g = perpetual dividend growth. It discounts all future dividends to today. Suits stable, predictable dividend payers (utilities, banks). If market < intrinsic, theoretically undervalued. WARNING: Requires r > g (else formula breaks); assumes perpetual constant growth; r and g subjective and highly sensitive — do sensitivity analysis, cross-check with P/E, DCF. Education, not advice.
計算公式
股票價值 = 下一期每股股息 ÷ (要求回報率 − 股息增長率)，即 P = D1 ÷ (r − g)。
$$P_0 = \dfrac{D_1}{r - g}$$使用說明
- Enter expected next-year dividend (D1).
- Enter required return (must exceed growth).
- Enter perpetual growth rate to view intrinsic value.
下一期股息 D1 = HK$3、要求回報率 r = 10%，在不同股息增長率 g 下的股票內在價值
| 股息增長率 g | 分母 (r − g) | 股票價值 P |
|---|---|---|
| 0% | 10% | HK$30.00 |
| 2% | 8% | HK$37.50 |
| 4% | 6% | HK$50.00 |
| 5% | 5% | HK$60.00 |
| 6% | 4% | HK$75.00 |
理財情境案例
案例一：估值一隻穩定派息股，並測試增長敏感度
投資者研究一隻成熟公用股，預期下一年每股派息 D1 = HK$3，按自身要求回報率 r = 10%、股息永續增長 g = 4% 估值。代入公式：股票價值 = 3 ÷ (10% − 4%) = 3 ÷ 6% = HK$50.00。
他隨即做敏感度測試：若增長略樂觀為 g = 5%，估值升至 3 ÷ 5% = HK$60.00 (+20%);若保守為 g = 3%，估值降至 3 ÷ 7% ≈ HK$42.86 (−14%)。可見估值高度依賴增長假設，因此他不把 50 元當作精準目標，而是視作約 HK$43–60 的合理區間，並在現價明顯低於區間下限時才積極考慮買入。
案例二：與現價比較、判斷貴賤
另一隻銀行股預期下一年派息 D1 = HK$2.4，投資者按 r = 9%、g = 3% 估值：股票價值 = 2.4 ÷ (9% − 3%) = 2.4 ÷ 6% = HK$40.00。
若該股現價為 HK$33，低於內在價值 40 元，按模型屬可能被低估、具吸引力;若現價已升至 HK$48，則明顯偏貴、缺乏安全邊際。不過投資者提醒自己：DDM 僅為單一估值角度，最終決策仍會結合市盈率、市帳率、盈利可持續性與行業前景交叉驗證，避免落入『數字便宜但基本面轉差』的價值陷阱。
常見問題
Why must required return exceed dividend growth?
Because the denominator is (r - g). If g ≥ r, the denominator is zero or negative, giving infinite or negative — meaning 'dividends grow forever at or above the discount rate', the present value diverges and the formula fails. Economically, no company can grow faster than the required return forever. Ensure r > g; for high-growth firms use multi-stage DDM or other models.
What companies does DDM suit?
The Gordon model best fits mature companies with stable, moderate, predictable dividends — utilities, large banks, telecom, REITs with steady cash flows and long payout records. Their future dividends are reasonable to forecast and the assumptions hold. It is unsuitable for non-paying growth stocks (tech), erratic cyclical payers, or high-expansion firms with unstable growth — use DCF or relative valuation there.
Why is the result so sensitive to assumptions?
Because the denominator (r - g) is usually small, and dividing by a small number amplifies the numerator. Example: D1=3, r=10%, g=4% → denom 6%, value 50; if g=5%, denom 5%, value jumps to 60 — a one-point growth change moves value 20%. The closer g to r, the more extreme. Never rely on a single number; sensitivity-analyse r and g, cross-check with other methods.
How should I set the required return r?
r is the minimum annual return you (or the market) require, commonly estimated by CAPM: r = risk-free rate + Beta x market risk premium. Higher risk/Beta → higher r. You can also use peer historical returns or the firm's cost of equity. Higher r means a stricter requirement and lower intrinsic value for the same dividends. Because r is subjective, set a reasonable range (e.g. 8%-12%) and view the valuation band, not a single point.
What if the company has multiple growth stages?
The single-stage Gordon model handles only one constant perpetual growth rate, unsuitable for high-expansion-then-mature firms. Use a multi-stage DDM: discount the high-growth period (e.g. first 5 years) dividends year by year, then use Gordon to estimate the terminal value of the stable period and discount it back; sum both for intrinsic value. This matches DCF terminal-value logic. This calculator focuses on the classic single-stage case for mature stable stocks; for growth firms, stage it or use DCF.
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參考資料
內容審核：香港計算器財經團隊。計算邏輯與公式參考香港金融管理局（HKMA）及投資者及理財教育委員會（IFEC）之個人理財計算指引，結果僅供參考，實際以相關機構公佈為準。