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Dividend Discount Model (DDM)
Intermediate level
In discounted cash flow (DCF) valuation techniques the value of the stock is estimated based upon present value of some measure of cash flow. Dividends are the cleanest and most straightforward measure of cash flow because these are clearly cash flows that go directly to the investor.
Intrinsic Stock Value (Valuation Summary)
Linde plc, dividends per share (DPS) forecast
US$
Year | Value | DPS_{t} or Terminal value (TV_{t}) | Calculation | Present value at |
---|---|---|---|---|
0 | DPS_{0}^{1} | |||
1 | DPS_{1} | = × (1 + ) | ||
2 | DPS_{2} | = × (1 + ) | ||
3 | DPS_{3} | = × (1 + ) | ||
4 | DPS_{4} | = × (1 + ) | ||
5 | DPS_{5} | = × (1 + ) | ||
5 | Terminal value (TV_{5}) | = × (1 + ) ÷ ( – ) | ||
Intrinsic value of Linde plc’s common stock (per share) | ||||
Current share price |
Based on: 10-K (filing date: 2020-03-02).
^{1} DPS_{0} = Sum of the last year dividends per share of Linde plc’s common stock. See details »
Disclaimer!
Valuation is based on standard assumptions. There may exist specific factors relevant to stock value and omitted here. In such a case, the real stock value may differ significantly form the estimated. If you want to use the estimated intrinsic stock value in investment decision making process, do so at your own risk.
Required Rate of Return (r)
Assumptions | ||
Rate of return on LT Treasury Composite^{1} | R_{F} | |
Expected rate of return on market portfolio^{2} | E(R_{M}) | |
Systematic risk of Linde plc’s common stock | β_{LIN} | |
Required rate of return on Linde plc’s common stock^{3} | r_{LIN} |
^{1} Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).
^{2} See details »
^{3} r_{LIN} = R_{F} + β_{LIN} [E(R_{M}) – R_{F}]
= + [ – ]
=
Dividend Growth Rate (g)
Dividend growth rate (g) implied by PRAT model
Linde plc, PRAT model
Based on: 10-K (filing date: 2020-03-02), 10-K (filing date: 2019-03-18), 10-K (filing date: 2018-02-28), 10-K (filing date: 2017-03-01), 10-K (filing date: 2016-02-24).
2019 Calculations
^{1} Retention rate = (Net income, Linde plc – Dividends) ÷ Net income, Linde plc
= ( – ) ÷ =
^{2} Profit margin = 100 × Net income, Linde plc ÷ Sales
= 100 × ÷ =
^{3} Asset turnover = Sales ÷ Total assets
= ÷ =
^{4} Financial leverage = Total assets ÷ Total Linde plc shareholders’ equity
= ÷ =
^{5} g = Retention rate × Profit margin × Asset turnover × Financial leverage
= × × × =
Dividend growth rate (g) implied by Gordon growth model
g = 100 × (P_{0} × r – D_{0}) ÷ (P_{0} + D_{0})
= 100 × ( × – ) ÷ ( + ) =
where:
P_{0} = current price of share of Linde plc’s common stock
D_{0} = the last year dividends per share of Linde plc’s common stock
r = required rate of return on Linde plc’s common stock
Dividend growth rate (g) forecast
Linde plc, H-model
Year | Value | g_{t} |
---|---|---|
1 | g_{1} | |
2 | g_{2} | |
3 | g_{3} | |
4 | g_{4} | |
5 and thereafter | g_{5} |
where:
g_{1} is implied by PRAT model
g_{5} is implied by Gordon growth model
g_{2}, g_{3} and g_{4} are calculated using linear interpoltion between g_{1} and g_{5}
Calculations
g_{2} = g_{1} + (g_{5} – g_{1}) × (2 – 1) ÷ (5 – 1)
= + ( – ) × (2 – 1) ÷ (5 – 1) =
g_{3} = g_{1} + (g_{5} – g_{1}) × (3 – 1) ÷ (5 – 1)
= + ( – ) × (3 – 1) ÷ (5 – 1) =
g_{4} = g_{1} + (g_{5} – g_{1}) × (4 – 1) ÷ (5 – 1)
= + ( – ) × (4 – 1) ÷ (5 – 1) =