Dividend Discount Model (DDM)
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 | DPSt or Terminal value (TVt) | Calculation | Present value at 13.03% |
|---|---|---|---|---|
| 0 | DPS01 | 5.10 | ||
| 1 | DPS1 | 5.26 | = 5.10 × (1 + 3.11%) | 4.65 |
| 2 | DPS2 | 5.54 | = 5.26 × (1 + 5.27%) | 4.33 |
| 3 | DPS3 | 5.95 | = 5.54 × (1 + 7.43%) | 4.12 |
| 4 | DPS4 | 6.52 | = 5.95 × (1 + 9.59%) | 3.99 |
| 5 | DPS5 | 7.28 | = 6.52 × (1 + 11.75%) | 3.95 |
| 5 | Terminal value (TV5) | 634.13 | = 7.28 × (1 + 11.75%) ÷ (13.03% – 11.75%) | 343.68 |
| Intrinsic value of Linde plc common stock (per share) | $364.73 | |||
| Current share price | $444.06 | |||
Based on: 10-K (reporting date: 2023-12-31).
1 DPS0 = Sum of the last year dividends per share of Linde plc 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 Composite1 | RF | 4.67% |
| Expected rate of return on market portfolio2 | E(RM) | 13.79% |
| Systematic risk of Linde plc common stock | βLIN | 0.92 |
| Required rate of return on Linde plc common stock3 | rLIN | 13.03% |
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).
3 rLIN = RF + βLIN [E(RM) – RF]
= 4.67% + 0.92 [13.79% – 4.67%]
= 13.03%
Dividend Growth Rate (g)
Dividend growth rate (g) implied by PRAT model
Linde plc, PRAT model
Based on: 10-K (reporting date: 2023-12-31), 10-K (reporting date: 2022-12-31), 10-K (reporting date: 2021-12-31), 10-K (reporting date: 2020-12-31), 10-K (reporting date: 2019-12-31).
2023 Calculations
1 Retention rate = (Net income, Linde plc – Dividends) ÷ Net income, Linde plc
= (6,199 – 2,482) ÷ 6,199
= 0.60
2 Profit margin = 100 × Net income, Linde plc ÷ Sales
= 100 × 6,199 ÷ 32,854
= 18.87%
3 Asset turnover = Sales ÷ Total assets
= 32,854 ÷ 80,811
= 0.41
4 Financial leverage = Total assets ÷ Total Linde plc shareholders’ equity
= 80,811 ÷ 39,720
= 2.03
5 g = Retention rate × Profit margin × Asset turnover × Financial leverage
= 0.36 × 12.20% × 0.37 × 1.90
= 3.11%
Dividend growth rate (g) implied by Gordon growth model
g = 100 × (P0 × r – D0) ÷ (P0 + D0)
= 100 × ($444.06 × 13.03% – $5.10) ÷ ($444.06 + $5.10)
= 11.75%
where:
P0 = current price of share of Linde plc common stock
D0 = the last year dividends per share of Linde plc common stock
r = required rate of return on Linde plc common stock
Dividend growth rate (g) forecast
Linde plc, H-model
| Year | Value | gt |
|---|---|---|
| 1 | g1 | 3.11% |
| 2 | g2 | 5.27% |
| 3 | g3 | 7.43% |
| 4 | g4 | 9.59% |
| 5 and thereafter | g5 | 11.75% |
where:
g1 is implied by PRAT model
g5 is implied by Gordon growth model
g2, g3 and g4 are calculated using linear interpoltion between g1 and g5
Calculations
g2 = g1 + (g5 – g1) × (2 – 1) ÷ (5 – 1)
= 3.11% + (11.75% – 3.11%) × (2 – 1) ÷ (5 – 1)
= 5.27%
g3 = g1 + (g5 – g1) × (3 – 1) ÷ (5 – 1)
= 3.11% + (11.75% – 3.11%) × (3 – 1) ÷ (5 – 1)
= 7.43%
g4 = g1 + (g5 – g1) × (4 – 1) ÷ (5 – 1)
= 3.11% + (11.75% – 3.11%) × (4 – 1) ÷ (5 – 1)
= 9.59%