# Linde plc (NYSE:LIN)

## 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 DPSt or Terminal value (TVt) Calculation Present value at 9.66%
0 DPS01 3.85
1 DPS1 3.99 = 3.85 × (1 + 3.68%) 3.64
2 DPS2 4.19 = 3.99 × (1 + 4.83%) 3.48
3 DPS3 4.44 = 4.19 × (1 + 5.98%) 3.36
4 DPS4 4.75 = 4.44 × (1 + 7.13%) 3.29
5 DPS5 5.15 = 4.75 × (1 + 8.28%) 3.25
5 Terminal value (TV5) 402.04 = 5.15 × (1 + 8.28%) ÷ (9.66%8.28%) 253.47
Intrinsic value of Linde plc’s common stock (per share) \$270.49
Current share price \$300.88

Based on: 10-K (filing date: 2021-03-01).

1 DPS0 = 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 Composite1 RF 2.26% Expected rate of return on market portfolio2 E(RM) 11.74% Systematic risk of Linde plc’s common stock βLIN 0.78 Required rate of return on Linde plc’s common stock3 rLIN 9.66%

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]
= 2.26% + 0.78 [11.74%2.26%]
= 9.66%

### Dividend Growth Rate (g)

#### Dividend growth rate (g) implied by PRAT model

Linde plc, PRAT model

Average Dec 31, 2020 Dec 31, 2019 Dec 31, 2018 Dec 31, 2017 Dec 31, 2016
Selected Financial Data (US\$ in millions)
Dividends 2,028  1,891  1,166  901  856
Net income, Linde plc 2,501  2,285  4,381  1,247  1,500
Sales 27,243  28,228  14,900  11,437  10,534
Total assets 88,229  86,612  93,386  20,436  19,332
Total Linde plc shareholders’ equity 47,317  49,074  51,596  6,018  5,021
Financial Ratios
Retention rate1 0.19 0.17 0.73 0.28 0.43
Profit margin2 9.18% 8.09% 29.40% 10.90% 14.24%
Asset turnover3 0.31 0.33 0.16 0.56 0.54
Financial leverage4 1.86 1.76 1.81 3.40 3.85
Averages
Retention rate 0.36
Profit margin 10.60%
Asset turnover 0.38
Financial leverage 2.54

Dividend growth rate (g)5 3.68%

Based on: 10-K (filing date: 2021-03-01), 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).

2020 Calculations

1 Retention rate = (Net income, Linde plc – Dividends) ÷ Net income, Linde plc
= (2,5012,028) ÷ 2,501
= 0.19

2 Profit margin = 100 × Net income, Linde plc ÷ Sales
= 100 × 2,501 ÷ 27,243
= 9.18%

3 Asset turnover = Sales ÷ Total assets
= 27,243 ÷ 88,229
= 0.31

4 Financial leverage = Total assets ÷ Total Linde plc shareholders’ equity
= 88,229 ÷ 47,317
= 1.86

5 g = Retention rate × Profit margin × Asset turnover × Financial leverage
= 0.36 × 10.60% × 0.38 × 2.54
= 3.68%

#### Dividend growth rate (g) implied by Gordon growth model

g = 100 × (P0 × rD0) ÷ (P0 + D0)
= 100 × (\$300.88 × 9.66%\$3.85) ÷ (\$300.88 + \$3.85)
= 8.28%

where:
P0 = current price of share of Linde plc’s common stock
D0 = 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 gt
1 g1 3.68%
2 g2 4.83%
3 g3 5.98%
4 g4 7.13%
5 and thereafter g5 8.28%

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 + (g5g1) × (2 – 1) ÷ (5 – 1)
= 3.68% + (8.28%3.68%) × (2 – 1) ÷ (5 – 1)
= 4.83%

g3 = g1 + (g5g1) × (3 – 1) ÷ (5 – 1)
= 3.68% + (8.28%3.68%) × (3 – 1) ÷ (5 – 1)
= 5.98%

g4 = g1 + (g5g1) × (4 – 1) ÷ (5 – 1)
= 3.68% + (8.28%3.68%) × (4 – 1) ÷ (5 – 1)
= 7.13%