In discounted cash flow (DCF) valuation techniques the value of the stock is estimated based upon present value of some measure of cash flow. Free cash flow to the firm (FCFF) is generally described as cash flows after direct costs and before any payments to capital suppliers.

Intrinsic Stock Value (Valuation Summary)
Weighted Average Cost of Capital (WACC)
FCFF Growth Rate (g)

Linde plc, free cash flow to the firm (FCFF) forecast

US$ in millions, except per share data

Year	Value	FCFF_t or Terminal value (TV_t)	Calculation	Present value at 12.16%
0¹	FCFF₀	5,918
1	FCFF₁	6,051	= 5,918 × (1 + 2.25%)	5,395
2	FCFF₂	6,295	= 6,051 × (1 + 4.02%)	5,004
3	FCFF₃	6,659	= 6,295 × (1 + 5.79%)	4,720
4	FCFF₄	7,163	= 6,659 × (1 + 7.57%)	4,527
5	FCFF₅	7,832	= 7,163 × (1 + 9.34%)	4,413
5	Terminal value (TV₅)	303,955	= 7,832 × (1 + 9.34%) ÷ (12.16% – 9.34%)	171,272
Intrinsic value of Linde plc capital				195,332
Less: Debt and finance lease liabilities (fair value)				18,243
Intrinsic value of Linde plc common stock				177,089

Intrinsic value of Linde plc common stock (per share)				$371.91
Current share price				$444.06

Based on: 10-K (reporting date: 2023-12-31).

¹ 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.

Linde plc, cost of capital

	Value¹	Weight	Required rate of return²	Calculation
Equity (fair value)	211,443	0.92	13.03%
Debt and finance lease liabilities (fair value)	18,243	0.08	2.00%	= 2.67% × (1 – 24.92%)

Based on: 10-K (reporting date: 2023-12-31).

¹ US$ in millions

Equity (fair value) = No. shares of common stock outstanding × Current share price
= 476,157,903 × $444.06
= $211,442,678,406.18

Debt and finance lease liabilities (fair value). See details »

² Required rate of return on equity is estimated by using CAPM. See details »

Required rate of return on debt. See details »

Required rate of return on debt is after tax.

Estimated (average) effective income tax rate
= (22.70% + 25.90% + 24.70% + 25.00% + 26.30%) ÷ 5
= 24.92%

WACC = 12.16%

FCFF growth rate (g) implied by PRAT model

Linde plc, PRAT model

	Average	Dec 31, 2023	Dec 31, 2022	Dec 31, 2021	Dec 31, 2020	Dec 31, 2019
Selected Financial Data (US$ in millions)
Interest expense		397)	180)	117)	170)	150)
Income from discontinued operations, net of tax		—)	—)	5)	4)	109)
Net income, Linde plc		6,199)	4,147)	3,826)	2,501)	2,285)

Effective income tax rate (EITR)¹		22.70%	25.90%	24.70%	25.00%	26.30%

Interest expense, after tax²		307)	133)	88)	128)	111)
Add: Dividends		2,482)	2,344)	2,189)	2,028)	1,891)
Interest expense (after tax) and dividends		2,789)	2,477)	2,277)	2,156)	2,002)

EBIT(1 – EITR)³		6,506)	4,280)	3,909)	2,625)	2,287)

Short-term debt		4,713)	4,117)	1,163)	3,251)	1,732)
Current portion of long-term debt		1,263)	1,599)	1,709)	751)	1,531)
Current finance lease liabilities		50)	42)	47)	38)	—)
Long-term debt, excluding current portion		13,397)	12,198)	11,335)	12,152)	10,693)
Long-term finance lease liabilities		143)	114)	129)	125)	—)
Total Linde plc shareholders’ equity		39,720)	40,028)	44,035)	47,317)	49,074)
Total capital		59,286)	58,098)	58,418)	63,634)	63,030)
Financial Ratios
Retention rate (RR)⁴		0.57	0.42	0.42	0.18	0.12
Return on invested capital (ROIC)⁵		10.97%	7.37%	6.69%	4.12%	3.63%
Averages
RR	0.34
ROIC	6.56%

FCFF growth rate (g)⁶	2.25%

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).

¹ See details »

2023 Calculations

² Interest expense, after tax = Interest expense × (1 – EITR)
= 397 × (1 – 22.70%)
= 307

³ EBIT(1 – EITR) = Net income, Linde plc – Income from discontinued operations, net of tax + Interest expense, after tax
= 6,199 – 0 + 307
= 6,506

⁴ RR = [EBIT(1 – EITR) – Interest expense (after tax) and dividends] ÷ EBIT(1 – EITR)
= [6,506 – 2,789] ÷ 6,506
= 0.57

⁵ ROIC = 100 × EBIT(1 – EITR) ÷ Total capital
= 100 × 6,506 ÷ 59,286
= 10.97%

⁶ g = RR × ROIC
= 0.34 × 6.56%
= 2.25%

FCFF growth rate (g) implied by single-stage model

g = 100 × (Total capital, fair value₀ × WACC – FCFF₀) ÷ (Total capital, fair value₀ + FCFF₀)
= 100 × (229,686 × 12.16% – 5,918) ÷ (229,686 + 5,918)
= 9.34%

where:

Total capital, fair value₀ = current fair value of Linde plc debt and equity (US$ in millions)
FCFF₀ = the last year Linde plc free cash flow to the firm (US$ in millions)
WACC = weighted average cost of Linde plc capital

FCFF growth rate (g) forecast

Linde plc, H-model

Year	Value	g_t
1	g₁	2.25%
2	g₂	4.02%
3	g₃	5.79%
4	g₄	7.57%
5 and thereafter	g₅	9.34%

where:
g₁ is implied by PRAT model
g₅ is implied by single-stage model
g₂, g₃ and g₄ are calculated using linear interpoltion between g₁ and g₅

Calculations

g₂ = g₁ + (g₅ – g₁) × (2 – 1) ÷ (5 – 1)
= 2.25% + (9.34% – 2.25%) × (2 – 1) ÷ (5 – 1)
= 4.02%

g₃ = g₁ + (g₅ – g₁) × (3 – 1) ÷ (5 – 1)
= 2.25% + (9.34% – 2.25%) × (3 – 1) ÷ (5 – 1)
= 5.79%

g₄ = g₁ + (g₅ – g₁) × (4 – 1) ÷ (5 – 1)
= 2.25% + (9.34% – 2.25%) × (4 – 1) ÷ (5 – 1)
= 7.57%

Linde plc (NASDAQ:LIN)

Present Value of Free Cash Flow to the Firm (FCFF)

Intrinsic Stock Value (Valuation Summary)

Weighted Average Cost of Capital (WACC)

FCFF Growth Rate (g)

FCFF growth rate (g) implied by PRAT model

FCFF growth rate (g) implied by single-stage model

FCFF growth rate (g) forecast