Present Value of Free Cash Flow to Equity (FCFE)
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 equity (FCFE) is generally described as cash flows available to the equity holder after payments to debt holders and after allowing for expenditures to maintain the company asset base.
Intrinsic Stock Value (Valuation Summary)
Linde plc, free cash flow to equity (FCFE) forecast
US$ in millions, except per share data
| Year | Value | FCFEt or Terminal value (TVt) | Calculation | Present value at 13.05% |
|---|---|---|---|---|
| 01 | FCFE0 | 6,578 | ||
| 1 | FCFE1 | 6,783 | = 6,578 × (1 + 3.11%) | 6,000 |
| 2 | FCFE2 | 7,102 | = 6,783 × (1 + 4.70%) | 5,557 |
| 3 | FCFE3 | 7,549 | = 7,102 × (1 + 6.30%) | 5,225 |
| 4 | FCFE4 | 8,144 | = 7,549 × (1 + 7.89%) | 4,986 |
| 5 | FCFE5 | 8,917 | = 8,144 × (1 + 9.49%) | 4,829 |
| 5 | Terminal value (TV5) | 273,877 | = 8,917 × (1 + 9.49%) ÷ (13.05% – 9.49%) | 148,323 |
| Intrinsic value of Linde plc common stock | 174,920 | |||
| Intrinsic value of Linde plc common stock (per share) | $367.36 | |||
| Current share price | $424.31 | |||
Based on: 10-K (reporting date: 2023-12-31).
Disclaimer!
Valuation is based on standard assumptions. There may exist specific factors relevant to stock value and omitted here. In such a case, the real stock value may differ significantly form the estimated. If you want to use the estimated intrinsic stock value in investment decision making process, do so at your own risk.
Required Rate of Return (r)
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.79% |
| Expected rate of return on market portfolio2 | E(RM) | 13.79% |
| Systematic risk of Linde plc common stock | βLIN | 0.92 |
| Required rate of return on Linde plc common stock3 | rLIN | 13.05% |
1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).
3 rLIN = RF + βLIN [E(RM) – RF]
= 4.79% + 0.92 [13.79% – 4.79%]
= 13.05%
FCFE Growth Rate (g)
FCFE growth rate (g) implied by PRAT model
Linde plc, PRAT model
Based on: 10-K (reporting date: 2023-12-31), 10-K (reporting date: 2022-12-31), 10-K (reporting date: 2021-12-31), 10-K (reporting date: 2020-12-31), 10-K (reporting date: 2019-12-31).
2023 Calculations
1 Retention rate = (Net income, Linde plc – Dividends) ÷ Net income, Linde plc
= (6,199 – 2,482) ÷ 6,199
= 0.60
2 Profit margin = 100 × Net income, Linde plc ÷ Sales
= 100 × 6,199 ÷ 32,854
= 18.87%
3 Asset turnover = Sales ÷ Total assets
= 32,854 ÷ 80,811
= 0.41
4 Financial leverage = Total assets ÷ Total Linde plc shareholders’ equity
= 80,811 ÷ 39,720
= 2.03
5 g = Retention rate × Profit margin × Asset turnover × Financial leverage
= 0.36 × 12.20% × 0.37 × 1.90
= 3.11%
FCFE growth rate (g) implied by single-stage model
g = 100 × (Equity market value0 × r – FCFE0) ÷ (Equity market value0 + FCFE0)
= 100 × (202,039 × 13.05% – 6,578) ÷ (202,039 + 6,578)
= 9.49%
where:
Equity market value0 = current market value of Linde plc common stock (US$ in millions)
FCFE0 = the last year Linde plc free cash flow to equity (US$ in millions)
r = required rate of return on Linde plc common stock
FCFE growth rate (g) forecast
Linde plc, H-model
| Year | Value | gt |
|---|---|---|
| 1 | g1 | 3.11% |
| 2 | g2 | 4.70% |
| 3 | g3 | 6.30% |
| 4 | g4 | 7.89% |
| 5 and thereafter | g5 | 9.49% |
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)
= 3.11% + (9.49% – 3.11%) × (2 – 1) ÷ (5 – 1)
= 4.70%
g3 = g1 + (g5 – g1) × (3 – 1) ÷ (5 – 1)
= 3.11% + (9.49% – 3.11%) × (3 – 1) ÷ (5 – 1)
= 6.30%
g4 = g1 + (g5 – g1) × (4 – 1) ÷ (5 – 1)
= 3.11% + (9.49% – 3.11%) × (4 – 1) ÷ (5 – 1)
= 7.89%