# Union Pacific Corp. (NYSE:UNP)

## Present Value of Free Cash Flow to Equity (FCFE)

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. 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’s asset base.

### Intrinsic Stock Value (Valuation Summary)

Union Pacific Corp., 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 12.97%
01 FCFE0 8,006
1 FCFE1 9,443 = 8,006 × (1 + 17.95%) 8,359
2 FCFE2 10,876 = 9,443 × (1 + 15.18%) 8,522
3 FCFE3 12,226 = 10,876 × (1 + 12.41%) 8,479
4 FCFE4 13,404 = 12,226 × (1 + 9.64%) 8,228
5 FCFE5 14,324 = 13,404 × (1 + 6.87%) 7,784
5 Terminal value (TV5) 250,658 = 14,324 × (1 + 6.87%) ÷ (12.97%6.87%) 136,207
Intrinsic value of Union Pacific Corp.’s common stock 177,578

Intrinsic value of Union Pacific Corp.’s common stock (per share) \$263.52
Current share price \$207.90

Based on: 10-K (filing date: 2020-02-07).

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 1.68% Expected rate of return on market portfolio2 E(RM) 12.11% Systematic risk of Union Pacific Corp.’s common stock βUNP 1.08 Required rate of return on Union Pacific Corp.’s common stock3 rUNP 12.97%

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 rUNP = RF + βUNP [E(RM) – RF]
= 1.68% + 1.08 [12.11%1.68%]
= 12.97%

### FCFE Growth Rate (g)

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

Union Pacific Corp., PRAT model

Average Dec 31, 2019 Dec 31, 2018 Dec 31, 2017 Dec 31, 2016 Dec 31, 2015
Selected Financial Data (US\$ in millions)
Cash dividends declared 2,598  2,299  1,982  1,879  1,906
Net income 5,919  5,966  10,712  4,233  4,772
Operating revenues 21,708  22,832  21,240  19,941  21,813
Total assets 61,673  59,147  57,806  55,718  54,600
Common shareholders’ equity 18,128  20,423  24,856  19,932  20,702
Financial Ratios
Retention rate1 0.56 0.61 0.81 0.56 0.60
Profit margin2 27.27% 26.13% 50.43% 21.23% 21.88%
Asset turnover3 0.35 0.39 0.37 0.36 0.40
Financial leverage4 3.40 2.90 2.33 2.80 2.64
Averages
Retention rate 0.58
Profit margin 29.39%
Asset turnover 0.37
Financial leverage 2.81

FCFE growth rate (g)5 17.95%

Based on: 10-K (filing date: 2020-02-07), 10-K (filing date: 2019-02-08), 10-K (filing date: 2018-02-09), 10-K (filing date: 2017-02-03), 10-K (filing date: 2016-02-05).

2019 Calculations

1 Retention rate = (Net income – Cash dividends declared) ÷ Net income
= (5,9192,598) ÷ 5,919
= 0.56

2 Profit margin = 100 × Net income ÷ Operating revenues
= 100 × 5,919 ÷ 21,708
= 27.27%

3 Asset turnover = Operating revenues ÷ Total assets
= 21,708 ÷ 61,673
= 0.35

4 Financial leverage = Total assets ÷ Common shareholders’ equity
= 61,673 ÷ 18,128
= 3.40

5 g = Retention rate × Profit margin × Asset turnover × Financial leverage
= 0.58 × 29.39% × 0.37 × 2.81
= 17.95%

#### FCFE growth rate (g) implied by single-stage model

g = 100 × (Equity market value0 × r – FCFE0) ÷ (Equity market value0 + FCFE0)
= 100 × (140,097 × 12.97%8,006) ÷ (140,097 + 8,006)
= 6.87%

where:
Equity market value0 = current market value of Union Pacific Corp.’s common stock (US\$ in millions)
FCFE0 = the last year Union Pacific Corp.’s free cash flow to equity (US\$ in millions)
r = required rate of return on Union Pacific Corp.’s common stock

#### FCFE growth rate (g) forecast

Union Pacific Corp., H-model

Year Value gt
1 g1 17.95%
2 g2 15.18%
3 g3 12.41%
4 g4 9.64%
5 and thereafter g5 6.87%

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 + (g5g1) × (2 – 1) ÷ (5 – 1)
= 17.95% + (6.87%17.95%) × (2 – 1) ÷ (5 – 1)
= 15.18%

g3 = g1 + (g5g1) × (3 – 1) ÷ (5 – 1)
= 17.95% + (6.87%17.95%) × (3 – 1) ÷ (5 – 1)
= 12.41%

g4 = g1 + (g5g1) × (4 – 1) ÷ (5 – 1)
= 17.95% + (6.87%17.95%) × (4 – 1) ÷ (5 – 1)
= 9.64%