# Vale S.A. (VALE) | Present Value of Free Cash Flow to the Firm (FCFF)

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 Summery)

Vale S.A., free cash flow to the firm (FCFF) forecast

USD \$ in millions, except per share data

Year Value FCFFt or Terminal value (TVt) Calculation Present value at 14.35%
01 FCFF0 2,134
1 FCFF1 2,335  = 2,134  × (1 + 9.41%) 2,042
2 FCFF2 2,572  = 2,335  × (1 + 10.14%) 1,967
3 FCFF3 2,851  = 2,572  × (1 + 10.87%) 1,907
4 FCFF4 3,182  = 2,851  × (1 + 11.60%) 1,861
5 FCFF5 3,574  = 3,182  × (1 + 12.33%) 1,828
5 Terminal value (TV5) 198,767  = 3,574  × (1 + 12.33%) ÷ (14.35% – 12.33%) 101,669
Intrinsic value of 's capital 111,274
Less: Debt (fair value) 33,149
Intrinsic value of 's common stock 78,125

Intrinsic value of 's common stock (per share) \$14.56
Current share price \$15.94

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.

## Weighted Average Cost of Capital (WACC)

Vale S.A., cost of capital

Value1 Weight Required rate of return2 Calculation
Equity (fair value) 85,523  0.72 17.99%
Debt (fair value) 33,149  0.28 4.94% = 5.50% × (1 – 10.14%)

1 USD \$ in millions

2 Required rate of return on debt is after tax (estimated effective tax rate is 10.14%)

WACC = 14.35%

## FCFF Growth Rate (g)

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

Vale S.A., PRAT model

Average Dec 31, 2012 Dec 31, 2011 Dec 31, 2010 Dec 31, 2009 Dec 31, 2008
Selected Financial Data (USD \$ in millions)
Income taxes   (833) 5,282  3,705  2,100  535
Net income attributable to the Company's stockholders   5,511  22,885  17,264  5,349  13,218
Tax rate1   -17.81% 18.75% 17.67% 28.19% 3.89%

Financial expenses   2,414  2,465  2,646  1,558  1,765
Financial expenses, after tax2   2,844  2,003  2,178  1,119  1,696
Add: Dividends and interest attributed to stockholders' equity   4,765  5,348  5,173  1,615  2,210
Interest expense (after tax) and dividends   7,609  7,351  7,351  2,734  3,906

EBIT(1 – Tax Rate)3   8,355  24,888  19,442  6,468  14,914

Short-term debt   22  139  30
Current portion of long-term debt   3,468  1,495  2,823  2,933  633
Long-term debt, excluding current portion   26,799  21,538  21,591  19,898  17,535
Company stockholders' equity   74,241  77,715  68,899  56,935  42,556
Total capital   104,508  100,770  93,452  79,796  60,724
Ratios
Retention rate (RR)4   0.09 0.70 0.62 0.58 0.74
Return on invested capital (ROIC)5   7.99% 24.70% 20.80% 8.11% 24.56%
Averages
RR 0.55
ROIC 17.23%

Growth rate of FCFF (g)6 9.41%

2012 Calculations

1 Tax rate = 100 × Income taxes ÷ (Net income attributable to the Company's stockholders + Income taxes)
= 100 × -833 ÷ (5,511 + -833) = -17.81%

2 Financial expenses, after tax = Financial expenses × (1 – Tax rate)
= 2,414 × (1 – -17.81%) = 2,844

3 EBIT(1 – Tax Rate) = Net income attributable to the Company's stockholders + Financial expenses, after tax
= 5,511 + 2,844 = 8,355

4 RR = [EBIT(1 – Tax Rate) – Interest expense (after tax) and dividends] ÷ EBIT(1 – Tax Rate)
= [8,355 – 7,609] ÷ 8,355 = 0.09

5 ROIC = 100 × EBIT(1 – Tax Rate) ÷ Total capital
= 100 × 8,355 ÷ 104,508 = 7.99%

6 g = RR × ROIC
= 0.55 × 17.23% = 9.41%

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

g = 100 × (Total capital, fair value0 × WACC – FCFF0) ÷ (Total capital, fair value0 + FCFF0)
= 100 × (118,672 × 14.35% – 2,134) ÷ (118,672 + 2,134) = 12.33%

where:
Total capital, fair value0 = current fair value of 's debt and equity (USD \$ in millions)
FCFF0 = last year 's free cash flow to the firm (USD \$ in millions)
WACC = weighted average cost of 's capital

### FCFF growth rate (g) forecast

Vale S.A., H-model

Year Value gt
1 g1 9.41%
2 g2 10.14%
3 g3 10.87%
4 g4 11.60%
5 and thereafter g5 12.33%

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)
= 9.41% + (12.33% – 9.41%) × (2 – 1) ÷ (5 – 1) = 10.14%

g2 = g1 + (g5g1) × (3 – 1) ÷ (5 – 1)
= 9.41% + (12.33% – 9.41%) × (3 – 1) ÷ (5 – 1) = 10.87%

g2 = g1 + (g5g1) × (4 – 1) ÷ (5 – 1)
= 9.41% + (12.33% – 9.41%) × (4 – 1) ÷ (5 – 1) = 11.60%