FCF and Economic Profit Valuation - … FCF and Economic Profit Valuation Greg Collett [email protected] +44 207 88 33 643 David Holland [email protected]

CONFIDENTIAL

FCF and Economic Profit

ValuationGreg [email protected]+44 207 88 33 643

David [email protected]+44 207 88 33 645

CONFIDENTIAL

1

What Is Free Cash Flow?

Free cash flow is the cash flow available to all providers of Capital. It is the after-tax operating profit (NOPAT) of the firm less any new investment in operating assets. This measure does not consider historic investments.

FCF calculation:

IncomeStatement

BalanceSheet T -1

Balance Sheet T

NOPAT ∆ Invested Capital FCF

FCF = NOPAT � Change in Invested Capital

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2

Calculation of NOPAT, ∆ Invested Capital and FCF

This simple example illustrates how the components of free cash flow are calculated.

Balance SheetDec-07 Dec-08

Current Assets 20 24Accounts Receivable 15 17Inventory 5 7Other Current Assets 0 0

Income StatementDec-071004060

Dec-08903753

Revenue- Cost of Goods Sold

= Gross Profit

- Operating Expenses= Operating Profit

5010

458

- Cash Tax @ 30% 3 2.4

= NOPAT 7 5.6

- Current Liabilities 14 12Accounts Payable 12 11Tax 2 1Other Current Liabilities 0 0

= Working Capital 6 12

+ Fixed Assets 32 30Invested Capital 38 42

Change in Invested Capital -4

= FCF 11

- Change in Invested Capital -4

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3

What Is Economic Profit?

Traditional accounting measures such as net income ignore the opportunity cost of capital tied up to generate earnings. Economic Profit is a measure of the residual or economic value generated on the Invested Capital.

Cost of Capital

EP

BalanceSheet

Invested Capital

IncomeStatement

NOPAT Capital Charge

Economic Profit calculation:

EP = NOPAT � Capital Charge or EP = (ROIC � DR) x Invested Capital

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4

Calculation of NOPAT and Invested Capital

This simple example illustrates how the components of Economic Profit are calculated.




Dec-08903753

Revenue- Cost of Goods Sold= Gross Profit


5010

458

- Cash Tax @ 30% 3 2.4

= NOPAT 7 5.6



+ Fixed AssetsInvested Capital

3238

3042

Capital Charge @ 10% 4.2

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5

Calculation of Economic Profit

The Economic Profit is calculated according to both methods in this example.




Dec-08903753

Revenue- Cost of Goods Sold= Gross Profit


5010

458

- Cash Tax @ 30% 3 2.4

= NOPAT 7 5.6



+ Fixed Assets 32 30Invested Capital 38 42

Capital Charge @ 10% 4.2

= EP (method 1) 2.8

- Capital Charge @ 10% 4.2

= EP (method 2)

ROIC (NOPAT/Inv Cap) 16.7%- WACC 10%

Spread 6.7%x Invested Capital 42

2.8

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6

Calculating the Value of a Firm

Economic a Profit indicates whether firm is creating economic value or destroying it. The value of a firm is related to the present value of its future EP and FCF streams.

EP Valuation: FCF Valuation:

IncomeStatement

BalanceSheet

IncomeStatement

BalanceSheet T -1

Balance Sheet T

Invested Capital

Cost of Capital

NOPAT Capital Charge NOPAT ∆ Invested Capital FCFEP

Present Value of Future FCF Streams

Corporate Value

Invested Capital

Present Value of Future EP Streams

Corporate Value

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7

Calculating the Terminal Value of a Firm

Also called perpetual, continuing or residual value, the terminal value is an estimate of the firm�s value after its explicit forecast period is complete and typically makes up 75% or more of the corporate value.

Value of Terminal Period

Corporate Value

Value of Forecast Period

Free Cash Flow Terminal Period Valuation

( )∑∞

= +=

1 1ii

i

DRFCF

Value

( ) NiNiii g

ROICgNOPATpitalInvestedCagNOPATFCF −

+− +⎟⎠⎞

⎜⎝⎛ −=×−= 1111 for i > N

( )∑∑∞

+== ++=

11 1Nii

iN

ii DR

FCFFCFValue

Assumes zero FCF growth or fade in ROIC

N = Forecast horizon

i = calculation year

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8

FCF Terminal Period Valuation

Simple analytical solutions can be derived for the valuation of the terminal period if growth and returns are assumed to be constant.

(1) Zero Growth

1+= Ni NOPATFCF for i > N

( )∑∑∞

+=

+

= ++=

1

1

1 1Nii

NN

ii DR

NOPATFCFValue

( )NN

N

ii DRDR

NOPATFCFValue

++= +

=∑ 1

1

1

(2) Constant Growth

( )

( )∑∑∞

+=

−−+

= +

+⎟⎠⎞

⎜⎝⎛ −

+=1

11

1 1

11

Nii

NiNN

ii DR

gROICgNOPAT

FCFValue

( )( )NNN

ii DRgDR

ROICgNOPAT

FCFValue+−

⎟⎠⎞

⎜⎝⎛ −

+=+

=∑ 1

11

1

Trick: use perpetuity model Trick: use Gordon growth model

Assumes all future growth is cost of capital.

Assumes no fade in ROIC or g after forecast.

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9

Tips & Tricks for FCF Valuation (1)

New investments made in the terminal period have a return of ROICI. Investments made during the explicit period maintain their last explicit return ad infinitum.

Growth in this case refers to the growth in NOPAT during the terminal period.

What if returns in the explicit and terminal period are different?

( )( )NI

NN

ii DRgDR

ROICgNOPAT

FCFValue+−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=+

=∑ 1

11

1

Growth in this equation refers to the growth in NOPAT during the terminal period.

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10

Example of FCF Valuation

FCF Example

Initial Growth 20% Value of Explicit FCF -112Terminal Growth 5% Value of Terminal Period 2,028Initial ROIC 15% Total Value 1,916Terminal ROIIC 10%WACC 10%

Year 0 1 2 3 4 5 6Sales 1,000 1,200 1,440 1,728 2,074 2,177NOPAT 150 180 216 259 311 327

Working Capital 500 600 720 864 1,037 1,115 1,196Net Fixed Assets 500 600 720 864 1,037 1,115 1,196Invested Capital 1,000 1,200 1,440 1,728 2,074 2,229 2,392

0.1NOPAT 150 180 216 259 311 327- Investment 200 240 288 346 156 163FCF -50 -60 -72 -86 156 163

MetricsFCF -50 -60 -72 -86 156 163EP 50 60 72 86 104 104ROIC 15% 15% 15% 15% 15% 15%NOPAT Growth 20% 20% 20% 20% 5%Invested Capital Growth 20% 20% 20% 20% 8% 7%Investment Growth 20% 20% 20% -55% 5%

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11


The use of NOPAT in the Gordon growth model is an aggressive assumption which implies incremental investments have an infinite return. It is a common mistake that can cause an enormous error in the valuation.

Can the terminal period be valued with NOPAT in the Gordon growth model?

( )( )NN

N

ii DRgDR

NOPATFCFValue

+−+= +

=∑ 1

1

1

Overestimates the value by the amount:

( )( )NI

N

DRgDRROICgNOPAT

Error+−

⎟⎟⎠

⎞⎜⎜⎝

⎛

=+

1

1

This is the change in invested capital and is not taken in to account in the equation above. NOPAT cannot grow without CAPEX!!

FCF = NOPAT � Change in Invested Capital ≠ NOPAT

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12


Growth doesn�t matter when ROICI = DR ! Simply use the perpetuity equation.

The NOPAT perpetuity equation is correct when growth =0 or ROIC = DR.

( )( ) ( )∑∑=

++

= ++=

+−

⎟⎠⎞

⎜⎝⎛ −

+=N

iN

NiN

NN

ii DRDR

NOPATFCF

DRgDRDRgNOPAT

FCFValue1

11

1 11

1

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13

FCF Sensitivity Model � terminal value considerations1 2 3 4 5 6

ROIC 15% 15% 15% 15% 15% 15%Invested Capital Growth 10% 10% 10% 10% 10% 3%Long Run Growth 3%NOPAT 150 165 182 200 220 242Invested Capital 1,000 1,100 1,210 1,331 1,464 1,611 1,659CAPEX 110 121 133 146 48

FCF 50 55 61 67 73 193PV Factor 10% 0.91 0.83 0.75 0.68 0.62 0.56PV FCF 45 45 45 45 45 109

Valuations T6 Value PV EVForecast 227T6NOPAT/WACC 2,416 1,500 1,727T6NOPAT/(WACC-g) 3,451 2,143 2,370T5FCF/WACC 732 455 682T5FCF*(1+g)/(WACC-g) 1,077 669 896T6FCF/(WACC-g) 2,761 1,714 1,942Fade Valuation 1,325 1,552

FCF = ICo x (ROIC � g)

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14

Calculating the Terminal Value of a Firm

Also called perpetual, continuing or residual value, the terminal value is an estimate of the firm�s value after its forecasted growth phase is complete.

Value of Terminal Period

Corporate Value

Value of Forecast Period

Economic Profit Terminal Period Valuation

( )∑∞

= ++=

10 1i

ii

DREP

pitalInvestedCaValue

( ) ( ) 1

11 1 −−+− +=×−= Ni

Nii gEPpitalInvestedCaDRROICEP for i > N

( )∑∑∞

+== +++=

110 1Ni

ii

N

ii DR

EPEPpitalInvestedCaValue

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15

EP Terminal Period Valuation

Simple analytical solutions can be derived for the valuation of the terminal period if growth and returns are assumed to be constant.

Trick: use perpetuity model(1) Zero Growth

( ) NN pitalInvestedCaDRROICEP ×−=+1

( )( )∑∑

∞

+== +

×−++=

110 1Ni

iN

N

ii DR

pitalInvestedCaDRROICEPpitalInvestedCaValue

( )

( )NN

N

ii DRDR


+

×−++= ∑

= 110

Dividing by the discount rate creates the perpetuity

Trick: use Gordon growth model(2) Constant Growth

( ) ( )( )∑∑

∞

+=

−−

= +

+×−++=

1

1

10 1

1Ni

i

NiN

N

ii DR

gpitalInvestedCaDRROICEPpitalInvestedCaValue

( )

( )( )NN

N

ii DRgDR


+−

×−++= ∑

= 110

Grow the EP by one year and then divide by (DR-g)

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16

Tips & Tricks for EP Valuation (1)

New investments made in the terminal period have a return of ROICI. Investments made during the explicit period maintain their last explicit return ad infinitum. Growth in this case refers to the growth in NOPAT during the terminal period.

What if returns in the explicit and terminal period are different?

( )

( )

( )( )NI

IN

NN

N

ii DRgDRDR

DRROICROICgNOPAT

DRDREP

EPInvCapValue+−

−⎟⎟⎠

⎞⎜⎜⎝

⎛

++

++=+

+

=∑ 11

11

10

Growth in this equation refers to the growth in NOPAT during the terminal period.

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17

Example of EP Valuation

EP Example

Initial Growth 20% Invested Capital 1,000Terminal Growth 5% Value of Explicit EP 273Initial ROIC 15% Value of Terminal Period 644Terminal ROIIC 10% Total Value 1,916WACC 10%

Year 0 1 2 3 4 5 6Sales 1,000 1,200 1,440 1,728 2,074 2,177NOPAT 150 180 216 259 311 327

Working Capital 500 600 720 864 1,037 1,115 1,196Net Fixed Assets 500 600 720 864 1,037 1,115 1,196Invested Capital 1,000 1,200 1,440 1,728 2,074 2,229 2,392

0.1NOPAT 150 180 216 259 311 327- Capital Charge 100 120 144 173 207 223EP 50 60 72 86 104 104

MetricsFCF -50 -60 -72 -86 156 163EP 50 60 72 86 104 104ROIC 15% 15% 15% 15% 15% 15%NOPAT Growth 20% 20% 20% 20% 5%Invested Capital Growth 20% 20% 20% 20% 8% 7%Investment Growth 20% 20% 20% 20% 8%

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18

Tips & Tricks for EP Valuation (2)

Fading the economic profit to zero is an excellent application of the Gordon growth model.

Can the value of a fading EP stream be valued?

( )fEPEP ii −=+ 11 for i > N

( )( )

( )( )

( )( )

( )( )( )∑

∞

=

−

+

−++++

+−

=+

−+

+

−+

+

−+

+=

1

1

1

11

3

21

211

11

11

11

11

1 ii

i

Ni

iNNNN

DRfEP

DRfEP

DRfEP

DRfEP

DREP

TV K

The equation has the same form as the Gordon growth model:

( )fDREP

TV N

+= +1

( )( )NN

N

ii DRfDR

EPEPpitalInvestedCaValue

++++= +

=∑ 1

1

10

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19

Which Metric Is the Better Measure of Value?

Economic Profit is a useful measure for understanding a company�s performance in any single year, while Free Cash Flow is not. Economic profit translates the value drivers ROIC and growth into a single figure.

PV of FCF and Growth Trajectory

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

1 5 9 13 17 21 25 29 33 37

Year

PV o

f FC

F

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

Gro

wth PV of FCF

Growth

PV of EP and ROIC Trajectory

0

20

40

60

80

100

120

140

160

180

1 5 9 13 17 21 25 29 33 37

YearPV

of E

P

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

RO

IC PV of EPROIC

FCF Analysis� FCF < 0 when g > ROIC� Negative FCF is not necessarily bad

EP Analysis� EP > 0 when ROIC > DR� Positive EP indicates wealth creation

Assumptions: Explicit growth of 20%; explicit ROIC of 14%; LT growth of 5%; DR of 10%; and fade rate of 10%.

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20

DCF Valuation � Common Errors

Forecast horizon too short � terminal value too high (>90%)

Uneconomic continuing value � no reversion to mean returns

Cost of capital � focus on value drivers instead

Mismatch between earnings and investment growth � Capex vs earnings

Improper reflection of other liabilities - pensions

Premium to public market value � increasing value to private buyer

Double counting � using new debt and acquisition

Scenarios � too few hence too much reliance on a single point valuation

Source: Mauboussin on Strategy, Legg Mason Capital Management, March 2006. http://www.lmcm.com/pdf/CommonErrors.pdf

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21

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Documents

FCF and Economic Profit Valuation - … FCF and Economic Profit Valuation Greg Collett [email protected] +44 207 88 33 643 David Holland [email protected]