CONFIDENTIAL
FCF and Economic Profit
Valuation
Greg Collett
[email protected]
+44 207 88 33 643
David Holland
[email protected]
+44 207 88 33 645
CONFIDENTIAL
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:
Income
Statement
Balance
Sheet T -1
Balance
Sheet T
NOPAT
∆ Invested Capital
FCF = NOPAT – Change in Invested Capital
1
FCF
CONFIDENTIAL
Calculation of NOPAT, ∆ Invested Capital and FCF
This simple example illustrates how the components of free cash flow are calculated.
Balance Sheet
Income Statement
Dec-07
100
40
60
Dec-08
90
37
53
50
10
45
8
- Cash Tax @ 30%
3
2.4
= NOPAT
7
5.6
Revenue
- Cost of Goods Sold
= Gross Profit
- Operating Expenses
= Operating Profit
- Change in Invested Capital
= FCF
Current Assets
Accounts Receivable
Inventory
Other Current Assets
- Current Liabilities
Accounts Payable
Tax
Other Current Liabilities
-4
= Working Capital
11
+ Fixed Assets
Invested Capital
Change in Invested Capital
2
Dec-07
20
15
5
0
Dec-08
24
17
7
0
14
12
2
0
12
11
1
0
6
12
32
38
30
42
-4
CONFIDENTIAL
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.
Economic Profit calculation:
Income
Statement
Balance
Sheet
Invested Capital
Cost of Capital
NOPAT
EP = NOPAT – Capital Charge
Capital Charge
or
EP
EP = (ROIC – DR) x Invested Capital
3
CONFIDENTIAL
Calculation of NOPAT and Invested Capital
This simple example illustrates how the components of Economic Profit are calculated.
Balance Sheet
Income Statement
Revenue
- Cost of Goods Sold
= Gross Profit
Dec-07
100
40
60
Dec-08
90
37
53
- Operating Expenses
= Operating Profit
50
10
45
8
- Cash Tax @ 30%
3
2.4
= NOPAT
7
5.6
Dec-07
20
15
5
0
Dec-08
24
17
7
0
14
12
2
0
12
11
1
0
6
12
+ Fixed Assets
Invested Capital
32
38
30
42
Capital Charge @ 10%
4.2
Current Assets
Accounts Receivable
Inventory
Other Current Assets
- Current Liabilities
Accounts Payable
Tax
Other Current Liabilities
= Working Capital
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CONFIDENTIAL
Calculation of Economic Profit
The Economic Profit is calculated according to both methods in this example.
Balance Sheet
Income Statement
Dec-07
20
15
5
0
Dec-08
24
17
7
0
14
12
2
0
12
11
1
0
6
12
+ Fixed Assets
Invested Capital
32
38
30
42
Capital Charge @ 10%
4.2
Revenue
- Cost of Goods Sold
= Gross Profit
Dec-07
100
40
60
Dec-08
90
37
53
- Operating Expenses
= Operating Profit
50
10
45
8
- Cash Tax @ 30%
3
2.4
= NOPAT
7
5.6
- Capital Charge @ 10%
4.2
= Working Capital
= EP (method 1)
2.8
ROIC (NOPAT/Inv Cap)
- WACC
Current Assets
Accounts Receivable
Inventory
Other Current Assets
- Current Liabilities
Accounts Payable
Tax
Other Current Liabilities
16.7%
10%
Spread
x Invested Capital
6.7%
42
= EP (method 2)
2.8
5
CONFIDENTIAL
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:
Income
Statement
FCF Valuation:
Balance
Sheet
Income
Statement
Balance
Sheet T -1
Balance
Sheet T
Invested Capital
Cost of Capital
NOPAT
Corporate
Value
Capital Charge
Invested
Capital
NOPAT
EP
Present Value of
Future EP Streams
Corporate
Value
6
∆ Invested Capital
FCF
Present Value of Future FCF
Streams
CONFIDENTIAL
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.
Corporate
Value
Value of Forecast
Period
Value of Terminal
Period
Free Cash Flow Terminal Period Valuation
∞
Value = ∑
i =1
N = Forecast horizon
FCFi
i = calculation year
(1 + DR )i
g ⎞
⎛
i−N
FCFi = NOPATi − g × InvestedCapital i −1 = NOPATN +1 ⎜1 −
⎟(1 + g ) for i > N
⎝ ROIC ⎠
N
Value = ∑ FCFi +
i =1
∞
FCFi
∑ (1 + DR )
i = N +1
i
Assumes zero FCF growth or fade in ROIC
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CONFIDENTIAL
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
(2) Constant Growth
FCFi = NOPATN +1 for i > N
g ⎞
⎛
i − N −1
(
)
−
NOPAT
1
1
+
g
⎜
⎟
+
N
1
N
∞
⎝ ROIC ⎠
Value = ∑ FCFi + ∑
(1 + DR )i
i =1
i = N +1
N
Value = ∑ FCFi +
i =1
N
Value = ∑ FCFi +
i =1
∞
NOPATN +1
∑ (1 + DR )
i
i = N +1
NOPATN +1
DR(1 + DR )
N
Trick: use perpetuity model
g ⎞
⎛
NOPAT
−
1
⎟
⎜
+
1
N
N
ROIC ⎠
⎝
Value = ∑ FCFi +
(DR − g )(1 + DR )N
i =1
Trick: use Gordon growth model
Assumes all future growth is cost of
capital.
Assumes no fade in ROIC or g after
forecast.
8
CONFIDENTIAL
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?
⎛
g
NOPATN +1 ⎜⎜1 −
N
⎝ ROIC I
Value = ∑ FCFi +
(DR − g )(1 + DR )N
i =1
⎞
⎟⎟
⎠
Growth in this equation refers to the growth in NOPAT during the terminal period.
9
CONFIDENTIAL
Example of FCF Valuation
FCF Example
Initial Growth
Terminal Growth
Initial ROIC
Terminal ROIIC
WACC
Year
Sales
NOPAT
Working Capital
Net Fixed Assets
Invested Capital
NOPAT
- Investment
FCF
Metrics
FCF
EP
ROIC
NOPAT Growth
Invested Capital Growth
Investment Growth
20%
5%
15%
10%
10%
Value of Explicit FCF
Value of Terminal Period
Total Value
-112
2,028
1,916
0
1
1,000
150
2
1,200
180
3
1,440
216
4
1,728
259
5
2,074
311
6
2,177
327
500
500
1,000
600
600
1,200
720
720
1,440
864
864
1,728
1,037
1,037
2,074
1,115
1,115
2,229
150
200
-50
180
240
-60
216
288
-72
259
346
-86
311
156
156
1,196
1,196
2,392
0.1
327
163
163
-50
50
15%
-60
60
15%
20%
20%
20%
-72
72
15%
20%
20%
20%
-86
86
15%
20%
20%
20%
156
104
15%
20%
8%
-55%
163
104
15%
5%
7%
5%
20%
10
CONFIDENTIAL
Tips & Tricks for FCF Valuation (2)
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?
N
Value = ∑ FCFi +
i =1
NOPATN +1
(DR − g )(1 + DR )N
Overestimates the value by the amount:
⎛ g ⎞
⎟⎟
NOPATN +1 ⎜⎜
⎝ ROIC I ⎠
Error =
(DR − g )(1 + DR )N
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
11
CONFIDENTIAL
Tips & Tricks for FCF Valuation (3)
Growth doesn’t matter when ROICI = DR ! Simply use the perpetuity equation.
The NOPAT perpetuity equation is correct when growth =0 or ROIC = DR.
g ⎞
⎛
NOPAT
1
−
⎟ N
⎜
N +1
N
DR
⎠ = FCF + NOPATN +1
⎝
Value = ∑ FCFi +
i
N
(DR − g )(1 + DR )N ∑
DR(1 + DR )
i =1
i =1
12
CONFIDENTIAL
FCF Sensitivity Model – terminal value considerations
ROIC
Inve ste d Ca pita l Grow th
Long Run Grow th
NOPAT
Inve ste d Ca pita l
CAPEX
FCF
PV Fa ctor
PV FCF
Va lua tions
Fore ca st
T6NOPAT/W ACC
T6NOPAT/(W ACC-g)
T5FCF/W ACC
T5FCF*(1+g)/(W ACC-g)
T6FCF/(W ACC-g)
Fa de Va lua tion
1,000
10%
1
15%
10%
3%
150
1,100
2
15%
10%
3
15%
10%
4
15%
10%
5
15%
10%
6
15%
3%
165
1,210
110
182
1,331
121
200
1,464
133
220
1,611
146
242
1,659
48
55
0.83
45
61
0.75
45
67
0.68
45
73
0.62
45
193
0.56
109
PV
227
1,500
2,143
455
669
1,714
1,325
EV
50
0.91
45
T6 Va lue
2,416
3,451
732
1,077
2,761
1,727
2,370
682
896
1,942
1,552
FCF = ICo x (ROIC – g)
13
CONFIDENTIAL
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.
Corporate
Value
Value of Forecast
Period
Value of Terminal
Period
Economic Profit Terminal Period Valuation
∞
Value = InvestedCapital 0 + ∑
i =1
EPi
(1 + DR )i
EPi = (ROIC − DR ) × InvestedCapital i −1 = EPN +1 (1 + g )
i − N −1
N
Value = InvestedCapital 0 + ∑ EPi +
i =1
∞
EPi
∑ (1 + DR )
i = N +1
14
i
for i > N
CONFIDENTIAL
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
EPN +1 = (ROIC − DR )× InvestedCapital N
N
Value = InvestedCapital 0 + ∑ EPi +
i =1
(ROIC − DR ) × InvestedCapital N
(1 + DR )i
i = N +1
∞
∑
(ROIC − DR ) × InvestedCapital N
Value = InvestedCapital 0 + ∑ EPi +
N
DR(1 + DR )
i =1
N
Dividing by the discount rate
creates the perpetuity
Trick: use Gordon growth model
(2) Constant Growth
(ROIC − DR ) × InvestedCapital N (1 + g )i − N −1
Value = InvestedCapital 0 + ∑ EPi + ∑
(1 + DR )i
i = N +1
i =1
N
N
Value = InvestedCapital 0 + ∑ EPi +
i =1
∞
(ROIC − DR ) × InvestedCapital N
(DR − g )(1 + DR )N
15
Grow the EP by one year
and then divide by (DR-g)
CONFIDENTIAL
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?
N
Value = InvCap0 + ∑ EPi +
i =1
EPN +1
DR(1 + DR )
N
⎛ g ⎞
⎟⎟(ROIC I − DR )
NOPATN +1 ⎜⎜
⎝ ROIC I ⎠
+
N
DR(DR − g )(1 + DR )
Growth in this equation refers to the growth in NOPAT during the terminal period.
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CONFIDENTIAL
Example of EP Valuation
EP Example
Initial Growth
Terminal Growth
Initial ROIC
Terminal ROIIC
WACC
Year
Sales
NOPAT
Working Capital
Net Fixed Assets
Invested Capital
NOPAT
- Capital Charge
EP
Metrics
FCF
EP
ROIC
NOPAT Growth
Invested Capital Growth
Investment Growth
20%
5%
15%
10%
10%
Invested Capital
Value of Explicit EP
Value of Terminal Period
Total Value
1,000
273
644
1,916
0
1
1,000
150
2
1,200
180
3
1,440
216
4
1,728
259
5
2,074
311
6
2,177
327
500
500
1,000
600
600
1,200
720
720
1,440
864
864
1,728
1,037
1,037
2,074
1,115
1,115
2,229
150
100
50
180
120
60
216
144
72
259
173
86
311
207
104
1,196
1,196
2,392
0.1
327
223
104
-50
50
15%
-60
60
15%
20%
20%
20%
-72
72
15%
20%
20%
20%
-86
86
15%
20%
20%
20%
156
104
15%
20%
8%
20%
163
104
15%
5%
7%
8%
20%
17
CONFIDENTIAL
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?
EPi +1 = EPi (1 − f ) for i > N
EPN +1
EP (1 − f ) EPN +1 (1 − f )
EPN +1 (1 − f )
TV =
+ N +1
+
+
K
(1 + DR ) (1 + DR )2
(1 + DR )3
(1 + DR )i
2
i −1
The equation has the same form as the Gordon growth model:
TV =
EPN +1
(DR + f )
N
Value = InvestedCapital 0 + ∑ EPi +
i =1
EPN +1
(DR + f )(1 + DR )N
18
i −1
(
1− f )
= EPN +1 ∑
i
i =1 (1 + DR )
∞
CONFIDENTIAL
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.
PVof EPand ROICTrajectory
PVof FCFandGrowthTrajectory
25.0%
200
150
20.0%
16.0%
160
14.0%
140
100
12.0%
0
-50 1
5
9
13
17
21
25
29
33
37
10.0%
-100
PV of FCF
Growth
PV of EP
15.0%
Growth
120
50
PV of FCF
180
10.0%
100
8.0%
80
6.0%
60
4.0%
40
-150
5.0%
-200
-250
2.0%
20
0
-300
0.0%
1
0.0%
Year
5
9
13
17
21
25
29
33
37
Year
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%.
19
ROIC
250
PV of EP
ROIC
CONFIDENTIAL
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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CONFIDENTIAL
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