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Spring 2009
NBA 5060 Lecture 10 – Implementing Valuation
1. Implementing valuation 2. Short-cut valuation using residual income model
For next time, read SBW chapter 14.
Lecture 10
Page 1 of 11
Implementing Valuation In theory, value depends on payoffs over an infinite forecast horizon. To simplify matters, however, the forecasting period is limited to a finite number of years, after which a simplifying assumption is used. In particular, if we forecast until the firm reaches ‘steady state’, then a perpetuity, or a perpetuity with a constant growth rate can be used (this is the familiar Gordon growth model):
Terminal Value =
DividendsT re − g
To get the present value, it needs to be discounted to today by a factor of (1+re)-(T-1)
Note: to use this formula, the terminal value estimate has to be a perpetuity or have a constant growth rate.
Lecture 10
Page 2 of 11
Implementing Valuation With the steady-state assumption and the perpetuity with growth formula, equity value can be expressed as: FCFE Valuation: T −1
Equity Value = ∑ t =1
FCFEt (1 + re ) t
+
FCFET
( re − g )(1 + re ) T −1
Residual Income Valuation: T −1 NI
Equity Value = BVE0 + ∑
- re BVEt −1
t
(1 + re ) t
t =1
+
NI T − re BVET −1
(re − g )(1 + re ) T −1
Residual Income Valuation based on ROE: T -1
Equity Value = BVE0 + ∑
t =1
Lecture 10
ROEt - re (1 + re )
t
BVEt −1 +
ROET - re (re − g )(1 + re )
T −1
BVET −1
Page 3 of 11
What values do we assign to the parameters? (1) Explicitly forecast FCFE, RI, and BVE using pro-forma financial statements. (2) Terminal Growth Rate (g) represent growth in abnormal earnings in perpetuity. Growth in GDP is a good assumption for g because it assumes that, in steady state, the company’s growth keeps pace with growth in the economy. At a maximum, g cannot exceed the GDP growth rate or else the firm would subsume the entire economy. Note that the forecasted financial statements in year T should equal the projected accounts in year 10, growing at your projected terminal growth rate (g) – see CBRL spreadsheet. (3) Cost of Equity Capital (re): This parameter is the source of ongoing debate in Finance. Alternatives include: (a) DCF approach or implied cost of capital – uses internal rate of return. (b) Asset Pricing Approach – e.g. Capital Asset Pricing Model. Implementing the CAPM:
re = r f + β ( E (rm ) − r f ) The risk free interest rate. Use long term US bond yield for long horizon projects
The systematic risk of a stock, estimated using time series regressions
The expected risk premium for the market index over long-term bonds.
rf and βcan be taken straight from Yahoo. Use the 10-year U.S. Treasury Bond for rf. As for the risk premium, 5.77% is the arithmetic mean from 1968-2007, so use this amount unless you have reason to adjust otherwise. You can also adjust betas for mean reversion as follows: adj
Lecture 10
= 1/3
+ 2/3*
historical
Page 4 of 11
e.g. CBRL Cost of Equity Capital: Unadjusted:
re = 2.70%+ 1.80*(5.77%) = 13.09%
Adjusted:
re = 2.70%+ 1.53*(5.77%) = 11.55%
10-year T-Bond in Feb. 2009
Lecture 10
Avg. equity premium, 1968-2007
Page 5 of 11
Valuation Date Adjustments:
All forecasts using pro-formas are inherently treated as of the date of the previous fiscal year end (i.e., the balance sheet date). Hence, adjustments need to be made to bring value current to today’s date. General Technique: 1. Estimate days outstanding from the valuation date and the last fiscal year end.
2. Adjust your final value to reflect the passage of time since the prior fiscal year end. Current value = Estimated value*(1+re)(months since last fiscal year end / 12) or Current value = Estimated value*(1+re)(days since last fiscal year end / 365) For example, if you are 9 months into the year (i.e., September 30 for a calendar year company), have a 10% cost of capital, and derived a value of $30 as of the last fiscal year end, your value today would be: $30*(1.10)9/12 = $32.22
Lecture 10
Page 6 of 11
Example of Final Valuation Parameters and Calculations Valuation Assumptions Long-run growth rate Beta (Adjusted) Risk-free rate Equity Risk Premium Cost of Equity Balance Sheet Date Valuation Date Days Since BS Date Valuation Date Adjustment Shares Outstanding (MM)
FCFE I Net Income Less: Increase in Equity FCFE PV of FCFE - Finite PV of FCFE - Terminal Equity Value - BS Date Valuation Date Adjustment Equity Value - Current Date Shares Outstanding Equity Value per Share
RIM I Net Income re Beg. BVE Residual Income Beg. BVE PV of RI - Finite PV of RI - Terminal Equity Value - BS Date Valuation Date Adjustment Equity Value - Current Date Shares Outstanding Equity Value per Share
Lecture 10
4.10% 1.53 2.70% 5.77% 11.55% 7/31/2008 2/17/2009 201 106.2% 22.39
2009 48.7 23.8 24.9
2010 50.4 76.7 -26.3
2011 58.9 75.7 -16.9
2012 67.5 76.8 -9.3
2013 75.7 75.2 0.5
2014 84.1 74.3 9.8
2015 92.3 70.0 22.2
2016 100.1 72.7 27.4
2017 107.4 74.7 32.7
2018 115.4 75.3 40.0
Terminal 120.1 32.3 87.8
2009 48.7 11.5% 92.8 38.0
2010 50.4 11.5% 116.6 36.9
2011 58.9 11.5% 193.3 36.6
2012 67.5 11.5% 269.0 36.4
2013 75.7 11.5% 345.8 35.7
2014 84.1 11.5% 421.0 35.5
2015 92.3 11.5% 495.3 35.1
2016 100.1 11.5% 565.3 34.8
2017 107.4 11.5% 638.0 33.8
2018 115.4 11.5% 712.8 33.1
Terminal 120.1 11.5% 788.1 29.1
$35.8 $395.2 $431.0 106.2% $457.75 22.39 $20.44
$92.8 $207.3 $131.0 $431.0 106.2% $457.75 22.39 $20.44
Page 7 of 11
Lecture 10
Page 8 of 11
Shortcut Valuation using the Residual Income Model Basic concept uses analyst forecasts of earnings to derive a quick residual income valuation that does not require forecasting pro-forma financial statements. Basic Idea: T -1
ROEt - re
t =1
(1 + re ) t
Equity Value = BVE0 + ∑
BVEt −1 +
ROET - re (re − g )(1 + re ) T −1
BVET −1
1. Use current book value and forecasts of future earnings, earnings growth rates, and dividend payout ratios (think of as 1 – plowback rate) to compute future ROEs. 2. Use this stream of future ROEs to compute the finite period valuation 3. Use industry median ROE to get the terminal value ROET 4. Compute an Equity Value. Can use this to determine intrinsic value estimate, given the cost of capital and other parameters. Alternatively, this framework can be used to back out the cost of capital given the forecasts and the current market price (uses excel’s goal seek command).
Lecture 10
Page 9 of 11
This Year (July 09)
Cracker Barrel
Next Year (July 10)
$2.65
$2.84
Growth for Years 3 to 5 11.03 %
Required Inputs to the shortcut valuation model: EPS Forecasts– get these from any commercial service collecting analyst forecasts. You need FY1, FY2, and Long-term growth forecasts. Book value per share – As of the last fiscal year end. Discount rate – cost of capital as computed elsewhere Dividend Payout ratio– the portion of earnings expected to be paid out as net dividends (including repurchases). This will impact the future book value, and hence the abnormal ROE computation. Current Fiscal Month – the adjustment to get value as of today Target ROE– the long-run ROE of the firm. The industry average is a good starting point. A conservative approach is to set the target ROE to the cost of equity capital – this implies no abnormal earnings beyond the terminal year.
Lecture 10
Page 10 of 11
Shortcut Residual Income Model for CBRL Based on Analysts Forecasts Cracker Barrel as of Feb. 2009 PARAMETERS EPS Forecasts Book value/share (last fye) Discount Rate Payout Ratio Next Fsc Year end Current Fsc Mth (1 to 12) Terminal Growth Target ROE (industry avg.)
FY1 2.65 4.14 11.55% 60.0% 2009 7 4.1% 15.0%
FY2 2.84
Ltg 11.03%
2011 0.1103 3.15 6.34 0.497 0.382 0.115 1.388 1.74
Implied price (date adjusted)
23.25
Year Long-term EPS Growth Rate (Ltg) Forecasted EPS Beg. of year BV/Shr Implied ROE Abnormal ROE required rate (r) discount rate PV of future Residual Income
2009
2010
2.65 4.14 0.640 0.524 0.115 1.115 1.95
2.84 5.20 0.546 0.430 0.115 1.244 1.80
PV of Finite Residual Income PV of Terminal Value RI Beg. of year BV/Shr Implied Price
14.83 2.84 4.14 21.81
Lecture 10
Model 1: 12-year forecasting horizon (T=12). and a 5-year growth period.
2012 0.1103 3.50 7.60 0.461 0.345 0.115 1.548 1.69
2013 0.1103 3.89 9.00 0.432 0.316 0.115 1.727 1.65
2014
2015
2016
2017
2018
2019
2020
4.13 10.56 0.392 0.276 0.115 1.926 1.51
4.29 12.21 0.351 0.236 0.115 2.149 1.34
4.33 13.92 0.311 0.196 0.115 2.397 1.14
4.24 15.66 0.271 0.155 0.115 2.674 0.91
4.00 17.35 0.231 0.115 0.115 2.983 0.67
3.61 18.95 0.190 0.075 0.115 3.327 0.43
3.06 20.40 0.150 0.035 0.115 3.711
Page 11 of 11
NBA 5060 Lecture 10 – Implementing Valuation
1. Implementing valuation 2. Short-cut valuation using residual income model
For next time, read SBW chapter 14.
Lecture 10
Page 1 of 11
Implementing Valuation In theory, value depends on payoffs over an infinite forecast horizon. To simplify matters, however, the forecasting period is limited to a finite number of years, after which a simplifying assumption is used. In particular, if we forecast until the firm reaches ‘steady state’, then a perpetuity, or a perpetuity with a constant growth rate can be used (this is the familiar Gordon growth model):
Terminal Value =
DividendsT re − g
To get the present value, it needs to be discounted to today by a factor of (1+re)-(T-1)
Note: to use this formula, the terminal value estimate has to be a perpetuity or have a constant growth rate.
Lecture 10
Page 2 of 11
Implementing Valuation With the steady-state assumption and the perpetuity with growth formula, equity value can be expressed as: FCFE Valuation: T −1
Equity Value = ∑ t =1
FCFEt (1 + re ) t
+
FCFET
( re − g )(1 + re ) T −1
Residual Income Valuation: T −1 NI
Equity Value = BVE0 + ∑
- re BVEt −1
t
(1 + re ) t
t =1
+
NI T − re BVET −1
(re − g )(1 + re ) T −1
Residual Income Valuation based on ROE: T -1
Equity Value = BVE0 + ∑
t =1
Lecture 10
ROEt - re (1 + re )
t
BVEt −1 +
ROET - re (re − g )(1 + re )
T −1
BVET −1
Page 3 of 11
What values do we assign to the parameters? (1) Explicitly forecast FCFE, RI, and BVE using pro-forma financial statements. (2) Terminal Growth Rate (g) represent growth in abnormal earnings in perpetuity. Growth in GDP is a good assumption for g because it assumes that, in steady state, the company’s growth keeps pace with growth in the economy. At a maximum, g cannot exceed the GDP growth rate or else the firm would subsume the entire economy. Note that the forecasted financial statements in year T should equal the projected accounts in year 10, growing at your projected terminal growth rate (g) – see CBRL spreadsheet. (3) Cost of Equity Capital (re): This parameter is the source of ongoing debate in Finance. Alternatives include: (a) DCF approach or implied cost of capital – uses internal rate of return. (b) Asset Pricing Approach – e.g. Capital Asset Pricing Model. Implementing the CAPM:
re = r f + β ( E (rm ) − r f ) The risk free interest rate. Use long term US bond yield for long horizon projects
The systematic risk of a stock, estimated using time series regressions
The expected risk premium for the market index over long-term bonds.
rf and βcan be taken straight from Yahoo. Use the 10-year U.S. Treasury Bond for rf. As for the risk premium, 5.77% is the arithmetic mean from 1968-2007, so use this amount unless you have reason to adjust otherwise. You can also adjust betas for mean reversion as follows: adj
Lecture 10
= 1/3
+ 2/3*
historical
Page 4 of 11
e.g. CBRL Cost of Equity Capital: Unadjusted:
re = 2.70%+ 1.80*(5.77%) = 13.09%
Adjusted:
re = 2.70%+ 1.53*(5.77%) = 11.55%
10-year T-Bond in Feb. 2009
Lecture 10
Avg. equity premium, 1968-2007
Page 5 of 11
Valuation Date Adjustments:
All forecasts using pro-formas are inherently treated as of the date of the previous fiscal year end (i.e., the balance sheet date). Hence, adjustments need to be made to bring value current to today’s date. General Technique: 1. Estimate days outstanding from the valuation date and the last fiscal year end.
2. Adjust your final value to reflect the passage of time since the prior fiscal year end. Current value = Estimated value*(1+re)(months since last fiscal year end / 12) or Current value = Estimated value*(1+re)(days since last fiscal year end / 365) For example, if you are 9 months into the year (i.e., September 30 for a calendar year company), have a 10% cost of capital, and derived a value of $30 as of the last fiscal year end, your value today would be: $30*(1.10)9/12 = $32.22
Lecture 10
Page 6 of 11
Example of Final Valuation Parameters and Calculations Valuation Assumptions Long-run growth rate Beta (Adjusted) Risk-free rate Equity Risk Premium Cost of Equity Balance Sheet Date Valuation Date Days Since BS Date Valuation Date Adjustment Shares Outstanding (MM)
FCFE I Net Income Less: Increase in Equity FCFE PV of FCFE - Finite PV of FCFE - Terminal Equity Value - BS Date Valuation Date Adjustment Equity Value - Current Date Shares Outstanding Equity Value per Share
RIM I Net Income re Beg. BVE Residual Income Beg. BVE PV of RI - Finite PV of RI - Terminal Equity Value - BS Date Valuation Date Adjustment Equity Value - Current Date Shares Outstanding Equity Value per Share
Lecture 10
4.10% 1.53 2.70% 5.77% 11.55% 7/31/2008 2/17/2009 201 106.2% 22.39
2009 48.7 23.8 24.9
2010 50.4 76.7 -26.3
2011 58.9 75.7 -16.9
2012 67.5 76.8 -9.3
2013 75.7 75.2 0.5
2014 84.1 74.3 9.8
2015 92.3 70.0 22.2
2016 100.1 72.7 27.4
2017 107.4 74.7 32.7
2018 115.4 75.3 40.0
Terminal 120.1 32.3 87.8
2009 48.7 11.5% 92.8 38.0
2010 50.4 11.5% 116.6 36.9
2011 58.9 11.5% 193.3 36.6
2012 67.5 11.5% 269.0 36.4
2013 75.7 11.5% 345.8 35.7
2014 84.1 11.5% 421.0 35.5
2015 92.3 11.5% 495.3 35.1
2016 100.1 11.5% 565.3 34.8
2017 107.4 11.5% 638.0 33.8
2018 115.4 11.5% 712.8 33.1
Terminal 120.1 11.5% 788.1 29.1
$35.8 $395.2 $431.0 106.2% $457.75 22.39 $20.44
$92.8 $207.3 $131.0 $431.0 106.2% $457.75 22.39 $20.44
Page 7 of 11
Lecture 10
Page 8 of 11
Shortcut Valuation using the Residual Income Model Basic concept uses analyst forecasts of earnings to derive a quick residual income valuation that does not require forecasting pro-forma financial statements. Basic Idea: T -1
ROEt - re
t =1
(1 + re ) t
Equity Value = BVE0 + ∑
BVEt −1 +
ROET - re (re − g )(1 + re ) T −1
BVET −1
1. Use current book value and forecasts of future earnings, earnings growth rates, and dividend payout ratios (think of as 1 – plowback rate) to compute future ROEs. 2. Use this stream of future ROEs to compute the finite period valuation 3. Use industry median ROE to get the terminal value ROET 4. Compute an Equity Value. Can use this to determine intrinsic value estimate, given the cost of capital and other parameters. Alternatively, this framework can be used to back out the cost of capital given the forecasts and the current market price (uses excel’s goal seek command).
Lecture 10
Page 9 of 11
This Year (July 09)
Cracker Barrel
Next Year (July 10)
$2.65
$2.84
Growth for Years 3 to 5 11.03 %
Required Inputs to the shortcut valuation model: EPS Forecasts– get these from any commercial service collecting analyst forecasts. You need FY1, FY2, and Long-term growth forecasts. Book value per share – As of the last fiscal year end. Discount rate – cost of capital as computed elsewhere Dividend Payout ratio– the portion of earnings expected to be paid out as net dividends (including repurchases). This will impact the future book value, and hence the abnormal ROE computation. Current Fiscal Month – the adjustment to get value as of today Target ROE– the long-run ROE of the firm. The industry average is a good starting point. A conservative approach is to set the target ROE to the cost of equity capital – this implies no abnormal earnings beyond the terminal year.
Lecture 10
Page 10 of 11
Shortcut Residual Income Model for CBRL Based on Analysts Forecasts Cracker Barrel as of Feb. 2009 PARAMETERS EPS Forecasts Book value/share (last fye) Discount Rate Payout Ratio Next Fsc Year end Current Fsc Mth (1 to 12) Terminal Growth Target ROE (industry avg.)
FY1 2.65 4.14 11.55% 60.0% 2009 7 4.1% 15.0%
FY2 2.84
Ltg 11.03%
2011 0.1103 3.15 6.34 0.497 0.382 0.115 1.388 1.74
Implied price (date adjusted)
23.25
Year Long-term EPS Growth Rate (Ltg) Forecasted EPS Beg. of year BV/Shr Implied ROE Abnormal ROE required rate (r) discount rate PV of future Residual Income
2009
2010
2.65 4.14 0.640 0.524 0.115 1.115 1.95
2.84 5.20 0.546 0.430 0.115 1.244 1.80
PV of Finite Residual Income PV of Terminal Value RI Beg. of year BV/Shr Implied Price
14.83 2.84 4.14 21.81
Lecture 10
Model 1: 12-year forecasting horizon (T=12). and a 5-year growth period.
2012 0.1103 3.50 7.60 0.461 0.345 0.115 1.548 1.69
2013 0.1103 3.89 9.00 0.432 0.316 0.115 1.727 1.65
2014
2015
2016
2017
2018
2019
2020
4.13 10.56 0.392 0.276 0.115 1.926 1.51
4.29 12.21 0.351 0.236 0.115 2.149 1.34
4.33 13.92 0.311 0.196 0.115 2.397 1.14
4.24 15.66 0.271 0.155 0.115 2.674 0.91
4.00 17.35 0.231 0.115 0.115 2.983 0.67
3.61 18.95 0.190 0.075 0.115 3.327 0.43
3.06 20.40 0.150 0.035 0.115 3.711
Page 11 of 11
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