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This page includes lessons with files and videos that address various corporate finance modelling issues associated with valuation, depreciation, multiples and cost of capital that are not covered in typical corporate finance analysis. There are many websites, videos, books and articles where you can see how to compute valuation using DCF to compute cash flows, but they are often written in a simple manner without: (1) specifying exactly what normalised terminal cash flow means; (2) correcting the value driver formula for inflation and changes in return; (3) deriving the cost of capital in a realistic manner; (4) understanding biases in different financial ratios such as EV/EBITDA; and, (5) making proper adjustments that move from the enterprise value to equity value. One of the most famous valuation books is the text titled: "Valuation: Measuring and Managing the Value of Companies" which has been published numerous times since 1990 and which I refer to as the "McKinsey Book." I hope this is not arrogant, but I think very few of the valuation articles or texts including the McKinsey Book miss crucial conceptual and mechanical issues. These issues include: (1) cost of capital measurement; (2) evaluating surplus capacity risk from earning high returns; (3) carefully structuring financial models with a historic switch; (4) understanding biases from the EV/EBITDA ratio with different asset lives; (5) flaws in the value driver formula EV = (NOPLAT x (1-g/ROIC)/(WACC-g); (6) careful calculation of the ROIC statistic in light of impairments, re-structuring, asset dispositions and other accounting write-offs; and (7) evaluation of deferred taxes valuation of derivatives and other items in the net debt or EV to EBITDA bridge.

To address advanced corporate finance issues, I have arranged the sets of analyses into sets that include: (1) why the value driver formula P/E = (1-g/ROE)/(k-g) or EV = NOPAT x (1-g/ROIC)/(WACC-g) does not work; (2) how to evaluate, understand and derive P/E, P/B and EV/EBITDA multiples and what they really mean in terms of cost of capital and growth; (3) how to adjust terminal value for stable capital expenditures, deferred taxes, working capital and cyclical ROIC to derive stable cash flow in a terminal period; (4) how to evaluate the return on invested capital (ROIC) when there are write-offs, asset sales and other factors; (5) how to segregate operating assets and liabilities versus non-operating assets and liabilities in deriving the bridge between equity value and enterprise value; and (6) how to address cost of capital issues related to risks of non-operating assets, cash balance and the tax effect of interest expense. Each of these subjects along with a whole host cost of capital subjects is addressed with some excel files and also some associated videos. There are a few tricky excel issues but most of the analysis in the files and videos describes the more important issues associated with valuation theory and why typical treatments are over-simplified.

Valuation Philosophy, Shareholder Value Maximisation and Monopoly Profit


When I first read the 1990 version of the Mckinsey Book and was very impressed -- the manner in which valuation boils down to only three factors -- the return on investment, the growth rate and the cost of capital. When I re-read a new version of the book recently, I was far less impressed. The book makes the point that what really matters is earning monopoly profits -- what they re-label shareholder value. General and irritating statements are made about mining, commodity companies and Asian companies not being any good compared U.S. companies that earn really high rates of return on investment. This general stuff about the virtues of earning shareholder value (monopoly profit) is all fine, but the real issue in valuation is forecasting whether the monopoly profits can continue. Any valuation discussion should begin with fundamental idea that valuation can be boiled down to only two things. One is forecasting cash flow. The second is assigning some kind of risk to the forecast. In the context of the McKinsey book, the forecasting issue really involves forecasting return on investment and assessing the future trajectory of returns. These days the real risks are of sudden declines in return due to "Uberisation" or surplus capacity from others entering the industry. For example, when the advantages of growing a company are touted, the risks of growth creating surplus industry capacity are not emphasized.The most important valuation issue in valuation continues be assessment of what will happen to ROIC versus WACC (or what will happen to shareholder value or what will happen to monopoly profits).

Lesson Set 1: Biases and Errors from Value Driver Formula (1-g/Return)/(Cost of Capital - growth)


In the first lesson set I demonstrate that the well known formula used in corporate valuation that some call the value driver formula is not accurate because it does not account from nominal increases in income from inflation and it does not work when the rate of return for existing assets is different from the growth rate in new assets. The valuation book written by consultants and McKinsey and used by many investment bankers emphasize value drivers and asserts that valuation can be boiled down to the following formula:

Value of Equity = Net Income x (1-g/ROE)/(cost of equity - g) and

Enterprise Value = NOPAT x (1-G/ROIC)/(WACC-g).

These two formulas can be used in computing terminal value, in evaluating management, in assessing multiples such as P/E and EV/EBITDA and in directly computing value. When discussing the above two formulas, the set of parameters for equity value can be substituted for enterprise value and vice versa (ROE vs ROIC), (NOPAT versus Net Income), Equity Value versus Enterprise Value), (growth rate in equity investment versus growth rate in net invested capital), (Equity Investment versus Invested Capital) and, (Cost of Equity (k) versus WACC). To illustrate how the value driver formula works, the equity value formula in various forms is derived in the appendix below. These two formulas only work under two extremely restrictive assumptions -- if there is no inflation that changes the value of invested capital over time and if the parameters remain constant. Derivation of the formulas is shown in the appendix below (I sometimes forget some of this derivation so I included for my own reference).

The video, file and powerpoint slides below work through how value drivers of return, growth and risk drive value. The spreadsheet demonstrates how to make a data table with a macro which allows much better presentation of the interactions that drive value. The spreadsheet file also demonstrates how changes in the return influence the value.










I go a little crazy with these two value driver formulas because the equations only accurately measure value in with highly constrained assumptions. Two of the absurd assumptions are that there is no inflation at all and that the growth rate over time is constant. When these assumptions are not made, the formula does not accurately compute value. To demonstrate this I have made a series of videos and worksheets related to the formulas with different alternative calculations. When the value driver formula is adjusted for inflation, the formula becomes:

P/E = [(ROE-g)/(k-g)] * [(1+inflation)/(ROE-inflation)]

P/E 1 = [(ROE-g)/(k-g)] / [ROE-inflation]

The video below on the left addresses the inflation issue associated with the value driver formula. The video is associated with the file available for download below that is named "Inflation and Value Driver Formula." An excerpt from the file shown below this paragraph demonstrates the errors in the value driver formula associated with inflation. The file is built up from a long-term analysis where real and nominal returns, growth rates and the cost of capital remain constant. The first scenario computes the equity value assuming that the nominal returns are realised in cash and used to payout dividends. The next simulation uses real rates rather than nominal rates and results in a different P/E ratio. The third simulation adjusts the nominal value for asset value increases that result from inflation. Inflation in assets does not produce cash to pay dividends but, as it is the base for computing ROE, it increases dividends over time. The excerpt shows that the P/E ratio and the value derived from multiplying the value driver formula by income can understate value by a wide margin.

Excerpt ROIC and Inflation.JPG



The video below on the right addresses biases in the value driver formula when the ROIC on existing net invested capital is different from the ROIC on new invested capital that has been termed RONIC (as if you can really segregate this -- what rubbish). This transition video is associated with the file available for download below that is named "ROIC Transition Problems." An excerpt from this file below demonstrates the errors in the value driver formula from changes in returns. The transition formula file simulates net investment from existing and new assets given a growth rate in net invested capital. The new investment is applied the return on existing assets and the new assets are assumed to earn the RONIC. When this is all put together with depreciation and capital expenditures, the enterprise value can be computed. The valuation from this detailed simulation is compared to the valuation that results from the value driver formula. The spreadsheet demonstrates that when the RONIC is below the ROIC that the value driver formula overstates value by a wide margin. The spreadsheet also shows the value that is generated by the simple constant growth formula with no change in return. If there is no growth, the simple formula produces the same value as the value driver formula. The workbook also includes a simulation where the ROIC is assumed to gradually decrease from current levels to stable levels using interpolation with the INTERPOLATE LOOKUP user defined function.

Exceprt ROIC and Transation.JPG

Videos Associated with Biases and Errors in the Value Driver Formula


Videos that demonstrate biases and errors with the value driver formula are below. The video on the left describes errors associated with inflation. The video on the right demonstrates biases from the value driver formula when the return on new assets is different from the return on existing assets.




I have made a lot of other videos that show how the value driver formula works. The video links are shown below. I am a little worried that some of these videos have poor quality.

Subject

Excel File

Video Link





Demonstrate Mechanics of Value Driver Formula

Value Driver - Equity

https://www.youtube.com/watch?v=WT-8PKtccVI
Use the Value Driver with Stable Rates and Timing Analysis with Switches

DCF Timing

https://www.youtube.com/watch?v=PxkKz3VKjyc
Compute EV from Free Cash Flow in Long-term Model

Value Driver - FCF 1

https://www.youtube.com/watch?v=FWCD5sYZanY
Use the Value Driver with Stable Rates

Value Driver - FCF 2

https://www.youtube.com/watch?v=hYqTH3oud4M
Use of Value Driver with Two Stage Model

Value Driver - FCF 3

https://www.youtube.com/watch?v=hzg8Rb_VcCQ
Value Driver Formula with Interpolation




Problems with Beta and Measuring Cost of Capital

Renewable Stock Price

https://www.youtube.com/watch?v=eTDjLjZo9cE
Use of Market P/E Ratio to Derive Cost of Capital

Economy Wide Cost of Capital

https://www.youtube.com/watch?v=GAolSYR1-pc
DCF Model

Integrated Electricity Model

https://www.youtube.com/watch?v=9rsxSVDbjxE

Files that Demonstrate Biases and Errors in the Value Driver Formula

The files below address the value driver formula. The first files demonstrate simple cases where the equity value is computed from sustainable growth rate and cash flow available to pay dividends after considering re-investment. After equity is value is demonstrated, similar files techniques are demonstrated to compute the enterprise value of a company.





Advanced Lesson Set 2: Reconciliation of IRR and ROI (Project IRR and ROIC or Equity IRR and ROE)


Economic evaluation of a new investment generally involves assessing the IRR on the investment. But management generally is concerned with presenting ROIC and ROE which are key measures of relative performance. The question addressed in this section is whether te return on investment and the IRR converge in the long run and whether a company that continually makes investments that earn a given IRR will converge to the same ROI. The video and files below show that if the IRR itself is used as the discount rate, then the ROI is a weighted average of ROI over the life of an investment. But,the ROI is only the same as the IRR in each year if a form of economic depreciation is used. More importantly, the ROI is lower than the ROI in early years of the investment and higher in later years. This means that if a corporation has recently made a large investment, a low ROE is expected. On the other hand, if investments are old then the ROI will be higher than the IRR.

The IRR and ROI reconciliation are explained in the spreadsheet file and the video below.




Advanced Lesson Set 3: Evaluation of the P/E Ratio, the EV/EBITDA Ratio and the P/B Ratio through Constructing the Underlying Drivers and Understanding the Economics of How Cash Flow Can Change


P/E ratios and EV/EBITDA ratios are used in valuation in all sorts of contexts and often discussed by experts on television. The question of why a multiple for an industry or a company in an industry should be high or low and whether the overall level of the multiple is high or low is not addressed in a rigorous manner in either finance texts or by those horrible television who shout so loudly on the TV. The exercises in this section demonstrate that both the P/E ratio and EV/EBITDA ratio are affected by future returns, growth and the cost of capital which are the standard drivers of value. The initial videos describe how P/E ratios can be computed from the value drivers with changes in growth and cost of capital. The EV/EBITDA analysis shows how the EV/EBITDA ratio is different from the P/E ratio because the EV/EBITDA ratio is affected by tax, capital expenditure and depreciation relative to EBITDA and working capital adjustments. A problem I have with all of this is that the true economic drivers of changes in return are not discussed, meaning that you cannot just predict returns but you should carefully think about how price can move to short-run marginal cost; how margins are driven by supply and demand; how technological obsolescence can ruin a business; how some industries are more exposed to surplus capacity than others; how monopoly or oligopoly profits can disappear; how valuable are brands and the ability of companies like Apple, Starbucks, Coke, Disney and McDonalds can continue to earn returns through making the unsuspecting public become strongly addicted to their products.

Videos Associated with Valuation Concepts Lesson Set 2 -- Evaluation of P/E, EV/EBITDA and P/B from Economic Drivers




Files Used in Valuation Concepts Lesson Set 2: Computation of P/E, EV/EBITDA and P/B from Economic Drivers




Advanced Valuation Lesson Set 4: Making Adjustments to Terminal Value through Computing Normalised Cash Flow with Stable Capital Expenditures, Stable ROIC relative to WACC, Stable Deferred Taxes and Stable Working Capital all of which depend on projected stable growth



This file below demonstrates issues associated with capital expenditures in the terminal value. It demonstrates that you should adjust the terminal value with capital expenditures to depreciation and that the stable ratio depends on both nominal terminal growth and the depreciation rate.








This file below demonstrates issues associated with working capital in the terminal value calculation. It demonstrates that you should adjust the terminal value with a formula the begins with the working capital to EBITDA and adjust the formula with the growth rate.


This file below demonstrates issues associated with deferred taxes in the terminal value calculation. It demonstrates that in the same way that capital expenditures should be adjusted in the terminal value analysis, the same kind of adjustment should be made to deferred taxes.



Advanced Valuation Lesson Set 5: Calculation of the Bridge Between Enterprise Value and Equity Value (otherwise known as Net Debt) including Fair Valuation of Derivatives, Operating Reserves, Deferred Tax Allocations, and Adjustments to WACC


The file below demonstrates how to evaluate whether various elements should be included or not included in the bridge between equity value and enterprise value. It deals with things like the value of derivatives and deferred taxes associated with the derivatives. The proofs develop both true cash flow and the accounting for cash flow.

In a similar manner as a high project IRR can be a danger sign of pending over-capacity in project finance, a high ROIC may suggest that companies will try and enter the industry and increase supply. While evaluating ROIC is important in corporate analysis, the statistic must be adjusted for goodwill write-offs, restructuring charges, impairments and other accounting items. Risk assessment in corporate finance involves judging how EBITDA can change due to factors such as technical obsolescence, changes in consumer tastes, changes in cost structure, and a host of factors including industry demand and supply that can create oversupply in an industry. Rigorous analysis of potential changes in EBITDA are hardly ever dealt with in finance texts. Assessments of business risk that is driven by volatility in EBITDA are treated using opaque and confusing jargon by credit rating agencies such as Standard and Poor’s.

Using multiples such as the P/E ratio and the EV/EBITDA ratio in valuation can be result in biases without understanding how the multiples are affected by assumptions with respect to long-term growth and long-term earnings potential. The EV/EBITDA ratio is strongly affected by the lifetime of assets used in the business and the necessity to replace capital expenditures.


This file is a corporate model for a chicken producer with returns that are affected by changing politics. It demonstrates how you can develop stable ratios and normlised cash flow. It includes stable ratio of capital expenditures and other issues as well as stable ROIC.



The first file demonstrates that when the target capital structure does not equal the current capital structure, discounting free cash flows at the WACC (which does not change in theory when the capital structure changes) gives the same answer as computing a new cost of equity with changing capital structure.

Appendix: Derivation of Value Driver Formulas under Restrictive Assumptions


Begin with the classic and simple integral calculus formula that applies free cash flow

Equity Value = Div1/(k-g)
Enterprise Value = Free Cash Flow1/(WACC-g)

For equity, use the Sustainable Dividend Growth and Re-arrange the formula -- growth is from retaining cash and earning returns.

g = (1 – DPO) x ROE
DPO = 1-g/ROE

For equity, compute Dividends as a function of Earnings and DPO (Substituted)

Div1 = EPS1 * (1-g/ROE)

Use the initial integral calculus formula and then substitute

Value = Div1/(k-g)
Value per share = EPS * (1-g/ROE)/(k-g)
Equity Value = Net Income * (1-g/ROE)/(k-g)

Re-arrange to compute the P/E Ratio, the ratio works best with forward P/E

P/E = (1-g/ROE)/(k-g)
P/E1 = (1-g/ROE)/(k-g)

The formula can easily be re-arranged to compute the cost of equity capital:

(k-g) = (1-g/ROE)/PE
k = (1-g/ROE)/PE + g

Re-arranged Formula

Value = Net Income * (1-g/ROE)/(k-g)
ROE = Net Income /BV
Value = BV * ROE * (1-g * BV/ROE)/(k-g)
Value = BV * (ROE - g)/(k-g)

Formula for Price to Book Ratio

Value/BV = (ROE-g)/(k-g)
PB = (ROE-g)/(k-g)

Implied formula for Cost of Capital with Price to Book Formula

k=(ROE-g)/PB+g




List of Videos and Associated Files Explaining my Comments and Philosophy on Valuation Issues


Category

Subject

Excel File

Video Link

Chapter Reference

Page Reference













General discussion of valuation problems

Normalising Cash Flow - 4 Components of EBITDA, WC changes, Cap Exp and Taxes









General discussion of valuation problems

Normalising Cash Flow - Cyclical Business and ROIC changes over life of project









General discussion of valuation problems

ROIC with Interpolate Function (adjusted lookup)









General discussion of valuation problems

Equity Analysis with Changing Returns, growth and cost of capital









General discussion of valuation problems

Flexible begin and end of valuation analysis with switches









General discussion of valuation problems

ROIC Calculation and Balance Sheet Analysis









General discussion of valuation problems

Critique of DCF Model and ROIC









General discussion of valuation problems

Alternative Terminal Value Methods





















Stable ratios in Terminal Value with Growth

How to normalise terminal value with capital expenditures to depreciation

Cap Exp to Depreciation

https://www.youtube.com/watch?v=-NUeYz_wm04

33

417

Stable ratios in Terminal Value with Growth

How to Make Function for Automatically Computing Stable Ratio of cap exp to depreciation









Stable ratios in Terminal Value with Growth

Stable WC changes in Terminal Value from Formula

Stable WC

https://www.youtube.com/watch?v=D1WWxM7ZbY0

33

425

Stable ratios in Terminal Value with Growth

Stable Deferred Tax from Capital Expenditures





















Drivers of Multiples

Interaction between Growth and ROIC in influencing multiples

Corporate and Project Model

https://www.youtube.com/watch?v=g6k3MRcEqs0





Drivers of Multiples

Transition and Interpolation in Valuation Model to compute derived multiples

Corporate and Project Model

https://www.youtube.com/watch?v=sonGGtUBtpQ





Drivers of Multiples

Long term Analysis and Presentation of P/E and EV/EBITDA with template model

EV/EBITDA and P/E Linear







Value Driver Formula - Equity

Demonstrate Mechanics of Value Driver Formula

Value Driver - Equity

https://www.youtube.com/watch?v=WT-8PKtccVI

33

417

Value Driver Formula - FCF

Use the Value Driver with Stable Rates and Timing Analysis with Switches

DCF Timing

https://www.youtube.com/watch?v=PxkKz3VKjyc

33

425

Value Driver Formula - FCF

Compute EV from Free Cash Flow in Long-term Model

Value Driver - FCF 1

https://www.youtube.com/watch?v=FWCD5sYZanY

33

425

Value Driver Formula - FCF

Use the Value Driver with Stable Rates

Value Driver - FCF 2

https://www.youtube.com/watch?v=hYqTH3oud4M

33

425

Value Driver Formula - FCF

Use of Value Driver with Two Stage Model

Value Driver - FCF 3

https://www.youtube.com/watch?v=hzg8Rb_VcCQ

33

425

Value Driver Formula - FCF

Value Driver Formula with Interpolation





33

425

Proofs of Items in EV/EBITDA Bridge

Proof of Timing in DCF









Proofs of Items in EV/EBITDA Bridge

Proof of why cannot treat AP as Financial Liability

AP Proof.xlsm

https://www.youtube.com/watch?v=NIPWylXN9hw





Proofs of Items in EV/EBITDA Bridge

Provisions for Warranties in DCF









Proofs of Items in EV/EBITDA Bridge

Deferred Taxes from Cap Exp









Proofs of Items in EV/EBITDA Bridge

Deferred Taxes from NOL









Proofs of Items in EV/EBITDA Bridge

ROIC and DCF with Fair Value of Derivatives









Proofs of Items in EV/EBITDA Bridge

Diluted Shares and Value of Stock Options









Proofs of Items in EV/EBITDA Bridge

Discontinued Operations in DCF









Cost of Capital

Use of M/B Ratio for Computing Cost of Captial









Cost of Capital Problems

Problems with Beta and Measuring Cost of Capital

Renewable Stock Price

https://www.youtube.com/watch?v=eTDjLjZo9cE

33

425

Cost of Capital

Use of Market P/E Ratio to Derive Cost of Capital

Economy Wide Cost of Capital

https://www.youtube.com/watch?v=GAolSYR1-pc





DCF from Corporate Model

DCF Model

Integrated Electricity Model

https://www.youtube.com/watch?v=9rsxSVDbjxE

33

425

General Value of Bonds

Valuation of Bonds

Bond Valuation

https://www.youtube.com/watch?v=f_t_hbLaVik

33

425

……………………………………………………………………………
…………………………………………………………………………………………………………..

…………………………………………………………….

…………………………………………………………………………………………

……………………………………….

………………………………………..
Cost of Capital Discussion








Discounting using 1/2 year assumption rather than end of year assumption





Complete Model of Implied Models with Linear Interpolation












Some of the advanced issues include:
- Calculating the stable ratio of capital expenditures to depreciation for terminal value
- Understanding that the value driver formula does not work when applied to NOPAT
- Computing P/E ratios and EV/EBITDA ratios that correctly account for returns, growth rates, plant lives, taxes and working capital requirements.
- Understanding that ROIC, EBITDA and earnings of companies cannot be compared without adjusting for the age of assets.
- Deriving reasonable estimates for the cost of capital
- Proving how various items such as deferred taxes, decommissioning costs, valuation of derivatives and other things should be accounted for in the bridge between enterprise value and equity value
- Proving the correct method to use in for the target capital structures and tax shields



Cost of Captial Database Introduction

Dow 30 Companies

https://www.youtube.com/watch?v=MOpSVBstv4o
Cost of Capital Sensitivity Analysis Using the P/E Ratio Formula

Price to Earnings Analysis

https://www.youtube.com/watch?v=A5FoWknb0HM
P/E Cost of Capital and Scenario Reporter

Scenario reporter

https://www.youtube.com/watch?v=j5DOUe6Wqbk
P/E ratio and Cost of Capital with Transition and Interpolation (Number 6)

Interpolate and Lookup

https://www.youtube.com/watch?v=XLVqKfvmjCM
P/B Regression Simulations for the Cost of Capital (Number 5)

Price to Book

https://www.youtube.com/watch?v=bhYlYSSWDVw
P/B Formulas and Cost of Capital

Price to Book

https://www.youtube.com/watch?v=s2NdJs8Su44
Demonstration of Problems with CAPM

Beer Companies Database

https://www.youtube.com/watch?v=PL0zOQe-_6c
Collecting Data with Ticker Symbols

Cost of Captial Database

https://www.youtube.com/watch?v=MTskVI_VERk
Bulding Cost of Capital Data with Indirect Function

Cost of Captial Database

https://www.youtube.com/watch?v=UBl_pAvxhbs

These files demonstrate how you can derive implicit multiples given value drivers such as return on invested capital, growth rates, plant lifetime and cost of capital.