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
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).
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.
Value Driver Sensitivty.xlsm
- Corporate Finance Analysis.pptx
IRR and ROIC.xlsm
low 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.
Inflation and Value Driver Formula.xlsm
ROIC Transition Problems.xlsm
Value Driver – Equity.xlsm
Value Driver – Free Cash Flow 1.xlsm
Analysis of Value Driver with EV.xlsm
Value Driver WC Only.xlsx
Value Driver – Free Cash Flow 2.xlsm
Capital Expenditure Analysis.xlsm
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 McDonald’s 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
PE and EV to EBITDA Multiples – Linear.xlsm
Proof of Timing in DCF Model.xlsx
PE and EV to EBITDA Multiples -Growth.xlsm
Variable WACC in DCF Model.xlsm
Corporate and Project Model.xlsm
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.
Ratio of Cap Exp.xlsm
Stable Ratio Analysis.xlsm
Exercise 4 – Free Cash Flow Exercise.xls
Stable Cap Exp to Depreciation with Historic Growth.xlsm
Stable Cap Exp Ratio.xlsm
Stable Working Capital.xlsm
Stable Cap Exp Ratio Closing Balance.xlsm
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.
Long-term Proof of Accounts Payable and Cash.xlsm
Proofs of Equity Value and Enterprise Value Bridge.xlsm
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.
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
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
Cost of Capital Discussion
Discounting using 1/2 year assumption rather than end of year assumption
Partial Year Discounting.xlsm
Complete Model of Implied Models with Linear Interpolation
Corporate Valuation Concepts.xls
valuation course finished.xlsm
Proof of Timing in DCF Model.xlsx
|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.
PE and EV to EBITDA Multiples -Growth.xlsm
PE and EV to EBITDA Multiples – Linear.xlsm
Innovations in Corporate Modelling