# Biases in McKinsey Value Driver Formula Part 1 – Changes in Growth Rate

I demonstrate that the well known  value driver formula (1-ROI/g)/(cost of capital-g) used in corporate valuation 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.

McKinsey States: “This formula underpins the discounted-cash-flow (DCF) approach to valuation, and a variant of the equation lies behind the economic-profit approach (i.e. monopoly profit)….You might go so far as to say that this formula represents all there is to valuation. Everything else is mere detail.”

Value Driver Sensitivty.xlsm

Corporate Finance Analysis.pptx

IRR and ROIC.xlsm

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. 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. ## 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.

Inflation and Value Driver Formula.xlsm

ROIC Transition Problems.xlsm

Value Driver – Equity.xlsm

Equity Basis.xlsx

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

## 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