50  Fundamental Principles of Value Creation ROIC can be defined in two ways: as the return on all capital or as the return on new, or incremental, capital. For now, we assume that both returns are the same. • Investment rate (IR) is the portion of NOPAT invested back into the business: IR Net Investment NOPAT = • Weighted average cost of capital (WACC) is the rate of return that investors expect to earn from investing in the company and therefore the appro- priate discount rate for the free cash flow. WACC is defined in detail in Chapter 15. • Growth (g) is the rate at which the company’s NOPAT and cash flow grow each year. Assume that the company’s revenues and NOPAT grow at a constant rate and the company invests the same proportion of its NOPAT in its business each year. Investing the same proportion of NOPAT each year also means that the company’s free cash flow will grow at a constant rate. Since the company’s cash flows are growing at a constant rate, we can begin by valuing a company using the well-known cash-flow perpetuity formula: Value FCF WACC = − = t g 1 This formula is well established in the finance and mathematics literature.20 Next, define free cash flow in terms of NOPAT and the investment rate: FCF NOPAT Net Investment NOPAT NOPAT IR NOPAT IR = − = − × = − ( ) ( ) 1 Earlier, we developed the relationship between the investment rate (IR), the company’s projected growth in NOPAT (g), and the return on investment (ROIC):21 g = × ROIC IR 20 For the derivation, see T. E. Copeland and J. Fred Weston, Financial Theory and Corporate Policy, 3rd ed. (Reading, MA: Addison-Wesley, 1988), Appendix A. 21 Technically, we should use the return on new, or incremental, capital, but for simplicity we assume that the ROIC and incremental ROIC are equal. The Math of Value Creation  51 Solving for IR, rather than g, leads to: IR ROIC = g Now build this into the definition of free cash flow: FCF NOPAT ROIC = −     1 g Substituting for free cash flow in the cash-flow perpetuity formula gives the key value driver formula:22 Value NOPAT ROIC WACC = −     − = t g g 1 1 This formula underpins the discounted-cash-flow (DCF) approach to valu- ation, and a variant of the equation lies behind the economic-profit approach. Chapter 10 describes in depth these two mathematically equivalent valuation techniques. You might go so far as to say that this formula represents all there is to valuation. Everything else is mere detail. Substituting the forecast assumptions given for Value Inc. and Volume Inc. in Exhibit 3.2 into the key value driver formula results in the same values we came up with when we discounted their cash flows: Company NOPATt=1, $ Growth, % ROIC, % WACC, % Value, $ Value Inc. 100 5 20 10 1,500 Volume Inc. 100 5 10 10 1,000 In most cases, we do not use this formula in practice. The reason is that in most situations, the model is overly restrictive, as it assumes a constant ROIC and growth rate going forward. For companies whose key value drivers are expected to change, we need a model that is more flexible in its forecasts. Nev- ertheless, while we do not use this formula in practice, it is extremely useful as a means to maintain focus on what drives value. Until now, we have concentrated on how ROIC and growth drive the DCF valuation. It is also possible to use the key value driver formula to show that ROIC and growth determine the multiples commonly used to analyze company 22 Technically, this formula should use the return on new invested capital (RONIC), not the company’s return on all invested capital (ROIC). For convenience throughout this book, we frequently use ROIC to denote both the return on all capital and the return on new invested capital. 52  Fundamental Principles of Value Creation valuation, such as price-to-earnings and market-to-book ratios. To see this, divide both sides of the key value driver formula by NOPAT: Value NOPAT ROIC WACC t g g = = −     − 1 1 As the formula shows, a company’s earnings multiple is driven by both its expected growth and its return on invested capital. You can also turn the formula into a value-to-invested-capital formula. Start with the identity: NOPAT = Invested Capital ROIC × Substitute this definition of NOPAT into the key value driver formula: Value Invested Capital ROIC ROIC WACC = × × −     − 1 g g Divide both sides by invested capital:23 Value Invested Capital ROIC ROIC WACC = − −           1 g g Now that we have explained the logic behind the DCF approach to valua- tion, you may wonder why analysts’ reports and investment-banking pitches so often use earnings multiples, rather than valuations based on DCF analysis. The answer is partly that earnings multiples are a useful shorthand for com- municating values to a wider public. A leading sell-side analyst told us that he uses discounted cash flow to analyze and value companies but typically communicates his findings in terms of implied multiples. For example, an analyst might say Company X deserves a higher multiple than Company Y because it is expected to grow faster, earn higher margins, or generate more cash flow. Earnings multiples are also a useful sanity check for your valua- tion. In practice, we always compare a company’s implied multiple based on our valuation with those of its peers to see if we can explain why its multiple is higher or lower in terms of its ROIC or growth rates. See Chapter 18 for a discussion of how to analyze earnings multiples. 23 If total ROIC and incremental ROIC are not the same, then this equation becomes: Value Invested Capital ROIC RONIC WACC = − −           1 g g where ROIC equals the return on the company’s current capital and RONIC equals the return on new invested capital.