## WACCg

The normalized level of NOPLAT in the first year after the explicit forecast period.

The expected growth rate in NOPLAT in perpetuity. The expected rate of return on net new investment. The weighted average cost of capital.

We call this the value-driver formula because the input variables (growth, ROIC, and WACC) are the key drivers of value discussed throughout this book. The formula is derived by projecting cash flows into perpetuity and discounting them at WACC while making the following simplifying assumptions:

• The company earns constant margins, maintains a constant capital turnover, and thus earns a constant return on existing invested capital.

• The company's revenues and NOPLAT grow at a constant rate and the company invests the same proportion of its gross cash flow in its business each year.

• The company earns a constant return on all new investments.

We start with the simple formula for a cash flow perpetuity that grows at a constant rate:

where FCFT+1 = The normalized level of free cash flow in the first year after the explicit forecast period.

This formula is well established in the finance and mathematics literature.1 Next, define free cash flow in terms of NOPLAT and the investment rate:

where NOPLATt+1 g =

1 For the derivation, see T. Copeland and J.F. Fred Weston, Financial Theory and Corporate Policy, 3rd ed. (Reading, MA: Addison-Wesley, 1988), Appendix A.

where IR The investment rate, or the percentage of NOPLAT reinvested in the = business each year.

In Chapter 8 we developed the relationship between the investment rate (IR), the company's projected growth in NOPLAT (g ), and the return on new investment:

Turning this equation around gives:

ROIC(

Now build this into the free cash flow (FCF) definition:

Substituting for free cash flow gives the value driver formula: NOPI .AT^iO-tf/ROICj)

Continuing value-

### VVACC-y

Many readers will be tempted to use the FCF perpetuity formula, rather than the value driver formula. After all, aren't they the same? Technically, yes, but applying the FCF perpetuity is tricky and most analysts get it wrong. The common error is to incorrectly estimate the level of free cash flow that is consistent with the growth rate you are forecasting. If growth in the continuing value period is forecast to be less than the growth in the explicit forecast period (as is normally the case), then the proportion of NOPLAT that needs to be invested to achieve growth is likely to be less as well. In the continuing value period more of each dollar of NOPLAT becomes free cash flow available for the investors. If this transition is not taken into consideration, the continuing value could be significantly understated. Later in this chapter, we give an example that illustrates what can go wrong when using this formula.

A simple example demonstrates that the value driver formula does, in fact, replicate the process of projecting the cash flows and discounting them to the present. Begin with the following cash flow projections:

Year

NOPLAT 100 106 112 120 126

Net investment 50 53 56 60 63

### Free cash flow 50 53 56 60 63

The above pattern continues after the first five years presented. In this example, the growth rate in NOPLAT and free cash flow each period is 6 percent. The rate of return on net new investment is 12 percent, calculated as the increase in NOPLAT from one year to the next, divided by the net investment in the prior year. The WACC is assumed to be 11 percent. First, use a long forecast, say 150 years:

Next, use the growing free cash flow perpetuity formula:

Finally, use the value-driver formula: cv ]UU{l-6%/12%)

All three approaches yield the same result. (If we had carried out the discounted cash flow beyond 150 years, the result would have been the same.)

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