## Noplat7 wacca

Here, g is the inflation rate. This formula can substantially overstate continuing value because it assumes that NOPLAT can grow without any incremental capital investment. This is unlikely (or impossible), because any growth will probably require additional working capital and fixed assets.

To show how this formula relates to the value-driver formula, let us assume that the return on incremental capital investment (ROIC) approaches infinity.

Exhibit 12.12 compares the two variations of the DCF formulas. This exhibit shows how the average return on invested capital (both existing and new investment) behaves under the two assumptions. In the aggressive case, NOPLAT grows without any new investment, so the return on invested capital eventually approaches infinity. In the convergence case, the average return on invested capital moves toward the weighted average cost of capital (WACC) as new capital becomes a larger portion of the total capital base.

### Non-Cash Flow Approaches

In addition to DCF techniques, non-cash flow approaches to continuing value are sometimes used. Four common approaches are liquidation value, replacement cost, price-to-earnings ratio, and market-to-book ratio.

The liquidation-value approach sets the continuing value equal to an estimate of the proceeds from the sale of the assets of the business, after paying Exhibit 12.12 Rates of Return Implied by Alternative Continuing Value Formulas

off liabilities at the end of the explicit forecast period. Liquidation value is often far different from the value of the company as a going concern. In a growing, profitable industry, a company's liquidation value is probably far below the going-concern value. In a dying industry, liquidation value may exceed going-concern value. Do not use this approach unless liquidation is likely at the end of the forecast period.

The replacement-cost approach sets the continuing value equal to the expected cost to replace the company's assets. This approach has a number of drawbacks. First, only tangible assets are replaceable. The company's ''organizational capital" can be valued only on the basis of the cash flow the company generates. The replacement cost of the company's tangible assets may greatly understate the value of the company.

Second, not all the company's assets will ever be replaced. Consider a machine used only by this particular industry. The replacement cost of the asset may be so high that it is not economical to replace it. As long as it generates a positive cash flow, the asset is valuable to the ongoing business of the company. Here, the replacement cost may exceed the value of the business as an ongoing entity.

The price-to-earnings (P/E) ratio approach assumes the company will be worth some multiple of its future earnings in the continuing period. Of course, this will be true; the difficulty arises in trying to estimate an appropriate P/E ratio.

Suppose today's current industry average P/E ratio is chosen. Today's P/E ratio reflects the economic prospects of the industry during the explicit forecast period as well as the continuing value period. However, prospects at the end of the explicit forecast period are likely to be very different from today's. We need a different P/E ratio that reflects the company's prospects at the end of the forecast period. What factors will determine that ratio? As we discussed in Chapter 8, the company's expected growth, the rate of return on new capital, and the cost of capital are the primary determinants of its P/E ratio. These are the same factors that are in the value driver formula. So unless you are comfortable using an arbitrary P/E ratio, you are much better off with the value driver formula.

When valuing acquisitions, companies sometimes fall into the circular reasoning that the P/E ratio for the continuing value will equal the P/E ratio paid for the acquisition. In other words, if I pay 18 times earnings, I should be able to sell the business for 18 times earnings. In most cases, the reason a company is willing to pay a high P/E for an acquisition is that it believes it can take actions to greatly improve earnings. So the effective P/E it is paying on the improved level of earnings will be much less than 18. Once the improvements are in place and earnings are higher, buyers will not be willing to pay the same P/E unless they can make additional improvements.

The market-to-book ratio approach assumes the company will be worth some multiple of its book value, often the same as its current multiple or the multiples of comparable companies. This approach is conceptually similar to the P/E approach and faces the same problems. In addition to the complexity of deriving an appropriate multiple, the book value itself is distorted by inflation and important accounting assumptions. Once again, the DCF approaches are easier to use.

### Advanced Formulas for Continuing Value

A variation of the value driver formula for DCF valuations is the two-stage value driver formula. This formula allows you to break up the continuing value period into two periods with different growth and ROIC assumptions. You might assume that during the first eight years after the explicit forecast period that the company would grow at 8 percent per year and earn an incremental ROIC of 15 percent. After those eight years, the company's growth would slow to 5 percent and incremental ROIC would drop to 11 percent:

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