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increase the dividend payout ratio while holding the projected operating performance constant (in other words, no changes in revenues or margins). Presto! The equity value has just increased because of the higher dividend payments despite the constant operating performance. The error here is that the discount rate was not changed. Increasing the dividend payout ratio requires more use of debt. More debt means riskier equity and a higher discount rate for the equity.
Another shortcoming of the direct equity approach appears when valuing business units. The direct equity approach requires allocating debt and interest expense to each unit. This creates extra work without any extra information being provided.
Option Valuation Models
Option-pricing models are variations on standard discounted cash flow models that adjust for management's ability to modify decisions as more information becomes available. Option models hold particular promise for valuing strategic and operating flexibility such as opening and closing plants, abandoning operations, or natural resource exploration and development. Chapter 20 discusses how option valuation approaches can be used.
You may also come across three other DCF variations:
1. Using real instead of nominal cash flows and discount rates.
2. Discounting pretax cash flows instead of after-tax cash flows.
3. Using formula-based approaches instead of explicitly forecasting cash flows.
We would not typically recommend these approaches except in limited circumstances.
Using Real Instead of Nominal Cash Flows and Discount Rates
Companies can be valued by projecting cash flow in real terms (for example, in constant 1999 dollars) and discounting this cash flow at a real discount rate (for example, the nominal rate less expected inflation). Most managers think in terms of nominal rather than real measures, so nominal measures are often easier to communicate. Interest rates are generally
quoted nominally rather than in real terms (excluding expected inflation). Moreover, since historical financial statements are stated in nominal terms, projecting future statements in real terms is difficult and confusing.
An important difficulty occurs when calculating rates of return on invested capital. The historical statements are nominal, so historical returns on invested capital are nominal. But if the projections for the company are real rather than nominal, returns on new capital are also real. Projected returns on total capital (new and old) are a combination of nominal and real, which are impossible to interpret. The only way around this is to restate historical performance on a real basis, a complex and time-consuming task. We have generally found that the extra insights from this effort are insignificant for most companies, except in high inflation environments as described in Chapter 19.
Discounting Pretax Cash Flow Instead of After-Tax Cash Flow
The enterprise model we recommend uses after-tax cash flow and an after-tax discount rate. It is conceptually valid to use pretax cash flow and a pretax discount rate, as the following example illustrates:
Afler-tax cash flow - Pretax cash flow x (l ~ tax rate)
After-ta* discount rdte = Pretax discount ratexfl- tax rate)
Substituting into the initial equation gives:
y | _ r>rcta5c cash flow x(I - tax rate)
Pretax discount rateJ<0 - tax rate)
Real-world after-tax cash flow is not simply pretax cash flow adjusted by the tax rate. Taxes are based on accrual accounting (for example, the tax benefit of purchasing a machine is received in a different period from when the machine is paid for), not cash flow. Therefore, after-tax free cash flow is not equal to pretax free cash flow times a tax rate. You cannot simply gross up the discount rate to a pretax rate and discount the pretax cash flow and get the same result as the recommended approach. It is virtually impossible to perform a real-world discounted cash flow analysis using the pretax approach.
Formula-Based DCF Approaches
Formula-based DCF approaches make simplifying assumptions about a business and its cash flow stream (for example, constant revenue growth and margins) so that the entire discounted cash flow can be captured in a concise formula. These formulas are most often too simple for real problem solving, though they may serve as valuable communication tools.
The Miller-Modigliani (MM) formula is useful for communicating the sources of a company's value. The MM formula (1963) values a company as the sum of the value of the cash flow of its assets currently in place plus the value of its growth opportunities.4 The formula is based on sound economic analysis, so it can be used to illustrate the factors that will affect the value of the company. Its simplifying assumptions (at least in the version given below) render it too inaccurate for precise valuations.