Background on Terminal Value Calculations
DCF models calculate the present value sum of the expected future cash flows of a business. Experts preparing DCF models typically start by examining financial projections from company management or third parties. Company projections often extend only a few years into the future, however. To capture the value of cash flows beyond the projection period, experts estimate a terminal value that reflects the lump-sum equivalent of all future cash flows after the period for which actual projections exist. In many DCF models, a significant portion of the subject firm’s estimated value is attributable to the terminal value. Embedded within the terminal value are explicit or implicit assumptions about the company’s future profits, growth, risk, and investment needs. These assumptions must be internally consistent. In particular, the investment rate—the fraction of after-tax profits that the company reinvests—will depend on the profitability and rate of growth.
One popular technique for estimating the terminal value involves extrapolating future cash flows from the final year of the projections at a constant long-term growth rate. Under this approach, the subject business’s profit margins, tax rate, and investment rate in the final year of the projections are assumed to remain constant in perpetuity. The simplicity of the approach has great appeal, and, unsurprisingly, its use is widespread. A 2006 survey of corporate financial advisers and private equity professionals, for example, found that 80 percent of participants used the extrapolation approach to estimate terminal value. The extrapolation approach is also prominent in popular reference books for investment banking professionals.
Despite its popularity, the extrapolation approach is problematic when there is a mismatch between the projected investment rate and the long-term constant growth rate chosen by the expert. As the court correctly observed in Ramcell, growth is not free. Instead, growth requires investment, and competition will tend to prevent continued returns in excess of the cost of capital. Thus, low investment but high growth yields an implausibly high return on investment. In Ramcell, for example, a terminal value calculation prepared by the petitioners’ expert using the extrapolation approach implied a return on investment ranging from 193 percent to 227 percent—more than ten times what is plausible in a competitive industry. The court credited an illustration of this fact prepared by the respondent’s expert in electing to adopt the convergence approach instead.
The Convergence Approach
The convergence approach, in contrast, explicitly constrains the subject firm’s long-run return on investment to a reasonable target rate. Often, a reasonable return on investment is the firm’s cost of capital—that is, the return that investors expect after paying for all the costs associated with operating the business. This is because a business consistently earning returns that exceed its cost of capital (thus increasing the value of the business) will tend to attract vigorous competition. Competition, in turn, will exert downward pressure on the company’s return on investment. For example, a competitor may need only reduce its prices a bit to steal market share and capture some of the “spread” between returns and capital costs in the industry. Outsized profits will also attract new entrants. As a result, excess returns—the spread between return on investment and the cost of capital—should disappear in the long run for competitive industries.
While the convergence approach assumes that a company’s excess returns will (slowly) dissipate, growth in revenue and profits is another matter. Under the convergence approach, a company may continue growing even while its excess returns disappear. The subtlety arises from the distinction between growth and value creation. When a company’s return on investment equals its cost of capital, growth does not create extra value because the cost of funding that growth just offsets the benefit. Two simple examples are investments in projects with zero net present value and an acquisition at a price that reflects the full value of the target. It is only when a company’s return on investment exceeds its cost of capital that growth creates value. On the other hand, growth reduces value when the cost of capital exceeds the return on investment. Thus, while the formula for the convergence model calculates terminal value as if the firm has no growth, it is more precise to say that the firm is growing but the cost of funding that growth offsets the benefit.
Every Terminal Value Calculation Embeds an Assumption about Long-Term Investment
Careful readers may object that tying the long-term return on investment to the cost of capital requires projecting a firm’s investment expenditures far into the future. In the Pivotal decision, for example, the court inferred that “[t]rying to ascertain a plowback ratio a decade from the valuation date appears speculative at best, at least under these facts.” While projecting the plowback ratio a decade out may appear speculative, other techniques for calculating terminal value also implicitly embed an assumed plowback ratio.
Consider, for example, the extrapolation approach discussed above. The extrapolation approach grows projected cash flows at a constant rate in perpetuity. Cash flow equals after-tax profits less investment, by definition, so the extrapolation approach inherently includes a specific, constant-growth projection of investment far into the future. The distinction is not that one terminal value calculation approach requires projecting investment and the other does not. By virtue of what the terminal value represents—the present value of a stream of cash flows—both terminal value approaches embed projections of long-term investment. Instead, what distinguishes these approaches is the nature of the specific investment projection and what it implies for other variables of interest, like return on investment. Under the convergence approach, the investment projection imposes economic discipline arising from competitive market conditions in setting the long-term return on investment in relation to the cost of capital. That modeling structure avoids unrealistic scenarios that often arise under the extrapolation approach, where investment returns significantly exceed the cost of capital forever, giving rise to an inflated valuation that is inconsistent with a competitive market.
Conclusion
Growing recognition of the merits of the convergence approach in valuation practice and case law puts the assumptions embedded in alternative approaches in sharp relief. Experts adopting alternative approaches, such as the extrapolation approach, are likely to face heightened scrutiny about whether the often-implicit assumptions embedded in their terminal value calculations are consistent with reasonable expectations for long-run market conditions. On the other hand, experts adopting the convergence approach may face challenges about the competitive forces driving up long-run investment requirements relative to management’s near-term expectations as reflected in company projections.
Disclosure: Michael Cliff was a member of the Analysis Group teams that supported valuation experts for the respondents in the PetSmart, Solera, and Jarden cases cited in the endnotes. Joseph Maloney was a member of the Analysis Group teams that supported valuation experts for the respondents in the PetSmart and Jarden cases. The opinions expressed are those of the authors and do not necessarily reflect the views of Analysis Group or its clients.