Investors can use several different formulas when calculating the terminal value of a firm, but all of them allow—in theory, at least—for a negative terminal growth rate. This would occur if the cost of future capital exceeded the assumed growth rate. In practice, however, negative terminal valuations don't actually exist for very long. A company's equity value can only realistically fall to zero and any remaining liabilities would be sorted out in a bankruptcy proceeding.

Since terminal value is calculated in perpetuity (extended forever into time), a company would have to be heavily subsidized by the government or have endless cash reserves to support a negative growth rate.

How Terminal Growth Rate Values Are Calculated

The terminal value of a company is an estimate of its future value beyond its projected cash flow. Several models exist to calculate terminal value, including the perpetuity growth method and the Gordon Growth Model.

Value of Stock=D1kgwhere:D1=Expected annual dividend per sharek=Investor’s discount rate or required rate of returng=Expected dividend growth rate (assumed tobe constant)\begin{aligned} &\textit{Value of Stock} = \frac { D_1 }{ k - g } \\ &\textbf{where:} \\ &D_1 = \text{Expected annual dividend per share} \\ &k = \text{Investor's discount rate or required rate of return} \\ &g = \text{Expected dividend growth rate (assumed to} \\ &\text{be constant)} \\ \end{aligned}Value of Stock=kgD1where:D1=Expected annual dividend per sharek=Investor’s discount rate or required rate of returng=Expected dividend growth rate (assumed tobe constant)

The Gordon Growth Model has a unique way of determining the terminal growth rate. Other terminal value calculations focus entirely on the firm's revenue and ignore macroeconomic factors, but the Gordon growth method includes an entirely subjective terminal growth rate based on any criteria that the investor would like.

For example, the rate of cash flow growth might be tied to projected GDP growth or inflation. It could be arbitrarily set at three percent. This number is then added to earnings before interest, taxes, depreciation, and amortization (EBITDA). Next, the resulting number is divided by the weighted average cost of capital (WACC) minus the same terminal growth rate.

Most academic interpretations of terminal value suggest that stable terminal growth rates must be less than or equal to the growth rate of the economy as a whole. This is one of the reasons why GDP is used as an approximation for the Gordon Growth Model.

Again, there is no conceptual reason to believe that this growth rate could be negative. A negative growth rate implies that the firm would liquidate part of itself each year until finally disappearing, making the choice to liquidate more attractive. The only instance when this seems feasible is when a company is being replaced slowly by new technology.

Why It's Hard to Value Declining Firms with Terminal Growth Models

Declining or distressed firms are not easy for investors to value with terminal growth models. It is very possible that such a firm will never make it to steady growth. Nevertheless, it doesn't make sense for investors to make that assumption whenever the current costs of capital exceed current earnings.

A negative growth rate is particularly tricky with young, complex, or cyclical businesses. Investors can't reasonably rely on using existing costs of capital or reinvestment rates, so they might have to make risky assumptions about future prospects.

Whenever an investor comes across a firm with negative net earnings relative to its cost of capital, it's probably best to rely on other fundamental tools outside of terminal valuation.