### 5. Modeling Continuing Value

#### 5.3. A Growing Perpetuity

The third popular approach is to assume that the firm will become "normal" at the end of the forecast period so that the future development of the free cash flows can be approximated with a simple model that assumes, for example, that the cash flows will grow at a constant rate of growth (g) forever. Such a model of a growing perpetuity could be implemented as follows:

Continuing Value (end of forecast period) =$$\frac{FCF_T \times (1+g)}{(WACC-g)}$$,

with: FCFT = forecasted free cash flow at the end of the forecast period, g = perpetual growth rate; WACC = "normal" WACC for a mature company.

To illustrate this approach, let us return to our hypothetical company. According to the cash flow projections, we have assumed that the firm will generate a free cash flow of 5 million in year 7 (FCF7). We have also assumed that the "normal" WACC is 10%. To model the continuing value with the approach outlined above, let us assume that the perpetual rate of growth is 2% (g). With this information, we can now estimate the firm's continuing value at the end of the forecast period:

Continuing Value (end of forecast period) =$$\frac{FCF_T \times (1+g)}{(WACC-g)} = \frac{5'000 \times 1.02}{0.1 - 0.02}$$ = 63'750.

Put differently, these assumptions imply that the firm will have a continuing value of roughly 64 million in 7 years. Given a PV factor of 0.239 for that period, the PV of continuing value is roughly 15.2 million:

PV(Continuing Value7) = Exit Value7 ×  PV Factor = 63.75 ×  0.239 = 15.24 million.

Consequently, the overall value of the firm is roughly 17 million:

Firm Value = PV(Forecast Period) + PV(Continuing Value) = 1.87 + 15.24 = 17.11 million.

Again, continuing value accounts for the largest part of firm value. And clearly, firm value will be very sensitive to our assumptions about the future growth rate and the "normal" level of FCF at the end of the forecast period. It is therefore crucial to make reasonable assumptions about these key value drivers.

 The separate module Continuing Value provides a comprehensive discussion of these issues as well as practical guidelines to estimate the firm's future growth rate as well as its "normal" cash flow level in a consistent manner. Please refer to this module for all the relevant details.

While we refer to the module Continuing Value to learn about the details of the key trade-offs at hand, let us quickly summarize the main takeaways of the relevant sections in that module:

• In the long run (remember, the perpetuity assumes perpetual cash flows...) a firm cannot grow faster than the (global) expected GDP growth rate. Otherwise, it will eventually become THE market and have to expand to other planets and solar systems to satisfy its growth appetite. The upper bound for g is, therefore, long-term expected global GDP growth.
• Also, it is difficult to imagine that a firm will be able to shrink each year forever (in real terms). Therefore, a reasonable lower bound for g could be the long-term expected rate of inflation (in the firm's reference currency).
• The two preceeding arguments imply that a reasonable long-term growth rate will be somewhere between the rate of inflation and GDP growth. A realistic long-term growth rate will, therefore, be somewhere around 1.5 to 3%.
• In order to grow, firms will have to make investments:
• If the firm only grows at the rate of inflation, a reasonable assumption is that it does not make any NEW investments. Hence, in the long run, capital expenditures should approximately equal depreciation and amortization charges.
• If the firm grows in real terms (faster than the rate of inflation), it will have to make NEW investments. Hence, in the long run, capital expenditures should be larger than depreciation and amortization charges.
• The previous argument implies that growth and investment policy are NOT independent from each other.

The above considerations apply to valuation models that assume perpetual growth. Now the reality of many startup firms is that they still expect to have significant growth opportunities at the end of the forecast period. What if, for example, the firm expects to be able to grow cash flows at a rate of 20% after the forecast period?

For such a situation, the assumption of a growing perpetuity is clearly wrong. No firm will ever be able to grow at 20% forever. But the firm might be able to grow at 20% for the 10 years that follow the forecast period.

Such a situation can be implemented fairly easily with a so-called "Competitive Advantage Period (CAP) Model". Also this approach is outlined in detail in the module Continuing Value. The main takeaways are:

• Instead of assuming a growing perpetuity right after the forecast period, we insert a period of "excessive" growth, the CAP, between the forecast period and the long-term continuing value.
• During that CAP the FCFs can theoretically grow at almost any (reasonable) growth rate.
• Eventually, however, the firm will exhaust its extraordinary growth potential and the CAP will come to an end.
• At the end of the CAP, we can then add a growing perpetuity that follows the principles outlined above.

With such a CAP model, firm value would consist of the three parts:

Firm value = PV(Forecast period) + PV(CAP) + PV(Continuing value).

This section has briefly summarized some key issues when estimating continuing value using the model of a growing perpetuity. Again, please refer to the module Continuing Value for more details about this important approach.