1. A Simple (Naïve) Model

A popular approach to compute the continuing value of a surviving firm is to assume that free cash flows become a constant or a constantly growing perpetuity after the forecasting period. Using the formula for a growing perpetuity, we can therefore compute continuing value at the end of the explicit forecast period as:

 

Continuing ValueT =\( \frac{FCF_{T+1}}{(WACC-g)} \).

 

where:

T = length of the explicit forecast period;

FCFT+1 = first free cash flow after the forecasting horizon;

WACC = Weighted Average Cost of Capital;

g = rate of growth of the free cash flow.

  

All variables are in nominal terms (with the appropriate corrections, one can replicate the analysis in real terms as well). It is important to note that the above expression will produce the continuing value of the firm at the end of the explicit forecast period. Therefore, this will be a future value of continuing value T years from now. To obtain the present value of continuing value, we will therefore have to discount Continuing ValueT over T years:

  

PV Continuing Value  =\( \frac{\text{Continuing Value}_{T+1}}{(1+WACC)^T} \). 

  

Let us illustrate the use of these equations in the context of firm valuation with a numerical example.

  

Let's assume that we are valuing a firm for which the forecast period only last two years (1 and 2) and that the firm is expected to generate the following future free cash flows during these years:

  

Cash flow statement (in thousands)

E1

E2

Net income

3'460

3'780

+ After-tax interest expenses

360

320

NOPLAT

3'820

4'100

+ Depreciation and amortization

3'135

3'230

- Increase in operating assets

452

238

+ Increase in operating liabilities

268

158

Operating cash flow

6'771

7'251

- Net investments

3'635

3'730

Free cash flow

3'136

3'521

  

Also let's assume that the relevant WACC of the firm is 7.38%.

  

Based on this information, we can estimate the firm's present value of the forecast period:

 

PV forecast period = \( \frac{FCF_{1}}{(1+WACC)} + \frac{FCF_{2}}{(1+WACC)^2} = \frac{3'136}{1.0738} + \frac{3'521}{1.0738^2} = 5'974. \)

 

Now let's assume that the free cash flows of the firm are expected to grow at a rate g of 3% per year forever after the explicit forecast period. We can estimate the continuing value using the formula for a growing perpetuity from above. At the end of the forecast period (T=2 years from now), the continuing value is:

 

Continuing valueT = \( \frac{FCF_{T+1}}{WACC-g}= \frac{FCF_T \times(1+g)}{WACC-g}= \frac{3'521 \times 1.03}{0.0738-0-03} = 82'804 \).

  

Therefore, the present value of the continuing value is:

  

PV Continuing value = \( \frac{Continuing \space value_T}{(1+WACC)^T} = \frac{82'804}{1.0738^2} = 71'814. \)

  

Now we can estimate the overall value of the firm:

  

Firm value = PV forecast period + PV continuing value = 5'974 + 71'814 = 77'788.

  

Based on our assumptions, the value of the firm is 77'788. Note that in these computations, the continuing value accounts for more than 90% of the firm value!

  

Clearly, firm value is very sensitive to our assumptions about the continuing value:

  • For example, when we set the expected growth rate g equal to 3.5% instead of 3%, it can be shown that firm value would be roughly 12.5% higher, whereas an expected growth rate of 2.5% would produce a 10% lower firm value. 
  • Similarly, if we overestimate the FCF of year 2 by 1 (dollar) the resulting firm value is 21 (dollars) higher wherease if we underestimate the FCF by 1 (dollar), the resulting firm value is 21 (dollars) lower.

  

  

The numbers from the previous example illustrate, that we have to be extremely careful when estimating continuing value, as it is very sensitive to a few assumptions. In the hypothetical case we have considered above, the sensitivities are a bit extreme because the explicit forecast period is only 2 years. However, also a more realistic setting will produce significant sensitivities of firm value to the long-term growth rate g as well as the free cash flow on which we base the continuing value estimation. Therefore, it is worthwhile to think a bit more about continuing value estimation and to come up with refined estimates of the two central parameters.