*The Life Cycle in Startup Valuation DOI: http://dx.doi.org/10.5772/intechopen.110765*

**Figure 22.** *The net value of the update of all flows up to period 20. Source: Prepared by the author.*

#### **Figure 23.**

*Generation of added value. Source: Prepared by the author.*

### *1.8.5 The effect of perpetuities*

In business valuation, the life cycle of the business generally extends for several years after its maturity stage. However, when using the perpetuity method, it is important to be sure that the business being valued is expected to have a duration of at least 40 years.<sup>7</sup>

<sup>7</sup> A 40-year period is considered since the Present Value of a 40-year economic flow is similar to the present value using the perpetuity method.

In the maturity stage, the growth rate of economic flows is approaching an almost vegetative growth, which in the case being analyzed is considered a g of 3%. Consequently, the Perpetuity Value can be determined as follows.

$$\begin{aligned} \text{VP FE Perpotential}\_{20} &= \frac{\text{FE}\_{21}}{\text{Ko} - \text{g}}\\ \text{VP FE Perpotential}\_{20} &= \frac{\text{FE}\_{20} \left(1 + \text{Ko}\right)}{\text{Ko} - \text{g}} = \frac{\text{109.1} \left(1 + \text{129\%}\right)}{\text{1296} - \text{396}} = \text{1,357.8} \end{aligned} \tag{12}$$

The Present Value of the perpetual economic flow is found updating the flows that begin the following period, 21,<sup>8</sup> which is discounted at the difference between the discount rate and the growth rate. To calculate the economic flow of period 21, the economic flow of period 20 is taken and carried to 21. Thus, it is finally obtained that the Present Value of the perpetuity for period 20 is equivalent to \$1357.8 MM, as presented in **Figure 24**.

The value of the perpetuity determined from the last economic flow of period 20 (\$1357.8 MM) is added to the economic flow of period 20 (\$109.1 MM), obtaining a total flow of \$1466.9 MM, as shown in **Figure 25**.

Then, in **Figure 26**, using a discount rate of 12%, the economic flow that considers the value of the perpetuity is updated and thus the Present Value of the economic flows is determined, which amounts to \$195.2 MM.

#### **Figure 24.**

*The Present Value of the perpetuity for period 20. Source: Prepared by the author.*


#### **Figure 25.**

*Total flow. Source: Prepared by the author.*

<sup>8</sup> Assuming that they continue to infinity (in practice 40 years).

#### **Figure 26.**

*Present value of the economic flows. Source: Prepared by the author.*

Considering an evaluation horizon of 20 periods, the Equity Valuation results in \$54.5 MM and if the value of the perpetuity of economic flows is considered, the value increases to \$195.2. Note that it is a significant increase, so it is important to keep in mind for the use of perpetuity that the business must reach at least 40 years or a discount rate must be considered that incorporates the little certainty that the business will mature. It is also important to determine the growth rate of economic flows (g), since this value can strongly modify the present value of the perpetuity.

#### *1.8.6 Identifying differentiated discount rates*

The capital costs that can be obtained in the market are generally from companies in progress and with a history of operating in the market, this is not the case of startups because by definition they are new companies that need investments in their stage of development. Development and in the introduction stage, even in part of the growth stage. These are periods where it is not yet possible to obtain profits or positive economic flows. Consequently, what must be done is separate the updating of the economic flows into two stages, one where the flows already reflect the consolidation of the business and another where the flows show that greater net investments are still being made.

The consolidation stage is from period 11 where the first positive economic flow is achieved and from then on it can be considered that the business is growing, which then enters maturity and finally has a perpetuity behavior with growth of g%. Then you can start to replace the average rate of 12% with a cost of capital of 9%, an expected return that corresponds to similar businesses but that are already in the market. With this modification, the value of the perpetuity of the flows from period 21 onwards increases from \$1357.8 MM to \$1982.2 (see **Figure 27**).

Since the idea is to have the value of the business at the stage where it could be similar to a business of the same type but that is already on the market, then we discount the positive economic flows from period 11 to 20, which includes the perpetuity value considering that this update is made at the cost of capital or expected


**Figure 27.** *New perpetuity value. Source: Prepared by the author.*

return of 9%. Thus, the Present Value of the business is obtained \$1231 MM, which will be located in period 10 and which represents the value of the business when the investments have already been made, as shown in **Figure 28**.

Then the economic flows from period 1 to 10 are updated, which includes the Present Value of the flows from 11 to 20, including perpetuity. **Figure 29** shows that, in this period a discount rate of 20% higher than the 9% that corresponds to the business consolidation stage is used. The reason is because at this stage investors assume the risk of the company's *default* without being sure of being able to reach the period where profits or positive flows begin to be generated, so this risk assessment derives in the use of a high expected return.

From the update, there is a Present Value of the economic flows of \$157.5 MM that considers the effect of the perpetuities and the discount rates in stages and that can be seen in the **Figure 30**.


#### **Figure 28.**

*The Present Value of the business. Source: Prepared by the author.*


**Figure 29.**

*Economic flow from 1 to 10 with perpetuity (11–20). Source: Prepared by the author.*

**Figure 30.** *Effect of the perpetuities and the discount rates. Source: Prepared by the author.*
