*1.8.2 The PER method*

In the market or stock market, the names of the components of the valuation formula are usually varied; however, the concepts that determine the valuation through the net profit method are maintained. The formula that is being used is the updating of the Net Profit of period 1 that grows at g% and the series of profits is discounted at the cost of capital K.

$$\text{Equity Value} = P\_0 = \frac{\text{UN}\_1}{K - \text{g}} \tag{4}$$

That same formula can be expressed by separating the Net Profit (UN1) from the quotient <sup>1</sup> *K*�*g* , leaving it as follows:

$$P\_0 = \frac{1}{K - \mathcal{g}} \propto U N\_1 \tag{5}$$

The quotient <sup>1</sup> *<sup>K</sup>*�*<sup>g</sup>* is renamed as the Price/Earnings Ratio or the PER (Price-to-Earnings Ratio) multiplier so that the formula for calculating the Equity Value is expressed as a multiple of the Net Income. This is the formula that is applied in the stock market, but as can be seen, it is the same that corresponds to the net profit method.

$$P\_0 = PER \propto U N\_1 \tag{6}$$

Then the PER could be calculated that corresponds to a cost of capital of 8% and a growth rate of profits of 3%.

$$PER = \frac{1}{K - \text{g}} = \frac{1}{896 - 396} = 20\tag{7}$$

Thus we will have that the equity value can be calculated by multiplying the Net Profit by the PER, obtaining the same equity value:

$$P\_0 = P \text{ER} \propto U \text{N}\_1 = 20 \propto \sharp 21' \text{7} = \sharp 4 \Im \mathfrak{F}' \text{9} \tag{8}$$

However, the use of the PER is made more frequently on the price per share, which initially results from dividing the Equity Value by the number of shares, which results in \$8.97/share.

$$\begin{aligned} \text{Price per share} &= \frac{\text{Equity Value}}{\text{Number of shares}}\\ p\_0 &= \frac{P\_0}{\#Acc} = \frac{\ $433'9}{48'4} = \$ 8.97/\text{Shares} \end{aligned} \tag{9}$$

The Equity Value formula could be expressed in the price per share by dividing the equity value and net income by the number of shares. Then the formula for the price per share based on the PER multiplier (20) times the earnings per share (\$0.448/ share) will be obtained, which will result in the same value of the price per share of \$8.97/share.

$$\begin{aligned} P\_0 &= PER \propto UN\_1 \blackrightarrow \frac{p\_0}{\#Acc} = PER \propto \frac{upa\_1}{\#Acc} \\ p\_0 &= PER \propto upa\_1 \\ p\_0 &= 20 \propto \ $0.448/shres = \$ 8.97/shres \end{aligned} \tag{10}$$

#### *1.8.3 The net income in the life cycle of a startup*

In calculating the Equity Value, it has been assumed that the Net Income of \$21.7 MM was in period 1 and from that period it grew at a rate of 3%, however, as can be seen in the **Figure 18**, In the initial periods there are losses in each annual exercise and then small profits until reaching a profit of \$21.7 MM in period 12.

Then the Equity Value determined previously is located in period 10 and not in the initial period 0. In the following Graph 14 it can be clearly seen that the update of the

**Figure 18.** *Net profits updated at present value. Source: Prepared by the author.*

series of net profits that begins with UN <sup>11</sup> of \$21.7 MM, generates a Present Value in period 10 (PV 01) of \$433.9 MM.

This Present Value at period 10 will be the Financial Value of the Shareholders' Equity, which will be related to the rights of the shareholders for that period. Once the business and equity have been valued, this value can be expressed in period 0, for which they must be updated together with the investments made up to the time of valuation (period 10) and thus have the value of equity in the initial period.

However, this financial value of the equity (located for the example in period 10), which is shown in **Figure 19**, is usually used to determine the right of the different shareholders that are added to the company, such as the initial promoters, venture capital funds, among others.

### *1.8.4 The life cycle and valuation by discounted cash flows*

The discounted cash flow valuation method begins with the determination of the projected economic flows of the business, which unite the investment flows in fixed assets and in contributions -or increases in working capital-, as well as the cash flows that are observed in **Figure 10**.

As can be seen in **Figure 20**, the economic flows are negative until period 9 and then they become positive and gradually grow until their growth rate decreases in the maturity stage, thus following the development of the business life cycle. This extended period of the business development stage corresponds to disruptive innovation businesses; however, in each case they can be varied periods. As can also be identified in the previous economic flow, the first investment to be made is \$12.3 MM and if we assume that the valuation will be carried out after having made this first capital contribution, we would have that the opening General Balance would be established with this investment and economic flows would be expected to occur from period 1 onwards.

Once the investment has been made, the financial value of the equity will be determined by updating the economic flows at a discount rate that in most cases is the

*Financial value of the equity (located for the example in period 10). Source: Prepared by the author.*

**Figure 20.** *Economic flow. Source: Prepared by the author.*

weighted average cost of capital<sup>6</sup> (Ko), which in this case is 12%, as it can be seen in **Figure 21**. Initially we will assume that the economic flows reach period 20 to later incorporate the effect of perpetuity. Thus, using the formula of the Net Present Value of Excel, where the economic flows and the discount rate are incorporated, the Present Value of the economic flows will be determined.

$$\text{VP Economic Flow} = \text{VNA} \left( \text{Ko}, \text{FE}\_1 \text{FE}\_2 \text{FE}\_3 \dots \dots \dots \dots \text{FE}\_{19} \text{FE}\_{20} \right) \tag{11}$$

From the extract of the spreadsheet presented in **Figure 22**, it can be verified that the Present Value of the economic flows between the periods 1 to 20 is \$54.5 MM, which will be located in the initial period 0. This value represents the net value of the update of all flows up to period 20.

Consequently, as shown in **Figure 23**, it will be necessary that the flow of the business throughout its life cycle is producing a value of \$54.5 MM greater than the initial investment of \$12.3 MM, which establishes the possibility of generating added value over the initial investment.


#### **Figure 21.**

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

<sup>6</sup> Since the startup is assuming no debt, the weighted average cost will be the shareholder opportunity cost of capital.
