**1.4 The relationship between the income and the projected costs and expenses**

After projecting income, the evolution of costs and expenses must be projected, concepts that are closely related, because although they do not vary perfectly

**Figure 5.** *Sales and income. Source: Prepared by the author.*

#### **Figure 6.**

*Income, costs and expenses. Source: Prepared by the author.*

proportionally, costs and expenses evolve in the same direction as income. On the one hand, fixed or semi-fixed costs will have to be projected, which have a stable behavior for a period of time, but grow over time with the increase in the company's capacity; on the other hand, there are variable costs that do evolve proportionally to income.

The projection of the expenses shows a behavior similar to the semi-fixed costs, the projection of the depreciation -or amortizations- is also carried out,<sup>2</sup> which will depend on the investments made in the development stage and the additional investments in fixed assets. In **Figure 6** it can be seen that in several periods -from 4 to 8- costs and expenses are greater than income despite the fact that the company has sales. This happens, because to achieve sales targets, the company must have a production capacity prepared to support growth and an organization that drives sales so that revenue forecasts are met. This means that initially the income cannot cover the costs until a certain moment in which the break-even point is achieved. It is expected that, from then on, revenues will grow at a higher rate than costs and expenses.

#### **1.5 The profit projection**

To project the profits, the Income Statements are built in the valuation horizon, as shown in **Figure 7**, finding the difference between the Income and the Costs and Expenses, which will result in the projection of Profit Before Taxes for each period. If this is positive, then the income tax is calculated, which the company must pay to the treasury, in the corresponding period; if it resulted in a loss then the tax would not be paid in that period.<sup>3</sup>

<sup>2</sup> Depreciation corresponds to tangible fixed assets, while amortization corresponds to intangible fixed assets.

<sup>3</sup> A loss can be used as a credit for future income tax payments, this benefit is regulated according to the tax legislation in each country.


#### **Figure 7.**

*Statements of Income. Source: Prepared by the author.*

As previously seen, between periods 4 and 8 costs and expenses are higher than sales revenue; consequently, it will be observed that there will be losses in each of these periods. Subsequently, in period 9, the income manages to exceed costs and expenses and there is a growth in profits following the pattern of the business life cycle; that is to say, that there is a notable growth rate in the growth stage and then it slows down until it has a more modest rate in the maturity stage, as see in **Figure 8**. In these periods of profit before positive taxes, the corresponding income taxes will be paid.

It is highly probable that, in the initial stage of the company, losses will be obtained by not obtaining sufficient income to cover its costs and expenses; however, a situation of losses could be maintained for a long time, since an organization is still proportionally large for the initial income. This scenario will be reflected in the need to make additional investments to sustain the business until the moment where profits are achieved (*break-even point*) and then have a surplus cash flow, where income is greater than expenses; which is generally achieved in the final stage of growth and especially in the stage of maturity. According to Tsorakidis, et al. Break-Even Point is

**Figure 8.** *Profit. Source: Prepared by the author.*

determined as the point at which total sales revenues are equal to total expenses (both fixed and variable). That is, it is the point that corresponds to this level of production capacity, under which the company operates at loss [2].

In the company valuation process, having an overview of the evolution of profits is important because it allows identifying the representative profit that will be used in the net profit valuation method, which will be explained later.

### **1.6 The projection of the economic cash flow**

The other most widely used method for company valuation is the discounted cash flow method, which consists of updating the company's projected economic flows. To build the economic flow, the company's operating cash flow, investments in fixed assets and investments in working capital must be projected. The operating cash flow is the difference between income and expenses of each period, where the income is the same as that which has been considered in the Income Statement, similarly the expenses are the costs and expenses of the same financial statement, with the difference that the cash flow does not consider the depreciation or amortization of tangible or intangible fixed assets, as appropriate. The operating cash flow is subtracted from the investments in fixed assets and working capital that are made in the first periods from 0 to 3- and the additional investments that are projected to be executed in the operational stage of the company. These last investments are necessary to support the growth in sales, since they imply increasing the capacity of fixed assets and a greater contribution of working capital to finance higher costs and expenses of incremental sales. The structure of the economic flow can be seen in **Figure 9**.

In **Figure 10**, you can see the preoperative stage where only investments are made—period 0 to 3—; subsequently, the operational stage begins with the first sales, but for a period of time—from 4 to 10 it is not possible to have a sufficient operating cash flow to finance investments in fixed assets and investments in working capital; finally, the stage is reached where the cash flow is surplus and therefore can cover the necessary investments.

In the economic cash flow of the previous Graph, it can be seen that there is an extensive period of negative economic flows that represents investments to be made, and from period 11, positive economic flows are obtained that grow in the same configuration as the cycle of life of the business or sales, which from a stage of growth


**Figure 9.** *Economic flow. Source: Prepared by the author.*

**Figure 10.** *Projection of the economic flow. Source: Prepared by the author.*

passes to a stage of maturity. This process is important, since it indicates that in the end the cash flow will have a value that grows at a moderate rate, important data for the treatment of perpetuities in the valuation process.
