Capital budgeting and valuation of investment decisions

1.1 Capital Budget

Capital budgeting decisions are one of the deciding factors for the success or failure of the business. A number of factors combine to make capital budgeting decisions perhaps the most important decisions financial managers must make.

capital-budgeting-and-valuation-of-investment-decisions

First, due to the fact that the results of capital decisions continue for many years, the decision maker loses some of their flexibility.

Timing is also an important consideration in capital budgeting, as Capital Assets must be ready to go when needed.

Finally, capital budgeting is also important because Asset expansion typically involves very large expenses, and before a business can spend a large amount of money, it must have sufficient funds available. Two examples of capital budgeting decisions:

Example 1. The Ford Motor Company decided in 1955 to launch a new car model: the Edsel. It was powerful, elegant, and well-equipped. Ford invested $ 250 million in the new model and it was launched in September 1957. Although the investment amount was a record capital investment for a consumer product, the Edsel was still fraught with problems. Not only did it have a tendency to stall, but its chrome, power, and equipment attracted more attention than customers. Only after two years of its appearance was the Edsel withdrawn from the market. It was one of the big mistakes in the evaluation of companies' projects. In addition to its initial investment, Ford lost more than $ 200 million during production, about $ 2,000 for every vehicle sold.

Example 2. Boeing decides to develop the model 757 and 767 aircraft. Boeing's investment in these aircraft was $ 3 billion, more than double the total value of its shares, according to the company's accounting at the time. By 1995, the estimated cumulative returns on their investment exceeded $ 6 billion, and the planes were still selling well. In 1996 Boeing had profits of 1.8 billion dollars, but in 1997 it had losses of 178 million dollars.

How to measure the success of a capital budgeting decision? It is measured in terms of value. Good investment projects have more returns than cost. The realization of good projects increases the value of the company, and consequently, the wealth of the shareholders.

Today's investment provides future earnings. Note that the finance manager is not only interested in the volume of profits, but also in when he expects to receive them. The sooner the return on investment, the better. But, note that these returns are rarely known with certainty: a new project could be a great success, but it could also be a tremendous failure. The finance manager needs a method to assign a certain value to these uncertain future earnings.

Sources of funding:

• Own resources: Own capital, includes contributions from owners and shareholders and, funds generated by the company that accumulate in the reserve accounts.

• Outside resources:

• Negotiated payable: Debt. Example: Banks, bonds and bonds.

• Spontaneous enforceable: Generated as a consequence of business activity: suppliers for example. They appear automatically. Not considered in this analysis.

1.1.1 Capital Budget and Strategic Decisions

The information needs required within the organization vary according to the level within the organizational structure. The decisions of senior executives or general directors are less structured in the sense that there are no repetitive situations and therefore no single solution recipes can be applied; on the contrary, evaluation criteria and points of view must be established for each situation where much of the data is inaccurate and must come from external and subjective sources in environments with risks and uncertainty. Because it is impossible to determine and control all the variables or factors that affect a situation,is that it is sought through models to represent reality for analysis in which it is expected that the decisions made are satisfactory and not optimal decisions within the context of rationality of who should make decisions (Bounded rationality). The decisions that executives make will be deployed at all levels of the organization translated into more specific and concrete objectives and actions at each level down to the lower levels. The information required in all these decisions represents the starting point to carry out actions that will ultimately affect the performance of the organization.The decisions that executives make will be deployed at all levels of the organization translated into more specific and concrete objectives and actions at each level down to the lower levels. The information required in all these decisions represents the starting point to carry out actions that will ultimately affect the performance of the organization.The decisions that executives make will be deployed at all levels of the organization translated into more specific and concrete objectives and actions at each level down to the lower levels. The information required in all these decisions represents the starting point to carry out actions that will ultimately affect the performance of the organization.

Information -> Decisions -> Actions -> Organizational Performance

The purpose of the performance of any organization is to Create Economic Value, and is therefore the ultimate overall objective that every managerial decision must achieve. Executives, according to the Agency Theory, are agents entrusted by a principal or owners to make decisions for themselves in order to improve profitability and value creation. However, these decisions are subject to controversy, given that executives also have other interests not related to the purely financial aspect such as leisure time, flexibility at work, etc. On the other hand, these are also more risk-averse compared to the owners, since they put their position at stake, since there are no alternative activities as a way to diversify the risk in the event that a bad decision compromises their work.This same situation occurs in intermediate dependency relationships from a senior management executive to an executive from a specific unit. From the above it follows that there is a problem of interests called the agency problem and is accentuated when the information is asymmetric and there is no way to verify the agent's behavior. This occurs when the executive handles information that his superior does not know, which can lead the executive to manipulate the information or make decisions that are not satisfactory for the principal but satisfactory for him as an agent, which is called Moral Risk.that there is a problem of interests that is called the agency problem and is accentuated when the information is asymmetric and there is no way to verify the agent's behavior. This occurs when the executive handles information that his superior does not know, which can lead the executive to manipulate the information or make decisions that are not satisfactory for the principal but satisfactory for him as an agent, which is called Moral Risk.that there is a problem of interests that is called the agency problem and is accentuated when the information is asymmetric and there is no way to verify the agent's behavior. This occurs when the executive handles information that his superior does not know, which can lead the executive to manipulate the information or make decisions that are not satisfactory for the principal but satisfactory for him as an agent, which is called Moral Risk.This can lead the executive to manipulate the information or make decisions that are not satisfactory for the principal but satisfactory for him as an agent, which is called Moral Risk.This can lead the executive to manipulate the information or make decisions that are not satisfactory for the principal but satisfactory for him as an agent, which is called Moral Risk.

Bad decisions destroy value and it is most evident in small organizations that have fewer accumulated resources and capabilities to support a loss in economic value. Good value-creating businesses are the result of good decisions and the efficient and effective use of resources and capabilities. Thus, a small company that does not have accumulated resources or capacities can achieve good business only by having made good decisions.

Good Business = Good Decisions + Resources and Capabilities

This includes the approach of Robert Grant (1991) and Paul Schoemaker (1991) called "Competitive strategy based on capabilities and resources" as a way to solve the generic strategies of Michael Porter that were static assuming a little changing industry. Currently, strategies must be based on resources and capacities difficult to imitate

Resources are those tangible and quality resources that the company has accumulated over the years and that generally have physical form and can be counted and given an economic value. In the analysis of the competition they are important, since they allow direct comparisons of the Assets of the competition.

The capabilities of an organization is the result of being able to develop and coordinate resource teams working together. In other words, it is "the collective knowledge existing in the organization on how to coordinate skills and integrate technologies with resources." These capabilities differ from Assets in that they are not tangible and are embedded within the culture, systems, and procedures of the company that cannot be negotiated or imitated. One of the useful tools to detect the capabilities of an organization is the Porter Value Chain.

Due to the dizzying globalized environment, less regularized, with more demanding clients and greater competencies, good decisions cannot guarantee good results in the future permanently, but they are a possible protection against bad results.

Because the creation of value is the ultimate objective of any decision and the result of many factors, as intermediate objectives to the creation of value are to achieve sustainable competencies over time in each of the businesses and in the functional aspect to promote competencies essential in internal activities. The latter refers to enhancing the capabilities of the intangible assets of each company that cannot be imitated by others.

This discards the traditional idea of evaluating performance in purely financial terms, which is of greater interest to the owners since profitability is a retrospective result that communicates what has been done in the past. The new decisions must be the result of a process that must also consider a perspective towards the future and the environment, attending not only the interests of the owners but also considering the present interests of the clients, learning within the organization taking into account it counts the intellectual capital and the efficiency of the internal processes with customer orientation. In this way, the causal factors that affect the financial result will be taken into account.

The decisions that an executive carries out in the senior management of a company or in the different units of an organization will be called Managerial Decisions.

Managerial Decisions can be classified from a management point of view into two types: Planning Decisions and Management Control Decisions. This is due to the fact that a director or executive mainly makes decisions in terms of planning (What is going to be done?) And a little less in control within the administrative process (Is the planned being done?). Planning and control functions are closely linked today due to the cyclical nature of the process, the dynamic environment and the adaptive nature of the organization. Management Control Decisions are at an intermediate point between Planning Decisions and Operations Control Decisions, since the latter must ensure the efficiency and effectiveness of individual tasks according to the implementation of the strategy.From here on, management control decisions will be called Control Decisions as a way of simplifying their name, since operations control decisions are oriented to transactions that require very little participation from directors because they are mostly systematic, with exact and specific data where it is possible to automate and use scientific tools (Example: numerical control for optimization, inventory control, etc.).with exact and specific data where it is possible to automate and use scientific tools (Example: numerical control for optimization, inventory control, etc.).with exact and specific data where it is possible to automate and use scientific tools (Example: numerical control for optimization, inventory control, etc.).

Due to the importance of strategy in this new environment and the commitments emanating from it throughout the organization, planning decisions are circumscribed mainly in the process called Strategic Planning, which is a systematic process where objectives are defined and they formulate the corresponding strategies to achieve it (What to do?); Long-term action programs are specified with the corresponding allocation of resources (How to implement them?). Planning decisions will be called Strategic Decisions when they are determined in the Strategy Formulation process where the objectives for the organization and the strategies to achieve them are defined, these have the property of being mostly proactive decisions,tending to delineate the future or establish a desired situation; On the other hand, Control Decisions are rather reactive in nature and tend to anticipate a future problem indicated by a reference indicator or, in the worst case, take corrective actions in response to a problem that has already occurred. In control decisions there is a detector (Measure) that stimulates an evaluator (Executive) to carry out an action. Control Decisions will also be called Strategic Control to the extent that there is a strategy linked to it.In control decisions there is a detector (Measure) that stimulates an evaluator (Executive) to carry out an action. Control Decisions will also be called Strategic Control to the extent that there is a strategy linked to it.In control decisions there is a detector (Measure) that stimulates an evaluator (Executive) to carry out an action. Control Decisions will also be called Strategic Control to the extent that there is a strategy linked to it.

However, Strategic Decisions can also be reactive, especially when they arise from unforeseen changes in the environment. When this happens and planning is carried out to face the changes, it is called Opportunistic Planning. The normal case when it is scheduled and carried out with a certain periodicity is called Formal Planning. Both are necessary to maintain the viability of the organization since opportunistic planning appears when problems have not been anticipated by formal planning.

The decisions taken in both areas derive different results and actions. Strategic decisions are not systematic, they arise in response to the environment, they are more long-term with more inaccurate data for the future, and they are represented in a Strategic Plan that describes how the strategy will be implemented, these are also expressed quantitatively through of a Budget.

The formulation of strategies requires a creative and innovative character for the executive ("You have to compete less, you must win the battle first"), it is not systematic, it derives from the conclusion of the analysis of the threats and opportunities in the environment, therefore it can come from any source and at any time.

Management control decisions, on the other hand, are represented in an Action Plan that has less scope and is more specific where a specific problem must be solved with a shorter response time. A corrective action plan in response to a problem requires previously the specification for each objective of adequate indicators and goals where it is necessary to measure, analyze and diagnose the cause of the problem and then select an adequate corrective action from among alternatives.

Table 1.1. Differences between Strategic and Management Control Decisions

Administrative Tools for strategic planning to support strategic decisions:

- Industry attractiveness analysis (Five Competitive Forces by Michael Porter).

- Internal analysis of the Value Chain of Michael Porter.

- SWOT Analysis (Strengths, Weaknesses, Opportunities, and Threats) or SWOT Analysis (Strengths, Weaknesses, Opportunities and Threats), SWOT Matrix.

- Boston Consulting Group (BCG) Matrix for business portfolio, Attractiveness Matrix.

- Forecasts (Analysis of time series, causal methods)

- Budgeting (Based on standards, Monte Carlo simulation).

- Market studies.

- Process reengineering.

- SixSigma.

- Total Quality (TQM Total Quality Management).

- Decision trees and payment matrix.

- Simulation.

- Statistical Analysis (Example: Regression Analysis –Regression Analysis-, Variance Analysis –Anova-).

- PERT and CPM programming.

1.1.2 Capital Structure of the Company

The optimal capital structure is one for which the cost of capital is minimal: if the company is financed with this debt / equity ratio, the market value of the company will be maximum.

The optimal ratio of the financing structure e = Debt / Equity in practice is difficult to determine. In general theoretically, financing projects with debt whose economic profitability is higher than the cost of the same project will increase the shareholder's profitability by that difference (based on the margin between the investment profitability and the cost of the debt).: You have to see the project independently of the rest of the company's projects.

This approach, however, considers only the explicit cost of debt, that is, that derived from comparing the income and disbursements originated by the indebtedness.: There are other costs apart from the explicit one, which reduces the profitability of that project or even is negative.

But the ability to borrow is not unlimited since if we go into debt now, we will have to opt for more expensive debt or own financing in the future. Therefore, debt has an implicit cost: financing yourself with debt today may mean having to give it up in the future. This is related to the formulation of the capital budget according to which the financing of a project has to be studied within the framework of the general and future situation of the company. That is why we speak of the weighted average cost of capital when comparing with the profitability of a project: the project must be considered as integrated into the company and not in isolation. You have to take all the debts of the company and find the weighted average cost to compare.

1.1.3 Practical Problem of Capital Budgeting

An extra component of the implicit cost is given by the greater risk involved.

EXAMPLE: A company needs 20 million. These funds can be obtained:

• Capital increase to 200%. If the par value of each share is US $ 1,000 AND if they are issued at 2,000, it will be necessary to sell 10,000 new shares.

• Hiring a loan for repayment in 5 annual installments and with a cost of 14% on the outstanding balance each year.

Once the investment is operational, it is estimated that the company's annual profit before interest and taxes (EBIT) will range between 10 and 23 million, with the most probable value being 16.

The following table calculates the relationship between earnings per share and EBIT for each of the two alternatives in the first year of exploitation of the investment.

Relationship between EBIT and Earnings per Share

Indeed, for the example described in the table the following data is obtained:

For the same variation in EBIT, earnings per share fluctuate more in the case of debt financing. As a consequence, the positive leverage effect has as its counterpart the introduction of greater risk: variations in EBIT have an amplified impact on earnings per share. That is, the variability of the shareholder's profitability and, therefore, its risk, grows with the debt. Another component of the implicit cost is the need to obtain higher EBIT in the case of financing with debt, due to the need to meet the debt commitments.: EBIT must be high enough if we have a debt to cover the interest on it.

Financing with an extension, if EBIT> 0, shareholders will already obtain a positive return.

But financing with debt also has advantages: in general, the cost of debt is lower than that of own resources:

• Interest is tax deductible.

• The risk assumed by the lender is lower than that of the shareholder and the risk premium will be lower: The company has to give more profitability to the shareholder plus the risk premium.

• The debt does not affect the control of the company.

• The debt is more flexible than the contributions of the partners since they will always have to be remunerated, while the debt has an expiration date.

• Debt is easier to come by than shareholder contributions.

1.2 Investment Decisions

1.2.1. Current value

1.2.1.1 Net Present Value.

The Net Present Value (NPV) is based on the Discounted Cash Flow (DCF) technique. Its implementation consists of several steps. First, the Present Value (VA) of each flow must be found, including both inflows and outflows, discounted at the cost of the project's capital. Second, these flows must be added to obtain the NPV of the project under study.

If the NPV is positive, the project should be accepted, while if it is negative it should be rejected.

A NPV equal to zero means that the project's CFs are just enough to repay the invested capital and to provide the required rate of return on that capital. If a project has a positive NPV, then it will be generating more cash than is needed to repay its debt and to provide the required return to shareholders, and this excess cash will accrue exclusively to the shareholders of the company. Therefore, if the company takes a project with positive NPV, the position of the shareholders will be improved.

1.2.1.2. Internal Rate of Return (IRR)

The IRR is defined as the discount rate that equals the VA of the expected inflows of a project with the VA of its expected costs (be careful with the definition as it does not coincide with the one proposed by the chair - Professor Alonso).

VA inflows = VA investment costs

Note that the IRR formula is simply the NPV formula, solved to obtain the particular discount rate that makes the NPV equal to zero.

Mathematically the NPV and IRR methods will always lead to the same acceptance decisions, in the case of independent projects. However NPV and IRR can lead to conflicts when applied to mutually exclusive projects.

If the IRR is higher than the cost of the funds that were used to finance the project, a surplus will remain after the principal has been paid, and that surplus will accrue to shareholders. It is precisely this breakeven characteristic that makes the IRR useful when evaluating capital projects.

1.2.1.3. Comparison of the methods. Relationship between the Net Present Value criteria and the Internal Rate of Return (NPV v. IRR)

These are complementary criteria that assess investment projects based on their profitability, measured both in absolute terms (NPV) and in relative terms (IRR).

The solution proposed by each of these two criteria before the decision to accept or reject an investment project is identical on some occasions, as is the case of investments whose cash flows have a simple or conventional structure. However, the results may be different when establishing an order of preference between several alternative projects or also when analyzing investments that do not have a conventional structure.

In the following sections, a comparative study is carried out to establish the differences between NPV and IRR under the following circumstances:

- Reinvestment of cash flows

- Conventional and independent

projects - Conventional and mutually exclusive

projects - Unconventional projects

That graph that relates the NPV of a project with the discount rate that has been used to calculate said value is defined as the profile of the net present value of a project.

To build it, we must note that at a discount rate of zero, the NPV is simply equal to the total of the project's undiscounted CFs. These values are graphed as the intercepts of the vertical axis. Next, we calculate NPVs at different rates and these values are plotted. The point where the profile of your NPV crosses the horizontal axis will indicate the IRR of a project.

By arranging the data points, we obtain the NPV profiles

Graph 5.1.

There are two basic conditions that can cause the profiles to cross e / yes and consequently lead to conflicting results e / NPV and IRR: 1) when there are differences in the size (or scale) of the project, which will mean that the cost of one project is higher than the other or 2) when there are differences in opportunity, which will mean that the opportunity of the CFs from the two projects will differ in such a way that most of the CFs of a project are presented in the first years and most of the CF's of the other project are presented in the final years.

The NPV method implicitly assumes that the rate at which cash flows can be reinvested will equal the cost of capital, while the IRR method implies that the company will have the opportunity to reinvest at the IRR.

1.2.1.4. Conventional and mutually exclusive projects

On many occasions, companies are faced with mutually exclusive projects whose acceptance prevents the realization of other alternatives. Each criterion can establish a different hierarchical order and, therefore, the decision to be made depends on the model chosen for the evaluation of the projects.

The analysis of exclusive projects presents a different problem depending on whether the projects are homogeneous or not. If they are homogeneous, then they are directly comparable and if not, it is necessary to homogenize them.

Homogeneous projects are those that have the same initial disbursement and the same time horizon. When the investor is faced with mutually exclusive projects, then he must establish an order of preference among them to choose those that are more convenient.

The NPV and IRR criteria do not always lead to the same decision. In this way, in some situations the assets with a higher NPV are those that offer a higher IRR, but in other cases this is not the case. This depends on how the respective functions of the NPV evolve in relation to the cost of capital.

Let two investment projects A and B have homogeneous characteristics and such that NPV (A)> NPV (B) when the cost of capital K = 0. Suppose that the NPV functions of both projects intersect at a point F, called point Fisher's intersection or Fisher's rate.

Figure 5.2: Fisher's rate of intersection

The hierarchical order of projects determined by the NPV and IRR criteria depends on the relationship between the cost of capital used as the discount rate and the Fisher rate. In some cases, when the investment projects do not meet certain conditions, we can find that the NPV functions present two or more Fisher intersection points or, alternatively, there are none. The hierarchical ordering between projects will depend on the relationship between the cost of capital and the Fisher rates.

The discrepancies in the hierarchical ordering of investment projects according to the NPV and IRR criteria can be explained, in part, by the different hypotheses in relation to the reinvestment of cash flows.

When we are studying mutually exclusive investments or investments that compete for a limited capital budget it is necessary to make a comparison between alternative investments.

In order for investments to be comparable, they must be homogeneous or, if they are not, they must be homogenized. The evaluation of non-homogeneous investments presents an additional problem to that of the homogeneous case, given the existing difficulty in comparing projects with different characteristics and therefore in establishing an order of preference between them.

The investment decision making in this case must start from the homogenization of the different alternative items as a previous step to the use of an assessment criterion.

The non-homogeneity may be due to differences in the size of the investment, differences in the cash flow profile and / or differences in the time horizon.

a) Differences in the size of the investment

The decision is problematic for mutually exclusive projects. Carrying out project A implies the allocation of fewer resources and a higher IRR, while carrying out project B implies the allocation of greater resources and a lower IRR. Ultimately the decision will depend on what the cost of capital is.

The way to make the decision is to estimate what the Fisher rate is by equating the NPV of the two projects and solving for the discount rate. For discount rates lower than the Fisher rate, project B will be chosen, and for discount rates higher than the Fisher rate, project A will be chosen.

-600 + 900 / (1 + K) = -8000 + 10000 / (1 + K) -> K = 23%

b) Differences in the cash flow profile

There are projects that have the same initial outlay in which the decision to make also depends on whether the NPV or the IRR is used to select the investment. These are cases in which cash flows present different profiles.

The following example shows two investment projects C and D, mutually exclusive, and whose cash flow profile is different

. Again, the solution is to estimate the Fisher rate and graphically represent the results obtained.

NPV (C, K) = NPV (D, K) -> K = 13.3%

Therefore, for discount rates lower than 13.3%, project C has a higher NPV than project D and, therefore, C will be chosen. For discount rates above 13.3%, project D will be chosen up to a maximum rate of 18%. From 18% no project will be selected.

c) Differences in the time horizon of the projects

The selection of investments poses a new problem when it comes to ordering projects that have different time horizons. In this case, the NPV and IRR criteria do not offer a clear solution. Thus, carrying out the longest project supposes an immobilization of resources for a longer period, while if the shorter-lived one is chosen, it is not possible to know in advance the profitability that the company can obtain from the resources generated since its end. useful life until the end of the longest project.

An alternative is to standardize the project durations considering a common investment time horizon that is obtained by repeating one or both projects the number of times necessary to obtain the least common multiple. Another alternative is to consider an unlimited investment horizon for both projects.

For example, let projects E and F have different useful lives.

Suppose that project E can be repeated until a time horizon of four years is reached. This would make it possible to compare projects E 'and F.

Once the time horizon has been homogenized, in this case, it coincides that the best project is E 'since it simultaneously has a higher NPV and a higher IRR. However, the question that arises is whether it is really possible to proceed with the reinvestment of the projects.

1.2.2. Risk, Return and Opportunity Cost of Capital

As indicated in previous chapters, one of the ratios that evaluates the profitability of the shareholder for their investment in the financing of the company is that of the financial profitability (ROE) or profitability of equity, which is obtained by dividing the Net Profit (UN), which will be calculated after taxes, among the own resources used during the year. That is to say:

ROE = UN / RP = (UN / AN) (AN / RP) = (UN / AN) ((RP * D) / RP)) =

= (UN / AN) (1+ (D / DRP))

AN = Net Assets, which is broken down into equity (RP) and debt (D)

r = average interest rate applied on the company's debt

t = tax rate on profits

ROI = economic profitability or return on investment

e = ratio debt or relationship between receivables and equity = D / RP

UN = (UAII - iD) (1 - t); where iD is the cost of Debt

Substituting:

SWR = ((UAII - iD) / AN) (1- t) (1+ (D / RP)); where D = e

ROI = UAII / AN

Substituting:

ROE = (ROI- (iD / AN)) (1-t) (1 + e)

AN = RP + D; e = D / RP D / AN = e / (1 + e)

Substituting and simplifying:

The ratio between debt and equity (e) has an impact on shareholder profitability (ROE):

• The first term in the bracket indicates that as debt increases, ROE is amplified, since equity will be lower: Yes and ROE.

• The second term in the bracket indicates that as there is more debt, the interests to be paid will be higher, therefore the company's financial profitability (ROE) will decrease.

• As the debt ratio increases (e), the interest rate will probably also (i), due to the greater financial risk that the company will bear (because we are financing more externally)

Thus, the final dominant effect will be a decrease or increase in the ROE.

What does it depend on whether the ROE increases or decreases? ROI (Yield) and discount rate r.

According to the formula, while the cost of the debt is lower than the economic profitability, a higher debt increases the financial profitability of the company. According to, while ROI> r, if e ROE.

But, it is unlikely that the new receivable will be paid at the same i, therefore it would be more convenient to compare the weighted average cost of financing the company (including the new debt) with the ROI of the firm if it started the project.

In summary, the ROE of the company depends on the effectiveness with the management of its investments (ROI); the tax rate (t) and the financing policy adopted (e).

The problem in this area of finance is to determine the most appropriate ratio between Debt and Equity. To compare different financing structures with each other, the weighted average cost of capital criterion is applied, among others: between two financing alternatives, the one with the lowest cost of capital will be chosen.

Example: suppose a company without debt and whose shareholders demand a minimum return of 12% on their investment. Let your trading account be the one summarized in the following table:

Since the Net Profit corresponds to the shareholders and they apply a capitalization rate of 12%, the market value of the equity is obtained by applying the formula of a perpetual income, amounting to 390 / 0.12 = 3,250

The average cost of capital K0 before taxes will be 18.46% calculated by:

K0 = EBIT / (Debt + RP) = 600 / 3,250

That after taxes it is reduced to 12%, which logically coincides with the cost of the RP, as these are the totality of the financing.

If the company can substitute its own resources (RP) for debt, and if its cost is, for example, 10%, it will be able to reduce its average cost of capital, since it will replace resources that it has to remunerate at 12% per others cheaper, which only require 6.5% after taxes. If the cost of capital K0 decreases, the valuation of the company will increase accordingly, since the profit will be capitalized at a lower rate.

Suppose RP is replaced by the equivalent of 1,000 currency units of 10% debt. If the shareholders do not consider the higher financial risk significant, the cost of equity, KE, will remain constant, that is, the expectations of the shareholders will not vary in terms of profitability.

The following table shows the consequences of this greater indebtedness.

With the same investments, the market value of the company is higher than in the previous situation (14.1% higher).

Consequently, the weighted average cost of capital or capitalization rate of profit amounts to 16.18%, according to the quotient:

K0 = EBIT / Company value = 600 / 3,708

and therefore, K0 = 16.18 (1 - 0.35) = 10.52%

This value is also calculated by weighting the cost of debt and equity, based on their participation in the total financing, according to the formula:

K0 = / 3.708

Therefore, it is advisable to increase the proportion of debt, since in this way the weighted average cost of capital is decreasing. However, this increases the financial risk of the company, that is, the variability of its profit and the possibility of not being able to satisfy the disbursements originated by the debt. Therefore, as the company gets into debt, the shareholders will perceive a greater risk and, consequently, will demand a higher return. In this way, the higher cost of equity will offset the positive effect induced by the higher share of debt at a lower cost. But even the interest rate will also increase from a certain level of debt. Indeed, the greater share of debt, in relative terms, will make it riskier to lend money to the company. To do it,the lender will ask for an increasing interest with the level of financial risk.

If in the example it is assumed that the debt reaches the figure of 2,000 NS, the calculations are modified according to the following table, where it is considered that, according to the reasoning in the previous paragraph, KE becomes, for example, 15% and the average cost of debt 13%.

The capitalization rate of the profit amounts to the situation before, after taxes, it gives the cost of capital of the company

K0 = 600 / 3.473 = 17.28%

K0 = 17.28 x (1 - 0.35) = 11.23

Therefore, after the initial positive phase, as the proportion of debt increases, the cost of capital increases as a consequence of the higher financial risk, which induces shareholders and lenders to demand a higher return on their investment. Now the effect is negative, that is, the increase in the debt share reduces the market value of the company.

1.2.3 Methods of Evaluation of Investments under Conditions of Certainty

1.2.3.1. Classic criteria for the evaluation and selection of investment projects

Given that we are evaluating investments under certainty conditions, we are going to list the starting assumptions:

- Collections and payments are known with total certainty.

- There is a perfect capital market in such a way that there is a single interest rate to invest and borrow without any limitation.

- The investment projects do not maintain any dependency relationship between them, that is, they are independent.

- Investment projects are perfectly divisible and the company can invest any amount of money in a project, no matter how small.

- Only investment opportunities existing at the present time are considered and not those that may potentially occur at future times.

- An economic situation of price stability is assumed (absence of inflation) and a tax system that does not tax the profits of the companies.

- Within the classic investment criteria we can distinguish between static models and dynamic models.

1.2.3.2. Static Models. Recovery Period

Static models are those models that do not take into account the chronology of cash flows. They value cash flows as if they were all referred to the same moment in time.

A static model is the payback period for an investment, defined as the period of time required for the cash flows generated by a project to equal the initial outlay.

In other words, it is the term, P, necessary to recover the amount invested, A.

In the event that the investment cash flows are constant and equal, the payback period is calculated as P = A / Q.

The application of this method to investment decisions involves the need to define a maximum payback period in such a way that those projects with a longer payback period are rejected and those with a shorter payback period are accepted.

1.2.3.3. Dynamic Models: the Net Present Value and the Internal Rate of Return.

The dynamic models make use of the concepts of NPV and IRR, which have already been studied previously.

Examples.

A company is presented with two investment alternatives.

Assuming an Income Tax Rate = 30% and WACC = 10%

Alternative A

I = 6,000 + 2,500 + 1,500 = 10,000 - Amortization = 3,333 per year

FC (annual) = Sales - Costs - (Sales - Costs - Amortization) × t =

FC = (0.57 / u - 0.23 / u) × 50,000u - 3000 - (14,000 - 3,333) × 0.3 = 10,800

Payback period = I / Q = 10,000 / 10,800 / annual = 0.9259 / annual = 11.11 / month

NPV (alternative A) = -10,000 + 10,800 A3 -10% = 16,858

A3-10% = 2.4868

Alternative B

I '= 4,500 + 3,000 + 1,000 = 8,500 - Amortization = 2,833 per year

FC = (0.61 / u - 0.39 / u) × 75,000u - 600 - 2,250 - (13,650 - 2,833) × 0.3 = 10,405

Payback period = I '/ Q = 8,500 / 10,405 / annual = 0.8169 / annual = 9.80 / month

NPV (alternative B) = -8,500 + 10,405 A3 -10% = 17,375.15

A3-10% = 2.4868

Comment: Investments A and B are not homogeneous since they do not have the same initial outlay.

1.2.3.4. Abandonment of some restrictive assumptions

We have previously analyzed the investment decision, simplifying it. This section introduces some additional elements that condition the investment decision, such as inflation, the effects of the term structure of interest rates and the possibility of capital rationing.

to. Project evaluation in an inflationary environment

Consideration of inflation has a significant effect on the investment decision. Thus, projects that have been accepted by the company may be rejected in an inflationary environment since the profitability of the projects is significantly reduced.

In addition, the priorities established in the management of mutually exclusive projects can be altered, with serious consequences for the decisions made by companies. In this way, the criteria used to assess the NPV and IRR projects must be adapted to these circumstances.

If inflation affects cash flows and the discount rate equally, there are two possibilities: either consider nominal cash flows and nominal discount rate or consider real cash flows and real discount rate.

The calculation of the IRR also becomes more complex. Sometimes the inflation of the receipts and the inflation of the payments is different so it may be necessary to differentiate between the two.

b. Consideration of the term structure of interest rates

So far we have analyzed investment decision making under the hypothesis that the cost of capital does not vary throughout the life of an investment project. If we consider the formation of different types according to maturity terms, the cost of capital of the company will vary from one period to another, so it will be necessary to adjust the definition of the selection criteria for NPV and IRR investments in light of this new circumstance..

Suppose that the capital costs for the different periods are represented by r1, r2,…, rn. Then, the NPV of an investment project will be calculated considering different discount rates.

NPV = -II + CF1 / (1 + r1) + CF2 / +… + CFN /

In situations in which the term structure of interest rates is a relevant aspect to take into account, it is advisable to be guided by the NPV, since the IRR criterion will not allow us to make a decision with clarity.

c. Selection of investments with limited resources

Most companies face capital limitations when carrying out their investment program, which prevents them from carrying out all the desired projects. In the case of independent projects, the decision will be made once the different assets have been ranked according to their highest NPV or IRR. In the case of projects, the budget will be allocated to those that present a higher profitability.

The need that companies face entails the need to plan their investment decisions over a long time horizon in which there are various restrictions. In these circumstances it is necessary to use techniques such as mathematical programming.

1.2.4 Methods of Evaluation of Investments in Conditions of Risk and Uncertainty

Until now, the investment analysis has been carried out under the hypothesis that the company was capable of estimating with certainty the expected cash flows generated by the different investment alternatives.

The decision models in certainty assume that the decision maker possesses complete information and is therefore capable of assigning a unique value to each alternative course of action. However, it is difficult to know precisely the future of an investment Decision-making must, therefore, be carried out with incomplete information and the estimates made may change over time due to a series of external circumstances, unrelated to the project, but which condition the results of it.

Most investment projects are presented under conditions of risk or uncertainty. It is possible to distinguish between an investment in risk or in uncertainty based on the amount of information that we know about said investment. In practice, if we know the states of nature and the probability associated with them, we will be facing a case of investment at risk and if we only know the states of nature but not the probabilities, then we will be facing a case of uncertainty.

1.2.4.1. Information required for the evaluation of investment projects with risk

Faced with an investment decision, the company is faced with different alternative action resources. In certainty, each alternative will offer only one possible result and the one that maximizes the objective function will be chosen. However, if the information is uncertain, each project will offer several possible outcomes to which they will assign probability coefficients.

In this way, it is considered that the investor is capable of raising the different events that determine the outcome of his decision. These events that refer to the general conditions of the business, the decisions of the competitors or the evolution of the demand are known as states of nature.

In these situations, the adoption of investment decisions requires the determination of the probability distribution of the cash flows generated by the project. Furthermore, the selection between different alternative projects entails the need to complete said information by taking into account the investor's preferences regarding risk.

Investor's attitude towards risk

Making investment decisions at risk requires knowing the probability distribution of the cash flows of each project. However, this is not enough when it comes to choosing between different alternative projects. Thus, the final decision may be different for each individual investor depending on the risk-return combination that is considered most appropriate. This implies the need to complete the above information by considering the investor's attitude towards risk.

One way of measuring investor preferences regarding risk can be obtained by determining their profit function. Von Neumann and Morgenstern construct this function from an ordinal index of utility through which they show the level of satisfaction that a decision maker obtains with different monetary amounts.

To do this, they distinguish between risk-prone, risk-averse and risk-neutral investors.

- Investors prone to risk are those for whom an additional unit gained offers more profit than is subtracted by the loss of a monetary unit.

- Risk-averse investors are those for whom an additional unit offers less profit than is subtracted by the loss of a monetary unit.

- Risk neutral investors are those for whom the marginal utility is constant and therefore an additional unit offers the same utility as that subtracted by the loss of a monetary unit.

Consider the case of an investor who is offered two investment alternatives with the same initial outlay.

The selected project will depend on the investor's attitude towards risk. If it is prone to risk, it will prefer the following order of projects C> B> A. If it is adverse to risk it will prefer project A> B and with respect to C it will be C> A or alternatively A> C. If it is neutral to risk C> B = A. That is, it will be indifferent between B and A.

1.2.4.2. Evaluation of investments in uncertainty

Sometimes the future of an investment is so uncertain that it is not possible to measure the probability associated with each of the states of nature. In these cases of uncertainty, companies also need to have different methods that allow them to evaluate and select investments.

Let us suppose that a company considers the selection of one of the following alternative investment processes whose cash flows depend on the evolution of the demand for its products.

Even in cases of uncertainty it is feasible to reduce the number of alternatives by eliminating those projects whose cash flows are exceeded by those of another project in all states of nature. Thus, project A is superior to project D so this is eliminated manually.

To select between projects A, B and C, it is necessary to apply one of the techniques described below.

a) Bayes-Laplace criterion

The Bayes-Laplace criterion considers that, if there is no information about the probability of occurrence of the different events that affect the future of an investment, the same probability coefficient should be assigned to each state of nature and used to estimate the expected value of each investment project. Thus, According to this criterion, project B is the most suitable since its expected value is the highest.

The main shortcoming of this method stems from the fact that, generally, the investor does not know all the possible events that affect the future results of each investment project, which makes the allocation of probabilities considerably difficult.

b) Maximal or pessimistic criterion

This method arises from the hypothesis that the investor behaves in a pessimistic way and, therefore, expects the worst cash flow to occur within each alternative. The minimum cash flow of each investment project is taken and the one that offers the highest value is selected. This is a suitable conservative approach only if the investor has a high risk aversion attitude.

Max {-500, 500, -400} = 500  The selected project is B

c) Maximax criterion

Part of the hypothesis that the investor is optimistic and risk-loving. The selected investment will be the one that offers a maximum value among the highest of each alternative.

Max {2500, 2000, 2000} = 2500  The selected project is A

d) Hurwicz criterion

Hurwicz proposes a decision method in uncertainty that falls between the two extremes, pessimistic and optimistic.

X´pessimistic + (1-X) ´optimistic

X + (1-X) = 1

In this way, the investor weights the cash flows of each alternative using coefficients that depend on his attitude towards risk. If it is optimistic it will assign a greater weight to the highest flow of each project and if it is pessimistic the highest weight will correspond to the lowest flow. Suppose the investor is quite risk averse and chooses a value of X = 0.8 then

According to this criterion, project B would be selected.

The problem with this method, like the previous two methods, is that it forgets the intermediate values generated by the projects.

5.3. Exercise Development

1) A firm tests an investment project that has the following characteristics:

• Initial investment: 80,000 NS

• Cash Flow 1st year: 30,000 NS

• For the rest of the years, cash flows are expected to be 10% higher than for the year previous.

• Time horizon: 5 years

• Residual Value: 20,000 NS

• Weighted Average Cost of Capital: 6%

According to the NPV criteria, can this investment be carried out?

If the company only accepts those projects that represent a profitability of 5% higher than the cost of capital. Will this investment be made?

Calculate the initial outlay that would have to be made for the profitability to be 50%

2) Calculate the return achieved by a shareholder who buys a share for 200 NS, having received 20 NS each year in dividends. Finding the profitability of the project for the shareholder

3) A company has to decide between 2 investment projects:

If the cost of capital is considered constant for the entire duration of the investment i = 6%. Select the best investment by the NPV criteria

What would have to be the initial investment of project B for the return on investment to be 30%?

4) A company incorporates a machine to its assets in the leasing mode under the following conditions:

* Value of the machine: 1,000 NS

* Time horizon: 5 years

* Annual leasing fees: 260 NS

Option to purchase the machine at the end of the fifth year for 40 NS

Find the effective cost that this acquisition represents for the company.

5) A company considers an investment project for the next four years that represents an initial outlay of 215,000 and has two options:

Calculate - using the financial table if necessary - the net present value of the two options A and B for a discount rate of 4%

6) Mrs. Palacios wants to start a business to manufacture sportswear. That is why you need to buy various machines, which will represent an amount of 15,000 NS. You will also need to buy a building valued at 20,000 NS and a truck that will cost 4,000 NS. You will also have to purchase raw materials such as thread, fabrics, buttons, etc. for a total of 2,000 NS and necessary utensils (scissors, needles, etc.) for an amount of 2,000 NS. To finance this investment, you have 23,000 NS for the rest, you have to request a loan from a financial institution. The financial entity will only give the loan if the project proves to be economically profitable. The following data are known:

- Weighted average cost of capital 5%

- Annual Net Cash Flows 10.00 NS

- Time horizon 4 years

The company will be liquidated at the end of the fourth year with the value of the assets at this time of 22,000 NS. Applying the NPV criterion, it reasons whether Mrs. Palacios will obtain the financing she needs, that is, if her product will be economically salable.

7) The Nautillius company wants to manufacture and sell a new detergent for washing machines. That's why you need to make an initial investment of 20,000 NS. Annual cash flows go up 7,000 NS. After 3 years the company is liquidated and the assets are sold for 15,000 NS. The cost of capital for this project is 5%. Determine using the NPV criterion, if this project is profitable and reason the conclusions.

8) A firm lends Bank XYZ a short-term amount in order to pay outstanding bills. The conditions of the loan are as follows:

* Amount: 500 NS

* Nominal interest rate: 6%

* Duration: 4 months

It is amortized at the end of the 4th month

Commission of 1% of the requested amount

The cost of the operation and the annual effective cost.

INVESTMENT PROJECT EXERCISE

Conclusion. For financial purposes the project is viable, since only 22% is financed with Debt, and this allows the obligations to be met, since the project generates sufficient resources and the amounts of these obligations are relatively small. Not so for economic purposes, since the initial investment is very high with respect to the future cash flows recovered, which is why an Internal Rate of Return (Econ. IRR = 6.34%) is lower than the Opportunity Cost of the Investor (Rate of Discount = 25%), and a negative NPV of 118,068

Bibliography

ALEXANDER, SHARPE AND BAILEY: Fundamentals of Investments. Theory and practice. Third edition. Pearson Education, Mexico, 2003. (ISBN 970-26-0375-7)

APARICIO, A., GALLEGO, R. et al. (2002): Financial Calculus. Theory and Practice.

Thompson-Paraninfo

ATHAYDE DE, GY FLORES R, 1998, “Introducing higher moments in the CAPM: some basic ideas”, Getulio Vargas Foundation, Rio de Janeiro.

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BREALEY RA and SC MYERS. Fundamentals of Business Financing. (Principle of corporate finance), 4th. Edition, McGraw Hill, 1993.

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