INVESTMENT EVALUATION

TOPIC IV. INVESTMENT EVALUATION

Goals

Upon completion of the study of this topic the student must:

a) Have an overview of an investment project

b) Know the elements for constructing the investor's flow of funds

c) Apply the most common asset depreciation methods.

d) Know how to use the methods for the financial evaluation process for efficient
decision making in an environment of certainty

e) Pose and resolve cases applied to the reality of the country

Introduction
Very often we are referring to carrying out projects, but what do we understand by
an investment project? A definition could be: "it is a discrete package of
investments, inputs and activities designed with the aim of eliminating or reducing
various constraints to development, to achieve one or more products or benefits, in
terms of increasing productivity and improving quality. quality of life of a group of
beneficiaries within a certain period of time". A project arises from the identification
of society's needs; Its goodness depends on its efficiency in satisfying these
needs, taking into account the social, economic, cultural and political context.

In general terms, the project is part of broader programs or plans, contributing to a

global development objective. Raises awareness of the general purposes and
objectives of plans and programs, whether governmental or private.

From the above, we deduce that investors, both state and private, frequently
compare the various investment alternatives that are presented in the environment.
The need to carry out these comparisons arises from the fact that it is desired to
optimize the use of the available economic and financial resources in the sense,
generally, of saving foreign currency, or of investment efficiency.

TO. BASIC ELEMENTS OF EVALUATION

Before addressing the methods of financial investment evaluation, we will analyze
some important elements to have a better understanding of the evaluation results.
The aspects that we will discuss in this chapter will be superficial, since they can be
expanded by consulting the indicated bibliography in order to have a broader
knowledge.

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1. Approaches to investment evaluation

The most important approaches in the evaluation of investment projects are:

1. Financial or private , in which a micro-economic analysis is made.
2. Economic or public , a macroeconomic analysis is carried out.
3. Social , an analysis of the externalities or environmental impact caused by the
project is carried out.
4. Environmental impact, an analysis of the impact on the environment and
mitigation measures is carried out.

In the evaluation of an investment project, it generally begins with a financial analysis

and is then complemented with the necessary adjustments to convert it into an
economic, social and environmental impact evaluation. We will only address the
aspect of the financial evaluation that makes it easier to answer the following
questions:

1. Is the investment project profitable?

2. In which of the investment projects that have been identified can the limited
financial resources available be invested?

3. What investment alternatives that have been detected should be chosen from a
financial point of view?
To evaluate a project from a financial point of view, market prices are used.
However, if the evaluation is from an economic and social perspective, the prices to
be taken into account are the so-called shadow or account prices and social
prices .

On the other hand, the financial evaluation of projects involves the determination of
the TIO opportunity interest rate. Investment alternatives are evaluated based on
the forecast that a reasonable rate of return can be expected, becoming a
minimum acceptable rate of return of MARR return, that is, the base rate for
projects. Generally this rate is much higher than the average rate of the financial
system because the latter responds to the minimum risk of the investment.

Every investor has in mind a minimum acceptable rate of return on the investment.
The serious question. What should an investor base on when setting his own MARR?

An investor would surely ask an investment for a MARR that guarantees two factors:
first, its profit must be such that it compensates for the inflationary effects, and
secondly, it must be a premium or excess rate for risking his money in the investment
and that makes your capital grow in a real way.

2. Basic estimates of an investment

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The basic estimates in an investment project are fundamental for preparing the
project's flow of funds and are the result of various studies.

a. Initial investment . The term initial investment or disbursement generally

refers to the negative flows that occur once at the beginning of the economic life
of a project for the acquisition of: fixed or tangible assets (land, buildings,
machinery, equipment, furniture, vehicles transportation, tools and others)
deferred or intangible assets (patents of invention, trademarks, commercial or
industrial designs, trade names, technical assistance, pre-operational and
installation and start-up expenses, energy services, telephones, telex, water, and
notarial) and assets in working capital

b. Benefits and costs. The projection of the benefits and costs throughout the
useful life of the project is what truly presents difficulties and the quality of the
evaluation depends on these estimates that result from the technical and
market studies, although other studies also contribute. that are considered
convenient.

c. Economic life . The economic life of the project is the time horizon that is
adopted for its evaluation. Some projects have well-defined end dates, after which
operational flows cease to exist. The term economic life refers to the period of
time over which the investment remains economically superior to the alternative
investment with which it could be compared for the same purpose. That is, the
period during which the investment does not become obsolete.

d. Salvage value . At the end of the economic life, the positive flows produced
by the residual values or salvages of depreciable and non-depreciable fixed
assets must be taken into account. Taxes related to the residual values of fixed
assets must be included in the analysis as negative or positive flows, depending
on the case.

e. Depreciation . Depreciation is due to the gradual wear and tear of the fixed
fund (machinery, equipment, buildings, etc.) or the principle of obsolescence,
which states that the item becomes outdated each year due to the availability of
more modern equipment on the market. Since most of these elements do not
wear out in a single year, the value of depreciation is distributed over a period of
years, which corresponds to the useful life of the asset.

a) Straight line method . This method assumes that depreciation is carried out
in equal annual items. That is to say:

where:

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D: Depreciation of the period

N: Number of years of useful life of the asset
V d : Value to be depreciated; V d = V a - V s
V a : Acquisition value
V s : Estimated salvage value

b) Depreciation and taxes on taxable profits

For tax purposes, an investment is treated as a prepaid expense and the
depreciation fee distributes this expense over the planning horizon. The
depreciations of a project and the amortizations of organizational expenses (deferred
assets) do not represent cash flows, since the true flow occurred when the assets
were acquired and the depreciations in subsequent accounting periods represent a
cost but not a disbursement. .
However, depreciation and other non-expenditure costs have an effect on a project's
cash flows through their impact on income tax, which is clearly a cash flow. Said tax
is calculated as follows:

IM = t(Y - C – D - I) ( 2 )

where:
IM: amount of direct taxes
t: income tax rate (IR)
Y: taxable income
C: tax deductible costs
D: depreciation
I: Financial costs

The higher the amount of depreciation declared, the lower the taxable income and
the lower the tax payable; The value of the depreciation fee must be calculated
according to the methods established by the tax law.

b. FINANCIAL STUDY

In this section we will analyze the financial viability of a project, the objective is to
organize and systematize the monetary information that is the result of the various
studies. Analytical and additional tables are important for the construction of the
project's cash flow, the classic case is the calculation of the amount that should be
invested in working capital or the scrap value and the cost of initial investments, as
well as project reinvestments. Operating costs and income are deduced from
information on market prices of the goods and services that the project will offer
and demand during the productive life of the project.

1. Funded and Pure Project Cash Flow

In any financial evaluation of investments, it is essential to estimate the cash flow
that each project will generate. The goodness of the final result achieved will

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depend on the care put into that estimate. The four basic elements that make up
the flow of funds are:

a Operating profits (income)

b The costs (expenses) of investment or assembly, that is, the initial costs
c Operating costs (expenses)
d The salvage value of the assets at the end of their useful life

The flow of funds is simply a scheme that systematically presents costs and income,
recorded year by year (or period by period). These costs and income are obtained
from the studies that are part of the formulation and evaluation of a project. Among
them we can mention the following: technical, market, legal, institutional,
organizational, financial, socioeconomic and environmental. The flow of funds is
a synthesis of all these studies carried out as part of the pre-investment stage or as
part of the post-investment or execution stage.

to. Flow of funds with external financing

The project is executed with external financing, the contribution of the investors'
own capital is important for the realization of the investment, that is, it is a scheme
from the point of view of the executing entity or owners of the project.

Example 1
In the Pacific tourist area of Nicaragua, a group of people interested in promoting
and developing tourism is studying the possibility of undertaking a project that
specifies an initial investment in year zero of $1,000 of which $600 will be invested
in fixed assets, $200 in deferred assets and $200 in working capital.

Of the fixed assets, $500 is fully depreciated on a straight-line basis in 5 years and
the remainder has a salvage value of $200 in year 5. The deferred asset is
recovered at an amortization rate of 20% per year

Income from the sale of services is scheduled at $1,000 from the first year, which
is equivalent to 85% of the installed capacity. Annual operating costs are expected
to be $400.

Tax on taxable profits is 30%. The opportunity cost rate for investors is 25%

To develop the project, there is a line of credit from a local bank that will finance
50% of the initial investment for a period of 5 years and payable in level annual
installments with 20% effective on balances.

Solution
The net cash flow of investors and the salvage value by the commercial method is
presented in table 1, later we will calculate the financial profitability indicators.

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CONCEPT Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

+ Total income 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00
- Total costs 400.00 400.00 400.00 400.00 400.00
- Financial costs 100.00 86.56 70.44 51.09 27.86
- Undisbursed expenses 140.00 140.00 140.00 140.00 140.00
= Profit before taxes 360.00 373.44 389.56 408.91 432.14
- Taxes (IR = 30%) 108.00 112.03 116.87 122.67 129.64
= Profit after taxes 252.00 261.41 272.69 286.24 302.50
+ Adjustment of undisbursed
expenses 140.00 140.00 140.00 140.00 140.00
+ Working capital recovery - - - - 200.00
+ Salvage value - - - - 170.00
- Total investments 1,000.00 - - - - -
+ Loans received 500.00 - - - - -
- Debt amortization 67.19 80.63 96.75 116.10 139.32
= Net investor flow (500.00) 324.81 320.78 315.94 310.14 673.18

Table 1

b. Project cash flow without financing

Table 2 shows the “pure” flow without external financing of a project, since the
total investments will be through the equity of the executing company. The
objective of this course is to be able to build a flow of funds, in addition to financial
indicators based on the investor's net flow.

The investor's net fund flow are the values that the analyst takes into account
to calculate the financial profitability indicators, with the discount or minimum
rate of return.

The flow of funds for example 1, without external financing, is presented in table 2.
This table does not record: interest or debt amortization.

CONCEPT Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

+ Total income 1,000.00 1,000.00 1,000.00 1,000.00 1,000.00
- Total costs 400.00 400.00 400.00 400.00 400.00
- Undisbursed expenses 140.00 140.00 140.00 140.00 140.00
= Profit before tax. 460.00 460.00 460.00 460.00 460.00
- Taxes (IR = 30%) 138.00 138.00 138.00 138.00 138.00
= Profit after tax 322.00 322.00 322.00 322.00 322.00
+ Adjustment of undisbursed
expenses 140.00 140.00 140.00 140.00 140.00
+ Working capital recovery - - - - 200.00
+ Salvage value - - - - 170.00

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- Total investments 1,000.00 - - - - -

= Net investor flow (1,000.00) 462.00 462.00 462.00 462.00 832.00

Table 2

c. Salvage value of fixed assets by the commercial method

To calculate the salvage value of a fixed asset at the end of the evaluation period of
the investment alternative, we follow the following procedure, assuming the values
given below:

+ Trade Value 200 (Market Offer)

- Book value 100 (Acquisition value – total depreciation)
= Value before taxes 100
- 30% tax 30
= Value after taxes 70
+ Book value 100
= Net salvage value 170 (value to be recorded in the flow of funds)

2. Financial profitability indicators

One of the fundamental problems in investment programming is determining

profitability. This is important since if we have a criterion or performance measure, we
will be able to decide which ones should be accepted and which ones should be
rejected.

The methods that use updating or discounting procedures and that therefore take into
account the chronology of fund flows, that is, they give money importance as a
function of time are: Net Present Value NPV, Internal Rate of Return IRR , RBC
Benefit Cost Ratio and CAE equivalent Annual Cost. These methods depend on two
variables: the update or discount rate also known as MARR and the time

to. Net Present Value: NPV

This method is based on the discounting of the flow of funds and considers the
importance of these flows as a function of time. It consists of finding the difference
between the updated value of the investments. Its value depends on the interest rate
used to calculate it. The rate used to update or discount the flows is the investor's
minimum acceptable MARR return.

In general, the Net Present Value (NPV) can be calculated in the following way:

The annual net benefits for each of the years of the project's useful life are
determined, subtracting the costs from the benefits:

where:

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I 0 = Initial investment year zero

B n = Net profit in year n
C n = Negative net benefit (Cost) in year n
n = 1, 2, 3, ... ,N (Years of useful life)
N = Last year of the project's useful life
k = Discount rate: (k = Opportunity cost of capital)

Then, each of these net benefits is converted to its equivalent in the reference year:

A project that presents a positive flow of funds after period zero, the net present value
is calculated through formula 3 considering the initial investment I 0 as a negative
benefit in the following way (see graph 1)

NPV criterion for decision making

1. If the NPV is greater than zero ( NPV > 0 ), the project is attractive and should
be accepted.

2. If the NPV is equal to zero ( NPV = 0 ) the investment is indifferent. In this case,
the investment project generates an interest exactly equal to the k (Update
Rate); Furthermore, this rate coincides with the IRR (Internal Rate of Return).

3. If the NPV is less than zero ( NPV < 0 ) the project is not worth it since there are
investment alternatives that yield greater benefits; (these are the ones that are
reflected in the opportunity cost of money).

BN
B1B2B3B4

B N-1

0 1 2 3 4 . . . N-1 N

Figure 1
I0

Example 2

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Consider the net funds flow of the investor in Table 1, and calculate the NPV, with
the minimum acceptable rate of return MARR of 25. The net flow is presented in
graph 2.

673.18
324.81 320.78 315.94 310.14

0 1 2 3 4 5 years

Chart 2
500

Solution
The cash flow structure is that of a conventional project. Thus, applying formula 3 we
have the NPV.

NPV (0.25) = - 500 + 259.85 +205.30+ 161.76 + 127.03 + 220.59 = -500 + 974.53 =
474.53 > 0

We observe that the investment project has a positive NPV and therefore the project
should be accepted.

The NPV is considered an excellent method to measure financial effectiveness and

determines the merit of the project, since it represents in current values, the total
resources that remain in the hands of the investor at the end of its entire useful life.

b. Internal Rate of Return: IRR

The IRR is the interest rate paid on unpaid balances of money borrowed or the
interest rate earned on the unrecovered balance of an investment (loan), which
causes the final payment or income to take the balance to zero. considered interest.
The internal rate of return IRR is what allows the net present value NPV of the
investment project to be equal to zero; The solution is found by solving for rate k from
formula 3 of the NPV, when this equation is equal to zero, that is:

When solving equation 4 for k, the result is: k = IRR, the solution can be found
manually through an approximation process, or trial and error through linear
interpolations or extrapolations. In general, the equation of formula 4 has multiple

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solutions, however in practice this equation has a single solution, if it is about

projects classified as conventional , in which the annual net expenditures occur in
the first years of the project and then are produce income, remaining this way for the
rest of the useful life of the project (see graph 2)

A flow of net funds can be presented where at the beginning there are income
followed by expenses; in these cases the flow is also conventional. This may be the
case for projects where all flows are positive or negative. In these cases the IRR
does not exist, since it is impossible for the NPV to be equal to zero.

In projects where there is more than one change of sign of the annual net flows (they
change from negative to positive, and again become negative, positive or vice versa).
In these cases, the possibility of no or multiple TIRES is presented.

IRR calculation method

1. Select an interest rate i 1 , which gives you a net present value greater than
zero, we will call it: NPV 1 > 0.

2. Select an interest rate i 2 , which provides you with a net present value less
than zero, we will call it: NPV 2 < 0 .

3. Once NPV 1 and NPV 2 are found, we apply interpolation formula 5

IRR criterion for decision making

1. If the IRR > k , the project is attractive and is accepted.

2. If the IRR = k indifference. The project yields interest exactly equal to k (refresh
rate or minimum rate of return)

3. If the IRR < k the project or the minimum required, it is rejected

Example 3
Let's calculate the IRR of example 1, net flow table 1

Solution. Applying the procedure we have:

1. Let's select the rate i 1 = 0.40 and applying formula 3 we find the NPV 1

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NPV (0.40) = - 500 + 232.00 +163.66+ 115.14 + 80.73+ 125.17 = -500 + 716.70 =
216.70 > 0

2. Let's select the rate i 2 = 0.80 and applying formula 3 again we find the NPV 2

NPV 2 (0.28) = - 500 + 180.45 + 99.00+ 54.17 + 29.54+35.63 = -500 + 398.79 = -

101.21 < 0

3. Let's apply interpolation formula 5 to find IRR which is between the range of 40%
and 80%

The IRR value is approximate, 64% is a good value to take into account for the
analysis. We can see that the result meets the project acceptance criterion, since IRR
>k

We can represent this result in graph 3

NPV 1 = 216.70 IRR

+
NPV = 0 0 40% 67% 80% i
-

NPV 2 = -101.21

Chart 3

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c. Benefit-Cost Ratio (RBC)

This profitability indicator is based on the NPV and its application is very common in
studies of public or social projects.

Method for calculating RBC

1. Calculate the Net Present Value of positive profits, with the rate k: VANB

2. Calculate the Net Present Value of negative profits, with the rate k: NCV

3. Establish the relationship:

The RBC is a function of the interest rate (k = Trema) that is used to calculate the
NPV of income and expenses, so that when calculating this indicator for decision-
making purposes, it is necessary to use the minimum acceptable profitability k.

RBC criteria for decision making

1. If the RBC > 1 , it is accepted, since the VANB is greater than the VANC

2. If the RBC = 1 , indifference. The net benefits barely offset the opportunity cost
of money

3. If the RBC < 1 , it is rejected, since the VANB is less than the VANC

CBR is used in projects related to investments financed by international organizations

such as the IDB or the World Bank (IBRD). These entities generally establish the use
of this indicator as a result of the prevailing practice in United States government
agencies that require, by law, an explicit comparison of benefits and costs.

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Example 4
Calculate the RBC of example 1, from the flow of funds in table 1. In this case,
applying formula 6 we obtain:

The result indicates that it is greater than unity, the project is accepted, that is; that
the result in current value is greater than the unit invested, which generates a profit.

d. Adjusted internal rate of return: TIRa

The IRR may contain in certain cases multiple solutions (MULTIPES IRRs), this
happens when the project is not conventional and the net investment flow profile
has more than one change of sign (see graph 4). The Adjusted IRR (IRR) has
been defined to resolve problems of non-existence or multiple existence of IRR.
With the adjusted IRR, the unification of a single rate will be guaranteed,
regardless of the structure of the flows.

Method for calculating RBC

1. Calculate F B the future value of all positive profits with rate k

2. Calculate P C the present value of all negative profits with rate k

P C = AVNC

3. From the formula we solve TIRa, that is, formula 8

TIRa criteria for decision making

1. If the STRIP > k , the project is attractive, it is accepted

2. If the STRIP = k, the project is indifferent to carry out

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3. If the STRIP < k the project is not attractive,

Example 5
Let us consider the following case for which it was not possible to find a unique IRR,
given the characteristics of the flow of the project that is called unconventional ,
where the minimum rate of return k of the investor studying the project is 20% per
year.

1,500
500 500 600

0 1 2 3 4 5 years

Chart 4
1,000
120

The flow of funds of the project is unconventional, by formula 3 we calculate the Net
Present Value; GO.

=-1,000 – 69.44 + 416.67 + 347.22 + 289.35 + 602.82 = -1,069.44 + 1,656.06 =

586.62 > 0

The benefit-cost relationship is:

Since the flow of funds is unconventional, we calculate the IRRa

F B =4,120.81

0 1 2 3 4 5 years
Chart 5

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P C = 1,069.44

P C = NCV = 1,069.44

In this case, the adjusted IRR is greater than the MARR (30.97% > 20%). This means
that the profitability of the project, assuming reinvestments of surplus resources to
Trema, is greater than the return on investment alternatives that yield 20%.

3. Analysis of the value of financial indicators

The NPV criterion states that the project should be accepted if its value is equal to
steel or greater than zero. If the result is zero, it indicates that the project returns just
what the investor demands from the investment; If the result were, for example, 200
positive, it indicates that the project yields that sum as a remainder over the minimum
required. If the result is a negative value, for example, 300 indicates that this amount
is missing for the project to earn what the investor demands. NPV is a powerful and
universal method for evaluating and comparing exclusive investments under
conditions of limited available capital. The NPV assumes that all financial resources
generated and released from the project are reinvested at the opportunity interest
rate.

The IRR criterion evaluates the project based on the single rate of return per period
where all the updated benefits are exactly equal to the disbursements expressed in
current currency. The IRR “represents the highest interest rate that an investor could
pay without losing money, if all the funds for financing the investment were borrowed
and the loan was repaid with the cash inflows from the investment as they became
available.” producing” (Bierman and Smidt “The Budget…”, p.39) The previous
statement does not include the concepts of opportunity cost, risk or the evaluation of
the company as a whole, the IRR simply represents the rate that would be paid on
the balance of a loan or on the capital of an unrecovered investment. The project
should be accepted if the IRR is higher than the investor's opportunity interest rate.

The RBC criterion states that the project is profitable if the ratio of the updated
benefits between all the updated disbursements is equal to or greater than unity,
which means that in updated terms the benefits are equal to or exceed the
disbursements. For example, if the RBC is 4.2, it means that the project in updated
values yields a remainder of 3.2 for each unit of investment, that is, above the
minimum required. If the project had, in updated values, an RBC of 0.68, which is a

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value less than one, it means that for each unit of investment, 0.32 is not recovered,
which causes a loss, therefore the project is not viable, it does not yield the minimum.
demanded.

c. Exercises proposed for self-study

1. A project requires an initial investment of $100,000 for its installation. Its

operation and maintenance expenses are on the order of $20,000 for the first
year and these costs are expected to grow in the future at a rate of 10%
annually. The estimated economic life of the project is 8 years at the end of
which its salvage value is estimated to be $40,000 after taxes. The income
generated is $50,000 the first year and is expected to increase at a constant
rate of $10,000 per year. If the minimum rate of return for investors is 25% per
year and the tax rate is 30%. Determine the profitability indicators and make
your comments: NPV, IRR and RBC. Answer: NPV(25%) = $19,084, IRR =
30.33%, RBC = 1.19

2. The INTERCASA company has a package of investment projects and for them
to be executed a financial analysis needs to be carried out. Each project is
designed for a horizon of 8 years and different opportunity interest rates due to
the specific activity for which they are intended. The net fund flows per year are
presented in the following table. Determine for each project: a) NPV b) IRR or
Adjusted IRR c) RBC.

PROJECT I00 1 2 3 4 5 6 7 8
TO 20%) (500) 140 140 140 140 140 140 140 150
B (18%) (450) --- --- 205 205 205 205 205 225
C (15%) (560) 120 120 120 120 150 150 150 170
D (18%) (230) 50 60 70 80 70 60 50 80
E (17%) (620) --- 180 185 190 200 205 210 240
F (15%) (300) 300 (120) 135 --- 150 (80) 150 400
G (16%) (1300) 300 300 300 280 280 280 280 270
H (22%) (800) --- 175 (275) 375 400 (165) 200 580

Answers:

PROJECT GO IRR Adjusted IRR RBC

TO $39.52 22.75% ----- 1.08
b $70.25 21.80% ----- 1.16
c $34.00 16.77% ----- 1.06
d $29.12 22.10% ----- 1.13
AND $37.83 18.80% ----- 1.06
F $186.03 ----- 20.34% 1.44
g ($41.93) 15% -------- 0.97
h ($398.73) ----- 14.50% 0.50

3. The investment in year zero of a project is $100,000. The investor's net flows
(profits) are as follows: from year 1 to 4, $25,000 and from year 5 to 8, $30,000.
The project has a useful life of 8 years and at the end of which it will have a

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salvage value of $50,000. If the opportunity interest rate is 18% annually,

determine: a) The NPV b) The IRR c) The RBC. Answers: a) $22,179 b) 25% c)
1.22

4. The gross revenue for a project is $120,000 annually and the operating costs
are $75,000 from years 1 to 5 and $60,000 from years 6 to 10. Taxes on
taxable profits are 20%. The useful life of the project is 10 years and has a
residual value of $80,000. The initial investment in year zero is $200,000 and
the opportunity interest rate is 15% per year. Determine: a) The NPV b) IRR c)
RBC Answers: a) $16,495 b) 17% c) 1.08

5. The pineapple cultivation project in the Ticuantepe area has an initial

investment of $25,000, the net income is $7,000 from year 1 to 5 and $8,000
from year 6 to 10. If the opportunity rate is 21%, determine and apply the
criteria of: a) NPV, b) IRR c) RBC Answers: a) $4,506.63 b) 27% c) $1.18

6. An industrial project works with an interest rate of 25% and has the following
investor cash flow. Calculate and apply the criterion of: a) NPV b) IRR c) RBC
Answers: a) $ <80.60> b) 23.5% c) 0.92

Year Flow Year Flow Year Flow

0 (1,000) 4 500 8 600
1 ( 400 ) 5 600 9 200
2 100 6 600 10 700
3 500 7 600 10 300

7. In the central region of the country, an international organization that promotes

ecology and the environment is studying the possibility of developing an
agroforestry project, which includes a forest reforestation program and
financing for small farmers in the area. The project contemplates an initial
investment of $70,000 and an additional reinvestment of $50,000 in year 5 that
will allow the project to continue for another 5 years for a total of 10 years of
useful life, at the end of which the salvage value is estimated. at $30,000. The
expected benefits will be $25,000 the first year with a 10% increase until year 5.
Over the next 5 years there is expected to be revenue of $25,000 with
increases of $5,000 per year until the end of the useful life. Operating costs will
be $8,000 annually. If the interest rate is 20%, determine. a) NPV b) IRR c)
RBC d) Comment from the point of view of financial performance. Answer:
a) $9,309.35 b) TIRA 21.35% c) 1.12

8. The "FINSA" Corporation is studying three possible investments that are

characterized by the data included in the attached table. Note that all three
investments have the same initial cash allocation, the same duration, and the
same monetary returns; Furthermore, the fund flows are different in the three
investments. All figures are given in thousands of córdobas.

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 INVESTMENT EVALUATION

Projects
Concept 1 2 3 Years
Initial Investment $400 $400 $400 0
cash receipts $200 $240 $160 1
cash receipts $200 $200 $200 2
cash receipts $200 $160 $240 3

The corporation has limited capital and cannot develop the three investments. Which
project is the most profitable? Use the 15% minimum return and calculate: NPV TIR
and RBC. Select the most profitable one. Answers:

Projects
Concept 1 2 3
GO 56.65 65.13 48.16
IRR 23.50% 25.50% 21.60%
RBC 1.14 1.16 1.12

9. A Public Limited Company provides capital of $500 (million dollars) for the
development of a timber investment project. It is estimated that the project will
generate annual net income in the order of $170 for 6 years. The Company is
interested in you calculating and guiding you in the following aspects: Calculate
the financial profitability indicators: Answers: NPV (25%) = 65.35 RRBC = 1.13
IRR = 25.2%

10. A real estate investor buys a property for $6,000 and sells it 8 years later for
$30,000. Taxes on the property were $80 the first year, $90 the second, and $10
more each year until it was sold. Determine the internal rate of return on the
investment. Response 21.44%

11. The Bel-Moreno family bought an old house for $25,000 with the idea of making
improvements, renting it out and then selling it. In the first year, they spent $5,000
on improvements, in the second they spent $1,500 on a fence, and in the third
they spent $1,200 on decoration. The annual taxes were $500 for the 7 years it
belonged to them. From year 4 to year 7 they rented it for $7,200 annually, finally
selling it for $40,000. Determine the rate of return they earned on the investment
over the 7 years. Answer: 12.2%

12. If a company spends $5,000 today and $800 annually for 7 years, with the first
disbursement in year 4, what rate of return will the company receive if revenue
over the 10 years was $3,000 at the end of year 3, and $1,200 annually from then
on? Answer: 9.51%

13. A person is deciding whether to buy artificial Christmas trees or continue cutting
down trees. The artificial tree costs you $34.00 and you can use it for 8 years after
which it is thrown away as trash. The other alternative is to continue cutting trees

262 Introduction to financial management. Noel Reyes Alvarado .

 INVESTMENT EVALUATION

at a cost of $8.00 today, $9.00 next year, $10.00 the year after that, etc., and so
on for those same 8 years. If you buy the artificial tree, what rate of return do you
achieve on the investment? Answer: 25.60%

14. A person invests $50,000 in a business that returns $10,000 net annually from
year 1 to 5 and $15,000 in the next 5, until completing 10 years. What annual rate
of return does he/she obtain? Answer: 18.90%

15. In an investment project the net income in year 1 is $12,000 and increases 20%
per year until year 6. The net income of year 7 is decreasing by 10% according to
the income of year 6. In the remaining years up to 10, they have the same value
as year 7. If the initial investment in year zero is $40,000 and the minimum cost of
capital rate is 22%, calculate the financial indicators. Answers: NPV = $36,974
RBC = 1.92 IRR = 42.5%

16. Analyze if it is convenient for you to invest in a project that observes the following
net flow of funds, at a minimum required rate of 20%. Answer. Yeah

Year 0 1 2 3 4 5 6
Wort (25,100) 14,000 7,000 (4,000) 8,000 10,000 9,000
h

17. A not very common project that has a minimum rate of 18% that presents the
following flow of net funds, we want you to analyze if it is profitable by calculating
the profitability indicators, (in this case the IRR < K for it to be profitable) Answers:
NPV = $5,387 RBC = 1.37 IRR = 7%

Year 0 1 2 3 4 5
Worth 20,000 (3,000) (4,000) (5,000) (6,000) (7,000)

18. An investor purchases 3 classes of shares (identified as group A, B and C). The
investor purchased 200 shares of A at $13.00 each, 400 of B at $4.00 each, and
100 of C at $18.00 each. Dividends were $0.50 per share of A for the 3 years, with
the share later selling for $15.00. Stock B did not produce dividends but sold for
$5.50, two years after its purchase. Stock C produced dividends of $2.10 each for
10 years, but due to a stock market depression its selling price was $12.00 each.
Determine: a) The internal rate of return on each group of shares. b) The internal
rate of return on the overall investment of shares. Answers: a) Group A: 8.50%
Group B: 17.60%, Group C: 9.50%. All investment 10.5%

19. The “San Juan” Cooperative is interested in developing a project to grow 20 “pink
pitahaya” apples in the Municipality of La Concepción de Masaya, which requires
an initial investment of $600 of which $200 is obtained through a source bank
financing with 20% interest on balances and payable in 5 annual proportional
installments. The estimated sales revenue from the annual production will be
$500 and operating costs will be $200. The project has fixed assets of $350 of

263 Introduction to financial management. Noel Reyes Alvarado .

 INVESTMENT EVALUATION

which $250 will be fully depreciated on a straight-line basis over 5 years. The
other $100 assets are not depreciated and will have a salvage value of $120 after
tax at the end of year 5. The previous studies of the project were $30 and the
investment in deferred assets is scheduled at $50, both will be amortized at a rate
of 20% annually. The working capital is $200 and will be used for the acquisition
of raw materials, inputs and agricultural work. The tax rate is 30% and the
opportunity interest rate is set at 22%. Determine the profitability indicators and
make a financial analysis of the results for an economic life of 5 years. Answers:
NPV(22%) = $ 207.54 RCB = 1.52 IRR = 43.40%

20. A project is going to be carried out in a country where there is no inflation.

Requires an investment in year zero of $100 million: half for depreciable fixed
assets and half for non-depreciable assets. The useful life of the project is 5
years and depreciable fixed assets have no salvage value. The loss on the sale
of the other assets, which amounts to $20 million, will be charged to the last
period.

The investment is financed with 50% own capital and 50% with a loan. This $50
million loan is repaid in 5 amortizations of $10 million each starting in year 1.
The interest rate on the credit is 10% annual effective on balances. Sales are
$150 million per year and operating expenses, not including financial expenses
or depreciation, are $80 million per year.

The income tax rate is 25% and the investor opportunity interest rate is 30%.
Depreciation is carried out on 100% of the acquisition value of the depreciable
assets, over a period of five years, using the straight line method. a) Prepare
the net flow of the project b) calculate the profitability indicators: Answers:

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

-50 41.25 42.00 42.75 43.50 79.29

NPV (25%) = $62.63 IRR = 82% RBC = 2.25

21. A company that will expand its investments in the area of agribusiness, after
carrying out the pre-feasibility, feasibility, market and technical studies on a
project, has reached the following results in thousands of dollars for a preliminary
useful life of the project. 5 years:

Investments Value year 0 Market value in year 5

Land $400.00 $550.00
buildings $1,000.00 $800.00
Machinery and equipment $200.00 $100.00

264 Introduction to financial management. Noel Reyes Alvarado .

 INVESTMENT EVALUATION

Intangibles $80.00
Working capital $50.00

Total $1,730

Depreciation is as follows: buildings 10%, machinery 20%, land is not depreciated,

amortization of intangibles is 20% and taxes on taxable profits are 22%.

Operating expenses and income are detailed:

year Organizational chart Operating costs

1 $1,250 $550
2 $1,300 $570
3 $1,350 $600
4 $1,400 $650
5 $1,450 $700

The minimum investor rate is 25%, and the evaluation assumes that everything
you produce is sold.
The investor obtains 50% bank financing for the initial investment through a loan
that must be paid in 5 level annual installments at an interest of 20% on balances .

Activities:
a) Prepare the investor's cash flow with financing considering the sale of
depreciated and non-depreciated fixed assets.
b) Calculate profitability indicators: NPV, IRR and RBC.
c) Explain each of the previous results.

Answers: NPV = $510, IRR = 62%, RBC = 1.59

Referenced bibliography

1. Ayres, Frank Jr. "Financial Mathematics", McGraw-Hill, Mexico, 1993.

2. Baca, Currea Guillermo, "Financial Mathematics and Systems", Limusa Noriega

Editores, Bogotá Colombia, 1997.

3. Blank, Leland T/Tarquin, Anthony J. "Economic Engineering", McGraw-Hill, Third

edition, Mexico, 1992.

4. Chiang, Alpha. "Fundamental Methods of Mathematical Economics", McGraw-

Hill, Mexico, 1987.

5. Delp, Peter and others "Project Analysis" ICAP, Costa Rica, 1992.

265 Introduction to financial management. Noel Reyes Alvarado .

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6. Díaz Mata, Alfredo “Financial Mathematics”, McGraw-Hill, Third Edition, Mexico,

1999

7. Fontanals Albiol, Hortensia “Financial Mathematics (Assumptions). Romanya

/valls SA, Barcelona Spain, 1992.

8. Jagdish C., Arya/Lardner, Robin. "Mathematics Applied to Economics and

Administration", Prentice-Hall, Mexico, 1992.

9. Merino, Ana Vicente and others “Actuarial and financial techniques of social
security”, Ibero-American social security organization, University of Alcalá, Spain,
2006

10. Mokate, Karen Marie. "Financial Evaluation of Investment Projects", Universidad

de los Andes Santafé de Bogotá, Colombia, 1994.

11. Moore, Justin H. "Manual of Financial Mathematics", Hispano-América, Spain,

1970.

12. Portus G., Lincoyán "Financial Mathematics", McGraw-Hill, Third edition, Mexico,
1990.

13. Ramírez C., Jesús A. "Financial Mathematics for projects", University of the
Amazon Florencia Caquetá, Colombia, 1994.

14. Sapag, Chain Nassir and Reynaldo “Project Preparation and Evaluation”
McGraw-Hill, Fourth Edition, Mexico, 2004

15. Tovar, Jiménez José “Manual of Financial Mathematics” University of Salamanca,

Spain, 2005

16. Villalobos, José Luis “Financial Mathematics”, Pearson Education, Second

Edition, Mexico, 2001.

17. Zima, Petr / Brown, Robert “Financial Mathematics” McGraw-Hill, Fourth edition,

Mexico, 2004

NOEL REYES ALVARADO

 Master's Degree in Mathematics Applied to Economic and Administrative

Sciences

266 Introduction to financial management. Noel Reyes Alvarado .

 INVESTMENT EVALUATION

 Graduate in Mathematics and Educational Sciences

 Post Degree in Project Formulation and Evaluation

Experience: 26 years of university teaching.

Full Professor, Department of Mathematics and Statistics, Faculty of Economic
Sciences, UNAN-Managua.
Schedule Professor, Department of Accounting and Economics, Faculty of
Economics and Business Sciences UCA
Professor of the Master's and Postgraduate Programs - Faculty of Economic
Sciences UNAN-Managua
Professor of the Master's and Post-Graduate Programs in the area of Economics,
Finance, Administration and Projects at the UCA

267 Introduction to financial management. Noel Reyes Alvarado .