Module

Basic Principles in Agricultural Economics

 

    The Theory of Investment

 

    Number of hours: 6

 

bullet Basic definitions and assumptions of theory of investment;
bullet Concepts underlying investments: time value of money, future value, present value;
bullet Economic profitability of investment;
bullet Methods in investment analysis: payback period, simple rate of return; net present value; internal rate of return;
bullet Financial feasibility of investment;
bullet Mutually exclusive investments
bullet Sensitivity analysis; break-even analysis; scenario analysis;

 

Chapter objectives

Introduction

6.1.  Basic definitions and assumptions of theory of investment

6.2.  Concepts underlying investments

6.2.1.      Time value of money

6.2.2.      Future value

6.2.3.      Present value

6.3.  Economic profitability of investment – Investment analysis

     6.3.1.  Simple payback period

6.3.2.      Simple rate of return

6.3.3.      Net present value

6.3.4.      Internal rate of return

6.4.        Financial feasibility of investment

6.5.        Mutually exclusive investments

6.6.        Additional methods related to investment analysis

6.6.1     Sensitivity analysis

6.6.2.      Break-even analysis

6.6.3.      Scenario analysis

 

Chapter objectives:

 

The overall objective of the chapter is to give basic knowledge about investments and calculations, analysis and business decisions related to them.

First of all, concept of time value of money will be explained, as well as concepts of future and present value.

Students will get very basic knowledge about principles of investment analysis – capital budgeting. Four methods: payback period, simple rate of return, net present value and internal rate of return. As a result, student should understand importance of investment analysis and should be able to analyze simple investment proposal using these methods in order to be able to answer whether or not some invested should be accepted or rejected. They will also be aware of all factors that need to be take into consideration in capital budgeting such as: income taxes, risk and inflation and to make difference between economic profitability and financial feasibility of investment.

 

 

Introduction

On the farm capital can be used to finance annual operating inputs such as feed, seed, fertilizer, chemicals or fuel or for capital assets such as land, machinery, buildings, orchards or cattle. Different methods should be used to make decision  when purchasing annual operating inputs and capital assets. The reason is in the fact that when we purchase capital assets there is a significant time difference in the timing of expenses and their associated returns. Both expenses and  income from investing in annual operating inputs occur within one production cycle, usually in one year or less. In contrast, investing in capital assets typically means a  large initial expense  with resulting returns spread over a number of future time periods. Partial budgeting can be used to analyze these investments by looking at changes in costs and returns for an average year. However, other analysis methods can be used to more accurately take into account the timing of expenditures and income.

 

The marginal principles used to find profit-maximizing level of allocation of operating inputs usually ignore timing. Expenses and returns are assumed to fall within the same year or production cycle, a relatively short time span. However, time can be incorporated into the analysis by including the opportunity cost of capital as part of the cost of the input. Enterprise and partial budgets recognize the timing by including opportunity costs on annual operating inputs, but the amounts are typically small due to the short time period.

 

While the time may be of minor importance when analyzing annual operating inputs, it becomes of major importance for capital assets. They usually require larger sums of money, and the expenses and returns occur in different time periods spread over many years. The amounts may be very irregular as well.  A proper analysis of these capital investments requires careful consideration of the size and timing of the related cash flows.

 

There are also other reasons for carefully analyzing potential capital investments capital investments before they are made. Decisions about operational inputs can be changed annually. However, capital investments are, by definitions, long-lasting assets; therefore, investment decisions are made less frequently. It is much more difficult to change a capital investment decision once the asset is purchased or constructed. That is why, sufficient time and proper analytical techniques and methods should be used when making these decisions.

  

6.1. Basic definitions and assumptions of theory of investment

Before going on with explaining main concepts, principles, calculations and methods related to investments it necessary to give definition of investment. The term investment(s) is very often used in many meanings and context. Investment is a scientific and expert term but, unlike many other terms of this kind, it is also used in every-day life among people without any knowledge or understanding about them.  Even in scientific and expert literature numerous and various definitions exist. Some of them are:

 

bullet

Investment is purchase of equipment or materials that will add to stock of capital;

bullet

Investment is the purchase of an asset that will  provide a return over a long period of time;

bullet

Investment is fixation of financial funds in material objects which promise to be of long-term use in approaching the investors objectives

bullet

Investment is “specifying” a part of actual consumption aimed to gain revenue in future;

bullet

Investment is any expenditure aimed to gain economic benefit, i.e. profit.

 

To simplify, let’s ask ourselves what would be an investment on farm?

Questions like: Should I buy more land? Should I expand my cow herd? Should I buy my own machinery instead to hire it when needed? How much I can earn if I raise an orchard?  – are investment question

 

Whatever definition we take we will come to some common characteristic elements of investments. Those elements  are:

 

1.      long-term character- if a farmer buys a combine he will use it and have benefit from it over many production periods

2.      time differences between  “spending” and getting revenues –it will take years from investing in new orchard until the moment when farmer can return his money invested

3.      lumpiness- investment usually involve the purchase of assets for which the marginal analysis is not appropriate because it is not possible to buy or use marginal unit for lumpy assets like combine or piece of land

4.      risk – decision about investment is made on the basis of actual assumptions, and as investment involves time as factor, there is possibility that some of assumptions proves to be wrong or some element misjudged .

 

Therefore, there are three following conditions for any investment to take place:

bullet

financial funds need to be raised;

bullet

investment has to be profitable and

bullet

proper decisions has to be made in order to bridge the  time-span between investment and returns .

 The problem is that farmers are very often in position to make investment decisions and, at the same time, skills required to do it is far beyond their capabilities.

 

Questions:

 

1.      In your own words, try to make the most appropriate definition for investment on farm?

2.      What are main differences between investment and expenditures related to operational activities?

3.      Where do you see the place and role of extension service in farm investment related issues?

 

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6.2. Concepts underlying investment

 

Before we start with investment analysis and related issues, it is necessary to get familiar with some basic concepts and principles incorporated in theory of investment and investment analysis. These basic concepts necessary to understand investments and “philosophy” behind them  and related calculations are time value of money, future value and present value.

Text Box: Definitions and Abbreviations:
 
Present Value (PV) – the current value of  some amount(s) to be received in the future
 
Future Value (FV) – the amount of money to be received at some future time, or the amount the present value will become at some future date when invested at a given interest rate.
 
Payment (PMT)- The amount to be paid or received at the end of each of a number of time periods.
 
Interest rate (i)- The interest rate used to find present or future valuequeal to the opportunity cost of capital.
 
Time periods (n)- The number of time periods to be used for computing present and future values. Time periods are often a year in length, but can be shorter (month). The annual interest rate (i) must be adjusted to correspond to the length of the tome periods;i.e., a monthly interest rate must be used if the time periods are months.
 
Stream of payments -Annuity- A term used to describe a series of equal periodic payments (PMT). The payments may be either receipts or nditures.
 
 

 

 

 

 

 

 

 

 

 

 

 

 

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6.2.1.Time value of money

 

Everyone would prefer to have 100 EUR today rather than 100 EUR at any time in the future, even those without any economic knowledge. Everyone instinctively recognize that any amount  today is worth more than the same amount at any future date.  Why is that so? There are several explanations:

 

bullet

The first explanation, and the simplest one, can be given from the standpoint of consumption. If the money is to be spent for consumer goods such as a new car, furniture, household appliances etc. everyone would prefer to have amount needed now so the item could be used and enjoyed immediately.

bullet

Every assumption that understands the future includes the risk, which means that unpredictable future circumstances could prevent us from getting money in future. Therefore, we prefer money now rather than letter.

bullet

Inflation also has to be taken in consideration, as inflation in the general cost of goods may diminish what a certain amount of money can buy in the future compared to today.

  

But, the focus of this chapter will be on investment explanation for the time value of money. According to it, money received today can be invested to earn interest, therefore it will increase to the amount plus interest by the  future date. In other words, interest represents opportunity costs of receiving some amount in the future rather than today. This explanation, i.e. the concept of time value of money that is behind it, is essential for any investment decision and calculation, as well as for  manager  or farmer who has to make such decision, wherever it has to be made, in an enterprise or on the farm. So, farm managers of farmers themselves whenever faced with investment decisions have to take it in account.

 

Key words

Time value of money

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6.2.2.Future value

 

The future value of money refers to the value of an investment at a specific date in the future. This concept assumes that the investment earns  interest during each time period, which is then reinvested at the end of each period so it will also earn interest in later time perods. Therefore, the future value will include the original investment and the interest it has earned, plus the interest on the accumulated interest. The procedure for determining future values when accumulated interest also earn interest is called compounding. It can be applied to one-time lump sum investment (PV) or to an investment that takes place through a series of payments (PMT) over time. Each case will be analyzed separately.

 

Future Value of a Present Value

 

The Question is: Starting with a given amount of money today, a PV, what will it be worth at some date in future?

The answer depends on three things: the PV, the interest rate it will earn and the length of the time it will be invested.

 

Assumptions: You have invested 1,000 EUR in a saving account that earns 8% interest rates compounded annually. You would like to know the future value of this investment after 3 years; i.e. how much money  you  have in your saving account after 3 years.

 

The data in  Table 6.1. illustrate how the balance in the account changes from year to year.

  

Table 6.1. Future value of 1,000 EUR 

Year

Value at the beginning of year

Interest rate

(%)

Interest earned

(EUR)

Value at the end of year

 

 

 

 

 

1

1,000.00

8

80.00

1,080.00

2

1,080.00

8

86.40

1,166.40

3

1,166.00

8

93.30

1,259.70

 

Notice that all interested earned is allowed to accumulate in the account, so it also earns interest for the remaining years. This is a principle of compounding and shows the results of using compound interest. In this example, a present value of 1,000 EUR, has a future value of 1,259.70 when invested at 8% interest for 3 years. Interest is compounded when the accumulated interest also earns in the following time periods.

 

Shown procedure for finding a future value would be very tedious if the investment is for a long period of time. This was only example, and in practice future value is found using mathematical equation:

 FV = PV (1  +  i)n

 Where the abbreviations are defined at the beginning of the chapter. Applied to our example the calculations would be

                                                             FV = 1,000 x (1+0.08)3

                                                                  = 1,000 x 1.2597

                                                                  = 1,259.70

As it can be seen the calculations gives the same future value as the one from previous Table.

 

Equation for FV without necessary tools, such as calculator that will raise numbers to power, financial calculators with built-in tools or a computer spread-sheets can become difficult to use, particularly when n is too large. To simplify the calculations of  future values, tables have been constructed giving values of (1+ i)n for different combinations of i and n. Any future value can be found by multiplying the present value with table value (factor)  that corresponds to the appropriate interest rate and length of the investment. The table value is always bigger than 1 as the future value is always bigger than the present one.

 

The concept of future value can be useful in a number of ways. It can be used to estimate future value of saving or future value of e.g. piece of land if we know what is expected annual rate of increase.

 

Questions:

1.      What will be  the value of 5 ha of land in 5 years from now  if the current  value of 1 ha is 11,000EUR and estimations are that it will increase by 6% annually?

2.       Is it better (more profitable) to deposit 5,000 EUR at interest rate of 10% for 5 years,  or at interest rate of 12% for three years?

 

 

Future Value of Annuity – Stream of Payments

 

Next examples illustrate concept of future value for regular series of payments, i.e. gives answer to question what is the future value of a number of  payments (PMT) made at the end of each year for a given number of years.

 

Assumption:

 1,000 EUR is deposited at the end of each year in a saving account that pays 8% annual interest rate. What is the value of this investment at the end of 3rd year?

 

The table illustrate how the future value of this investment can be calculated

 

Table 6.2.  Future Value of Annuity

First payment

1,000 (1 + 0.08)2 =

1,166.40

Second payment

1,000 (1 + 0.08)1 =

1,080.00

Third payment

1,000 (1 + 0.08)0 =

1,000.00

Future value

 

3,246.40

 

Future value of investment is equal to sum of future values of each payment.

Because the money is deposited at the end of each year, the first 1,000 earns interest for only 2 years, the second 1,000 earns interest for 1 year and the third 1,000 earns no interest. Total deposited amount is 3,000 EUR and the FV value of it is 3,246,40, which means that earned interest is 246,40 EUR.

 

This procedure, in case of  annuity with many payments may require many computations. The easiest and quickest way is to use existing equation

 where PMT is the amount invested at the end of each time period. Similar to FV of PV, tables are available for for different interest and time periods and using these already calculated values the whole calculation is much easier.

 

In given example, table value for 8% interest rate and 3 years is 3.2464. Multiplying this factor by the annual payment, or annuity, of 1,000 confirms the previously found FV of 3,246.40

 

FV = 1,000 x 3.2464 = 3,246.40

 

 Questions:

1.      Compare FV of investing 7,000 EUR at interest rate 12% for 7 years period and FV of investing 1,000 each year at 12% interest rate after 7 years. Try to explain the difference!

2.       Assume someone wishes to have 50,000EUR  ten  years from now to purchase new machine for land cultivation: a) How much money would have to be invested today at 7% compound interest? How much would have to be invested annually at 7% interest?

 

 

Key words:

 

present value     future value

payment             compounding

annuity             compound interest                             

 

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6.2.3.  Present value

 

The concept of present value refers to the today value of a sum of money to be received or paid in the future. Present values are found using a process called discounting. The future value is discounted back to the present to find its current or present value. Discounting is done because the sum to be received in the future is worth less than the same amount available today. A present value can be interpreted as the sum of money that would have to be invested now at the certain interest rate to equal a given future value on the same date. When used to find present value, the interest rate is often referred to as  the discount rate.

 

Compounding and discounting are opposite, or inverse procedures and both have time value of money concept in their basis.  A present value is compounded to find its future value, while a future value is discounted to find its present value. These inverse relations will become more apparent in the following discussion.

 

Present Value of a Future Value  (Present Value of a single payment )

 

The present value of a future value depends on the interest rate and the length of time before the payment will be received. Higher interest rates and longer time periods will reduce the present value, and vice versa. The equation to find the present value of a single payment to be received in the future is

 

PV = FV / (1 + i )                or                      PV = FV  x 1/(1+i)n

 

Let’s use this equation to find present value of 1,000 EUR to be received in 5 years using an interest rate of 8%. The calculations would be:

 PV = 1,000 x  1/ (1+0.08)5

=1,000  x 0.68058

= 680.58

A payment of 1,000 EUR  to be received in 5 years has a present value of 680.58EUR at 8% compound rate. Stated differently, 680.58 EUR invested for 5 years at 8% compound interest would have a future value of 1,000EUR. This again shows the inverse relation between compounding and discounting. A more practical use of explanation would be that the investor should not pay more than 680.58 EUR for an investment that will return 1,000EUR in 5 years, if there are other alternatives that will pay 8% interest or more. Investment analysis makes heavy use of present value, as will be shown later.

 

Tables are also available to assist in calculating present values. In these tables, factors 1/(1+i)n can be found for appropriate interest rate and number of years. These factors are called discounted factors. When multiplied by a future value of an amount it gives present value.

 

Present value of Annuity (Present value of stream of payments)

 

Let’s suppose that a payment of 1,000EUR will be received at the end of each year for a period of 3 years, and the interest rate is 8%. If we want to know the present value of this income stream we talk about present value of annuity.

 

Illustration for finding PV of annuity is given in following table:

 

Table 6.3 Present Value of Annuity

Year

Amount

(EUR)

Present value factor

Present value

(EUR)

1

1,000

0.92593

925.93

2

1,000

0.85734

857.34

3

1,000

0.79383

793.83

Total

 

 

2,577.10

 

 Equation for finding present value of annuity is:

 

 It is much easier to take table value of factor. This factor is called annuity factor. The value corresponding to the proper interest rate and number  of years is simply multiplied by the annual payment to find present value of the annuity.  In case from our example it is

 

PV = 1,000  x  2.5771 (table value) = 2,577.10

 

For an investor PV of 2,577.10EUR will  represents the maximum an investor should pay for an investment that will return 1,000EUR  at the end of each year for three years period, if an 8% interest rate is required. Higher interest rate will reduce PV and vice versa.

 

Present value is much more useful than future value when making decisions related to investments. Reasons for such statement are following:

bullet

Not all investments have the same useful lives nor pattern of net cash flows.

bullet

Future values that occur in different years and in different amounts are not directly comparable until they are discounted to a common point in time, the present.

 

Questions:

1.      How would you explain concepts of future value and present value using your own words to someone hearing about them for the first time?

2.      Explain the difference between compounding and discounting?

3.      If you require a 7% rate of return, how much could you afford to pay for an ha of land that has expected annual net cash revenue of 600 EUR per ha for 10 years and expected selling price of 15,000EUR per ha at the end of 10 years?

 

Key words:

Present value of future value;                 Discount factor

Present value of annuity;                        Annuity factor;

Discounting

Discount rate

 

  

Summary

 

Time value of money is concept understanding that same payments of money have different value if take place in different time.

The future value of a sum of money is greater than its present value because of the interest it can earn over the time. Future values are found through a mathematical operation called compounding.

The present value of the sum of money is smaller than its future value, because the money invested today at compound interest will grow into the larger future value. A process for finding present values for amounts to be received in the future is called discounting.

 

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6.3.  Economic profitability of investment - Investment analysis

 

Investment  deals with other than short-term or annual expenditures. It refers to the addition of long-term or noncurrent assets to the business. Because these assets last a number of years, or indefinitely in case of land, these investment decisions will have long-lasting consequences and often involve large sums of money. Such investments should be thoroughly analyzed before the investment decision is made.

 

Investment analysis, or capital budgeting, as it is often called is the process of determining the profitability of an investment or comparing the profitability of two or more alternative investments. Four basic information are requested for thorough analysis of investment:

 

  1. the initial cost of the investment;
  2. the annual net cash revenues realized;
  3. the terminal or salvage value of the investment and
  4. the interest or discount rate to be used.

 

Initial cost. The initial cost of the investment should be the actual total expenditure for its purchase, not the list price nor just the down payment if it is being financed. Of the four types of information required, this will generally be the easiest to obtain.

 

Net cash revenues. Net cash revenues or cash flows must be estimated for each time period in the life of investment. Cash receipts minus cash expenses equals net cash revenues generated by the proposed investment. Depreciation is not included, because it is non-cash expense and it is already accounted for by the difference between the initial cost and the terminal value of the investment. Any interest and principal payments on a loan needed to finance the investments are also omitted from the calculation of net cash revenue. Investment analysis methods are used to determine the  profitability of investment without considering the method or amount of financing needed to purchase it. However, investment analysis techniques can be used to compare several different alternatives for financing an investment.

 

Terminal value. The terminal value need to be estimated, and is usually the same as the salvage value for a depreciable asset. For an nondepreciable asset such as land, the terminal value should be the estimated market value of the asset at the time the investment is terminated. Or, if the land will be held indefinitely, its terminal value can be ignored, because the net cash revenues are assumed to go on forever.

 

Discount rate is often one of the more difficult values to estimate. It is the opportunity cost of capital, representing the minimum rate of return required to justify the investment. If the proposed investment will not earn this minimum, the capital should be invested elsewhere, as investment is considered unprofitable.  If funds will be borrowed to finance the investment, the discount rate can be set equal to the cost of borrowed capital. If a combination of borrowed and equity capital will be used, a weighted average of the interest rate on the loan and the equity opportunity cost should be used. Because risk must also be considered, the discount rate should be equal to the rate of the return expected from an alternative investment of equal risk. Elements that have to be taken into consideration when setting discount rate are : income taxes, risk and inflation. Adjustment of discount rate for these elements will be discussed in more details later on.

 Following table is given as the example of the information needed for investment analysis. For simplicity, the terminal values are assumed to be zero. Whenever terminal value exist it should be added to the net cash revenue for the last year, because it represents additional  cash receipt. Information for the two potential investments in our table will also be applied to illustrate four methods that can be used to analyze and compare investments. These methods are:

 

1.      Payback Period;

2.      Simple Rate of Return;

3.      Net Present Value;

4.      Internal Rate of Return.

 

Those four methods used in investment analysis are methods to determine economic profitability of investment.

 

Table 6.4. Net cash revenues for two 10,000EUR investments (no terminal value)

 

Net cash revenues (EUR)

Year

Investment A

Investment B

1

3,000

1,000

2

3,000

2,000

3

3,000

3,000

4

3,000

4,000

5

3,000

6,000

Total

15,000

16,000

Average return

3,000

3,200

Less annual depreciation

2,000

2,000

Net revenue

1,000

1,200

 

 

Questions:

1.      Define the difference between investments and operational expenditures?

2.      What is investment analysis and what profitability of investment?

3.      How can net revenue be defined and how it can be presented using equation?

4.      What are basic information needed for investment analysis?

 

 

Key words:

investment analysis;         capital budgeting;             initial cost of investment;

net cash revenues;           profitability of investment;          terminal value;

discount rate

 

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6.3.1. Simple Payback Period

 

The simple payback period is the number of years it would take an investment to return its original costs through the annual net cash revenues it generates. If net cash revenues are constant each year, the payback period can be calculated from the equation:

P = C/E

 Where:

P = payback period in years;

C= initial cost of the investment;

E = expected annual net revenue.

 

For investment A, with constant annual net revenues payback period is:

 

P = 10,000/3,000 = 3.33

 

Which means that it will take 3.33 year for investment A to recover or return its original or initial cost.

 

When annual cash revenues are not equal, as in the case of investment B, they should be summed cumulatively year by year to find the year in which the total is equal to initial cost of investment. For investment B, the payback period would be 4 years, because the accumulated net cash revenues reach 10,000 EUR in the fourth year. In this case, investment A is preferred over investment B, because it has shorter payback period.

 

The payback period method can be used to rank investments as we already did. Limited capital can be invested first in the highest ranked investment and then on down the list until the investment capital is exhausted. Another application may be to establish a maximum payback period  and reject all investments with longer one. For example, a manager can select a 4-year payback as a standard and invest only in alternative with a payback of 4 year or less.

 

Advantages of payback period method

 

bullet

It is easy to use and doesn’t require good knowledge or particular computing skills to be used;

bullet

It quickly identifies the investments with the most immediate cash returns

 

Disadvantages of payback period method

 

bullet

It ignores any cash flows that occur after the end of the payback period;

bullet

It ignores the timing during the payback period;

bullet

Doesn’t really measure profitability of investment but rather how quickly investment can contribute to liquidity of business;

bullet

It doesn’t  recognize time value of money;

  

Having in mind all disadvantages mentioned above it can be said that payback period method can not be recommended as serious and accurate method for investment analysis.

 

Managers often use the discounted payback rule to correct for disregarding the time value of money. This method involves the calculation of the payback period in terms of the present value of future cash flows generated by the investment. However, the rule still does not give any weight to to cash flows after arbitrary cut-off date.

 

 Questions:

1.      Use example from the table and apply discounted payback rule to it. Analyze and comment the difference with payback period. Any disadvantage observed that could be added to listed above?

2.      Having in mind everything mentioned about the method can you say in what cases payback period is applicable- i.e. when using method to rank investments- is it applicable to rank investments with different cash flow profiles? If not why not?

 

 

Key words:

 

payback period;                       discounted payback rule;

 

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6.3.2.Simple rate of return

 

The simple rate of return expresses the average annual net revenue as a percentage of the investment. Net revenue is found by subtracting the average annual depreciation from the average annual net cash revenue. In our table example, the net revenue for investment A is 1,000  and for investment B 1,200 EUR. The simple rate of return is calculated from the equation

 

 

Simple rate of return = average annual net revenue/ initial cost

 

Applying the equation to the example in the table gives the following results:

 

Simple rate of return for investment A = 1,000/10,000 = 10%

 

Simple rate of return for investment B = 1,200/10,000 = 12%

 

As it can be seen, this method would rank investment B higher than A, which is opposite result with the one obtained from payback method.

 

Advantages of simple rate of return:

bullet

Required calculations are simple and quick;

bullet

Better than payback method for analyzing profitability of investments as it considers an investment’s earning over its entire life;

 

Disadvantages of simple rate of return:

 

bullet

It uses average annual earnings and fails to recognize the size and the timing of earnings;

bullet

Doesn’t recognize time value of money.

 

Simple rate of return is considered as not accurate method for investment analysis and it is not recommended for serious investment decisions, especially for investments with variable annual net revenues.

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6.3.3.Net Present Value Method

 

The net present value method is very often used and preferred method of investment analysis. It considers the time value of money as well as the size of the stream of cash flows over the entire life of the investment. It is also called discounted cash flow method, as the discounted cash flow of an investment is its basis.

Text Box: Net present value (NPV): the difference between the present value of the benefits of investment and its costs.

 

 

 

In other words, net present value of investment is the sum of the present values for each year’s net cash flow (or net cash revenue) minus the initial cost of investment. The equation to calculate NPV of investment is

NPV =   P1 / (1 +i)1  +  P2 / (1 +i)2 +……..+ Pn / (1 +i)n – C

 NPV – net present value of investment;

Pn – net cash flow in year n

i – the discount rate

C – initial cost of investment

 

Investments with positive NPV  should be accepted while investments with negative NPV should be rejected by investors.

 

If we assume that investment net cash flows for 5 years are  3,000 each year and estimated discount rate is 9% and initial cost of investment is 10,000 NPV would be:

 

NPV = 3,000/ (1+0.09)1 + 3,000/(1+0.09)2 + 3,000/(1+0.09)3 + 3,000/(1+0.09)4 + 3,000/(1+0.09)5  - 10,000 =

=3,000 (0.917431) + 3,000 (0.841680) + 3,000(0.772183) + 3,000 (0.708425) + 3,000(0.649931) – 10,000 =

= 2,752 + 2,525  + 2,316 + 2,125 + 1,948 – 10,000 = 11,666 – 10,000 = 1,166

 

Using NPV as the decision tool for investment analysis implies two rules:

 

  1. Investment is profitable and thus acceptable if NPV of investment is positive (NPV>0)

  2. Investment with highest NPV is preferable when there are more than one  investment alternatives

 

Positive NPV of investment for investor means:

 

bullet

The actual rate of return on the investment is greater than the discount rate used in calculation, i.e. the percent return is greater than the cost of capital

bullet

Investor could afford to pay more for the investment and still achieve a rate of return equal to the discount arte used in calculating the NPV.

 

Question:

A particular care must be taken to select the appropriate discount rate when calculating NPV of an investment. Explain using previous example what would be consequence of misjudgment in both directions (two high or two low discount rate).

 

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6.3.4. Internal Rate of Return (IRR)

 

Besides in calculation of NPV of investment, the time value of money is also used in the internal rate of return, or IRR. This is the method commonly used, together with NPV to determine profitability of investment, as it provides some information not available directly from the NPV method. IRR is the actual rate of return of an investment or the discount rate that makes NPV of investment zero.

As the result, IRR could be found by solving following operation for i

 

0 =   P1 / (1 +i)1  +  P2 / (1 +i)2 +……..+ Pn / (1 +i)n – C       or

 C  =   P1 / (1 +i)1  +  P2 / (1 +i)2 +……..+ Pn / (1 +i)n

 

This means that IRR is discount rate that makes net cash flows of investment equal to initial cost of investment.

IRR is found directly using computer program or a financial calculator. Without it IRR can be found by trial and error. In this case, procedure is following: We calculate NPV of investment using any chosen discount rate. If NPV value obtained is positive, than IRR is higher than the one applied and we try again with higher discount rate as long as we get a negative NPV. Then we conclude than the IRR is between two nearest discount rates that make NPV positive and negative.

 

Rule when using IRR for investment analysis.

bullet

 If the IRR of an investment is higher than the opportunity cost of capital, investment is profitable and acceptable

 

Disadvantages of IRR

bullet

It is complicated  and time consuming calculation;

bullet

It ignores the size of initial investment;

bullet

It can lead to overestimation of actual rate of return

  

Questions:

1.      Assume you have only 40,000EUR to invest and you have to choose between the two investments below. Analyze each using all four methods discussed (payback method, simple rate of return, net present value, internal rate of return) and apply 9% opportunity cost for capital. Which investment you would choose? Why?

 

 

Investment A (EUR)

 

Investment B (EUR)

 

Initial cost

20,000

20,000

Net cash revenues

 

 

Year 1

6,000

5,000

Year 2

6,000

5,000

Year 3

6,000

5,000

Year 4

6,000

5,000

Year 5

6,000

5,000

Terminal value

0

8,000

 

2.      Why do we use IRR if it, as method for determining to invest or not, it gives the same answer as NPV? What is information that IRR provides and NPV does not?

3.      Why IRR as method is not sufficient, but is most often used in combination with NPV?

4.      Pay particular attention and compare payback with discounted payback, and simple interest rate with internal rate of return.

 

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 6.4. Financial Feasibility of Investments

  

The investment analysis methods discussed so far are methods to analyze economic profitability of investment. They are meant to answer the question “Is the investment profitable?” The question of how the investment was financed was ignored, except for calculating the discount rate. However, when the method and amount of financing used to make the investment are included in the analysis, investment identified as profitable may have years of negative cash flows. Thus, besides the profitability of an investment, an equally important question may be “Is the investment financially feasible”? In other words, will the investment generate sufficient cash flows at the right time to meet the required cash outflows, including loan payments? Determination of financial feasibility should be the final step in any investment analysis.

  

A potential problem is illustrated in Table 6.5. for  the investments A and B used throughout this analysis.

 

Assumptions: Each investment is totally financed with a 10,000 EUR loan at 8% interest, to be repaid over 5 years equal annual principal payments, plus interest.

 

Table 6.5.  Cash flow analysis of investments

 

Investment A

 

Investment B

 

Year

Net cash revenue

Debt payment

Net cash flow

Net cash revenue

Debt payment

Debt payment

 

 

 

 

 

 

 

1

3,000

2,800

200

1,000

2,800

-1,800

2

3,000

2,640

360

2,000

2,640

-640

3

3,000

2,480

520

3,000

2,480

520

4

3,000

2,320

680

4,000

2,320

1,680

5

3,000

2,160

840

6,000

2,160

3,840

 

Both interest and principal are included in the debt payment column, and are subtracted from the net cash revenue to find the net cash flow.

 

Investment A shows a positive net cash flow for each year, because the net cash revenue is greater than the debt payment. However, investment B has lower net cash revenues the first 2 years, which cause negative cash flows in those years. Both investments had positive net present values using as 8% discount rate, and investment B actually had a slightly higher NPV than A. However, it is not unusual to find profitable investments that have negative cash flows in the early years if the net cash revenues start slowly and the investment requires a large amount of borrowed capital. The problem can be further compounded if the loan must be paid off in relatively short period of time.

If an investment such as B is undertaken, something has to be done to make up for the negative cash flows. There are several possibilities, which can be used individually or in combination. First, some equity capital can be used for part or all of the initial cost of the investment, in order to reduce the size of the loan and the annual debt payments. Second, the payment schedule for the loan may be lengthened to make the debt payment more nearly equal to the net cash revenues. Arranging for smaller payments with a balloon payment at the end, interest-only payments for the first few years, would be other possibilities.

Should cash flow related financing ever be included in the calculation of the NPV of an investment? Generally not, because the decision to make an investment and the question of how to finance it should be considered separately. Occasionally,  though, an investment and the method to finance it may be closely linked.

In some cases, it may be possible to finance the same investment several different ways. Once the investment is accepted, the financing alternatives can be compared by discounting the payment streams for each one and selecting the one with the lowest NPV.

 

Factors that have to be included in investment analysis

 

In previous chapter, only basic procedures, methods and elements were taken into the account in order to simplify examples of investment analysis. But, at this stage, some important factors have to be, at least mentioned, as they have big influence and deserve attention in any investment analysis. These factors are:

bullet

Risk

bullet

Inflation

bullet

Income taxes

 

 

Questions:

1.      Discuss economic profitability and financial feasibility of investment?

2.      Explain what is the difference and how are they inter-related?

3.      Why should both economic profitability and financial feasibility be considered when analyzing potential investment?

 

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6.5. Mutually exclusive investments

(comparison of NPV and IRR)

 

When capital to be invested is limited and there are more than one request for investing, and when decision to finance one investment excludes financing the other (e.g. two capital assets to be purchased) then we talk about mutually exclusive investments.

 

What method to use to rank mutually exclusive investments?

 

When taken as the basis for investment decision, the IRR method will often result with the same conclusion as the NPV method if taken as the basis for decisions. However, in mutually exclusive investments, application of the IRR and NPV rules can sometimes lead to conflicting recommendations.  Illustration of such situation is presented in following simplified example.

 

A farmer can select to finance one of two mutually exclusive projects. Estimated assumptions are given:

 

 

Initial investment

Cash inflow over 3 years of investment life

 

(EUR)

Year 1

Year 2

Year 3

Cost of capital = 10%

 

 

 

 

Investment X

5,600

2,700

2,700

2,700

Investment Y

9,600

4,400

4,400

4,400

 

Net present value and Internal rate of return calculations give the following results:

 

 

NPV (EUR)

IRR (%)

 

 

 

Investment X

1,115

21

Investment Y

1,342

18

 

It can be seen from the example that IRR method ranks X first, while NPV method ranks Y first. If the investments were independent, this would be immaterial, ad both investments would be accepted and financed. But in the context of  mutually exclusive projects, the ranking is crucial, as only one project can be accepted.

 

The main problem with IRR method is that it expresses the result as a percentage rather than in monetary terms. Comparison in percentage returns can be misleading if no other information are available.

 For example,  let us  compare investment of 50 EUR which produces IRR of 80% with an investment of 500EUR  producing IRR 20%. If the capital is not a constraint, the investment costing 500EUR would be chosen as it yields 100EUR, compared to 40 EUR generated by the other investment, although the second one has a superior IRR.

Second problem with the IRR is encountered when unconventional cash flows occur, with negative cash flows coming in later years. If the sign of the net cash flows changes in successive periods, it is possible for the calculations to produce multiple IRRs. While multiple rates of return are theoretically possible, only one rate of return is significant in an ‘accept’ or ‘reject’ decision. Analysts should be aware of such situations where the NPV rule gives an unambiguous decision criterion.

 

The assumption concerning the reinvestment of interim cash flows from the acceptance of investments provides another reason for supporting the superiority of  NPV method. The implicit assumption, when NPV is applied, is that interim cash flow will be reinvested at the cost of capital, i.e. the discount rate. However, the IRR rule makes a different implicit assumption about the reinvestment of the interim cash flows. It assumes that all proceeds from investment can be reinvested to earn a return equal to the IRR of the original investment. In mentioned above example, NPV method assumes that annual cash inflow of 2,700 EUR for Investment X will be reinvested at the cost of capital of 10%, whereas the IRR method assumes that they will be reinvested at 21%. In theory, investment which offer a return exceeding the cost of capital, and any other funds which become available can only be reinvested at the cost of capital. This is the assumption implicit in the NPV method.

 

Conclusion:

 

Net Present Value (NPV) method is superior to Internal Rate of Return for mutually exclusive investments because:

bullet

IRR is unreliable in ranking investments when different outlays are involved;

bullet

IRR can not be used if cost of capital changes during the investment life;

bullet

Calculations can produce multiple IRRs

 

Regardless everything mentioned IRR is quite often used in mutually investments because:

bullet

Managers find it much easier to interpret;

bullet

Cut-off rate need not to be determined and specified beforehand.

 

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6.6. Additional methods related to investment analysis

 

6.6.1.Sensitivity analysis 

 The purpose of sensitivity analysis is to identify the variables to which the NPV is most sensitive. Sensitivity analysis is useful in determining consequences of specified changes in variables such as product price, sales volume, input costs and investment life span. However, sensitivity analysis is not useful tool to indicate the likelihood that such events will actually occur. Only risk analysis can answer such questions. Sensitivity analysis is tool to identify key variables and  to focus managerial attention on the most important components of forecast that are underlying the expected investment cash flows.

The analysis is carried out by measuring the change of the value of investment after shifting the value of one underlying variable up and down, corresponding to a more optimistic or pessimistic forecast. The magnitude of the change in the net present value shows the sensitivity of the investment to that particular variable.

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6.6.2. Break-even analysis

 Break-even analysis goes one step further than the scenario analysis. It points out the critical value of each underlying variable at which the investment’s NPV is zero. In other words it will tell manager or farmer what is the break-even value of variable at which farmer starts to loose money on investment.

 

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6.6.3.Scenario analysis

 The previous two investment analysis tools are concerned with only one underlying factor at a time, thereby treating them as non-interrelated. However, from experience we know that, for example, certain market events will surely result in a change of several underlying variable at the same time. Example can be when new competitor enter existing market. In such situation, both market share as well as the product price is expected to drop. Scenario analysis allows management to investigate the effects of potential future scenario of events, which are translated in discounted cash flow valuation model as consistent changes of various combinations of the underlying variables.

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Summary

 

Investments can be analyzed by one or more methods. Payback period, simple rate of return, net present value, discounted payback period and internal rate of return are some of them. First two are easy  to calculate but have the disadvantage of not accurately incorporating the time value of money into the analysis. This may cause the error in deciding in terms of approving, selecting or ranking alternative investments.

The net present value (NPV) method is widely used, as it properly accounts for the time value of money. Any investment with a  positive NPV is profitable.

The internal rate of return is dynamic methods used to determine the return of capital invested. Any investment with internal rate of return higher than the cost of capital is profitable.

Discounted payback period gives the answer to the question when the investment returns the capital invested.

Whatever method is used, there is requirement to estimate net cash revenues over the life of investment as well as terminal value of investment. NPV methods requires selection of a proper discount rate. Both cash revenues and discount rate  should be on after-tax basis in a practical application of these methods. The discount rate may need to be adjusted to risk and inflation.

A final step in analyzing any investment should be a financial feasibility analysis, particularly when a large amount of borrowed capital is used to finance the investment.

Further illumination can be provided by sensitivity analysis (calculating the impact of changing one or more variables), break-even analysis (pointing out critical value of each variable where NPV is zero), and scenario analysis.

 

Suggested Reading:

  1. Ronald D.Key, William M. Edwards (1994): Farm management , Mc Grow-Hill
  2. H. Evan Drummond, John W. Goodwin: Agricultural Economics, Prentice Hall;
  3. Silvije Orsag: Procjena investicijskih projekata, Masmedia, Zagreb, 2002.
  4. J.Price Gittinger: Economic Analysis of Agricultural Projects; The Johns Hopkins University Press Baltimore and London;
  5. Dr. Frank-Michael Litzka University of Hohenheim, Institute for Agricultural Economics, Dept. for Farm Management "The Theory of Investment".
  6. FAO Investment Centre: Financial analysis in agricultural project preparation.

 

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Revised: 10/08/03.



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