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ModuleBasic Principles in Agricultural Economics
The Theory of Investment
Number of hours: 6
Chapter objectives Introduction 6.1. Basic definitions and assumptions of theory of investment 6.2. Concepts underlying investments 6.3. Economic profitability of investment – Investment analysis 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
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.
IntroductionOn 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:
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:
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?
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.
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:
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 wordsTime value of money
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
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
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
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
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 ) n 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
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:
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.
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:
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)
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