Present value method. Net present value: what is it, what is this indicator
Investments will be justified only when they contribute to the creation of new values \u200b\u200bfor the owner of capital. In this case, the value of these values \u200b\u200bis determined that exceeds the cost of their acquisition. Of course, the question arises as to whether it is possible to evaluate them more than real value. This is available if the final result is more valuable in comparison with the total price of the individual stages, the implementation of which allowed to achieve this result. In order to understand this, you should find out what the net present value is and how it is calculated.
What is the present value?
Current or present value is calculated based on the concept of money in time. It is an indicator of the potential of funds allocated to generate income. It allows you to understand how much the amount that is currently available will cost in the future. Conducting an appropriate calculation is of great importance, since payments made in a different period can only be compared after they have been reduced to the same time period.
The present value is formed as a result of reduction to the initial period of future receipts and expenses of funds. It depends on how the interest is calculated. For this, simple or compound interest is used, as well as annuity.
What is net present value?
The net present value of NPV is the difference between the market price of a particular project and the cost of its implementation. The abbreviation used to refer to it stands for Net Present Value.
Thus, the concept can also be defined as a measure of the added value of the project, which will be obtained as a result of its financing at the initial stage. The main task is to implement projects that have a positive indicator of net present value. However, to begin with, one should learn to define it, which will help to make the most profitable investments.
NPV basic rule
You should familiarize yourself with the basic rule that the net present value of investments has. It lies in the fact that the value of the indicator must be positive for the consideration of the project. It should be rejected when receiving a negative value.
It is worth noting that the calculated value is rarely zero. However, upon obtaining such a value, it is also advisable for the investor to reject the project, since it will not make economic sense. This is due to the fact that the profit from the investment will not be received in the future.
Calculation accuracy
In the process of calculating NPV, it is worth remembering that the discount rate and revenue forecasts have a significant impact on fair value. The end result may be errors. This is due to the fact that a person cannot make a forecast for future profit with absolute accuracy. Therefore, the obtained indicator is only an assumption. He is not immune to fluctuations in different directions.
Of course, the investor needs to know what profit will be received by him before the investment. To ensure that deviations are minimal, the most accurate methods should be used to determine efficiencies in combination with net present value. The common use of various methods will help to understand whether investments in a particular project will be beneficial. If the investor is confident in the correctness of their calculations, you can make a decision that will be reliable.
Calculation formula
When searching for programs for determining the net present value, one may encounter the concept of “net present value”, which has a similar definition. It can be calculated using MS EXCEL, where it is found under the acronym NPV.
The formula used uses the following data:
- CFn - the amount of money for the period n;
- N is the number of periods;
- i is the discount rate, which is calculated from the annual interest rate
In addition, cash flow for a certain period can be zero, which is equivalent to its complete absence. When determining income, the amount of money is recorded with a "+" sign, for expenses - with a "-" sign.
As a result, the calculation of net present value leads to the possibility of evaluating the effectiveness of investments. If NPV\u003e 0, the investment will pay off.
Application restrictions
Trying to determine what the NPV net present value will be, using the proposed methodology, one should pay attention to some conditions and limitations.
First of all, the assumption is made that the indicators of the investment project during its implementation will be stable. However, the probability of this may approach zero, since a large number of factors affect the value of cash flows. After some time, the cost of capital allocated for financing may change. It should be noted that in the future the obtained indicators may change significantly.
An equally important point is the choice of the discount rate. As it can be used the cost of capital raised for investment. Depending on the risk factor, the discount rate may be adjusted. A premium is added to it, so the net present value is reduced. This practice is not always justified.
The use of a risk premium means that the investor first of all considers only the loss. He may mistakenly reject a profitable project. The discount rate may also be the return on alternative investments. For example, if the capital used for investing is invested in another business at a rate of 9%, it can be taken as the discount rate.
Benefits of using the technique
The calculation of net present value has the following advantages:
- the indicator takes into account the discount factor;
- when making a decision, clear criteria are used;
- the ability to use when calculating project risks.
However, it is worth considering that this method has not only advantages.
Disadvantages of using the technique
The net present value of the investment project has the following negative qualities:
- In some situations, it is quite problematic to correctly calculate the discount rate. This most often applies to multidisciplinary projects.
- Despite the fact that cash flows are predicted, using the formula it is impossible to calculate the probability of the outcome of the event. The applied coefficient can take into account inflation, but basically it is the rate of profit laid down in the settlement project.
After a detailed familiarization with the concept of “net present value” and the calculation procedure, the investor can conclude whether it is worth using the methodology in question. To determine the effectiveness of investments, it is desirable to supplement it with other similar methods, which will allow you to get the most accurate result. However, there is no absolute probability that it will correspond to the actual receipt of profit or loss.
We calculate the net present value and the internal rate of return using the formulasMsEXCEL.
Let's start with the definition, more precisely with the definitions.
Net present value (NPV) is called the sum of the discounted values \u200b\u200bof the payment stream reduced to today (taken from Wikipedia).
Or so: Net present value is the current value of future cash flows of the investment project, calculated taking into account discounting, net of investments (websitecfin.ru)
Or so: Current the value of a security or investment project, determined by taking into account all current and future income and expenses at an appropriate interest rate. (Economy .
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Note1. Net present value is also often called Net present value, Net present value (NPV). But, because the corresponding MS EXCEL function is called NPV (), then we will adhere to this terminology. In addition, the term Net Present Value (NPV) clearly indicates a relationship with.
For our purposes (calculation in MS EXCEL) we define NPV as follows:
Net present value is the sum of cash flows presented in the form of payments of arbitrary value, carried out at regular intervals.
Tip: when you first get acquainted with the concept of Net Present Value, it makes sense to get acquainted with the materials of the article.
This is a more formalized definition without reference to projects, investments and securities, as this method can be used to assess cash flows of any nature (although, indeed, the NPV method is often used to evaluate the effectiveness of projects, including comparing projects with different cash flows).
Also in the definition there is no concept of discounting, because the discount procedure is, in fact, the calculation of the present value by the method.
As it was said, in MS EXCEL, the NPV () function is used to calculate the Net Present Value (the English version is NPV ()). It is based on the formula:
CFn is the cash flow (cash amount) in period n. The total number of periods is N. To show whether cash flow is income or expense (investment), it is recorded with a certain sign (+ for income, minus - for expenses). The amount of cash flow in certain periods may be \u003d 0, which is equivalent to the absence of cash flow in a certain period (see note 2 below). i is the discount rate for the period (if the annual interest rate is set (let it be 10%), and the period is equal to the month, then i \u003d 10% / 12).
Note2. Because cash flow may not be present in every period, then the definition of NPV can be clarified: Net present value is the present value of cash flows presented in the form of payments of arbitrary value, carried out at time intervals that are multiples of a certain period (month, quarter or year). For example, initial investments were made in the 1st and 2nd quarter (indicated with a minus sign), there were no cash flows in the 3rd, 4th and 7th quarter, and in the 5-6th and 9th quarter project revenue (indicated with a plus sign). For this case, NPV is considered exactly the same as for regular payments (amounts in the 3rd, 4th and 7th quarter must be specified \u003d 0).
If the sum of the reduced cash flows representing income (those with a + sign) is greater than the sum of the reduced cash flows representing investments (expenses, with a minus sign), then NPV\u003e 0 (the project / investment pays off). Otherwise NPV<0 и проект убыточен.
Choosing a discount period for the NPV function ()
When choosing a discount period, you need to ask yourself the question: “If we forecast 5 years in advance, can we predict cash flows with an accuracy of a month / to a quarter / to a year?”.
In practice, as a rule, the first 1-2 years of receipt and payment can be predicted more accurately, say monthly, and in subsequent years, the timing of cash flows can be determined, say, once a quarter.
Note3. Naturally, all projects are individual and no single rule for determining the period can exist. The project manager must determine the most probable dates of receipt of the amounts based on current realities.
Having determined the timing of cash flows, for the NPV () function, you need to find the shortest period between cash flows. For example, if in the 1st year receipts are planned monthly, and in the 2nd quarterly, then the period should be chosen equal to 1 month. In the second year, the cash flows in the first and second months of the quarters will be 0 (see sample file, NPV sheet).
In the table, NPV is calculated in two ways: through the NPV function () and formulas (calculating the present value of each amount). The table shows that already the first amount (investment) is discounted (-1 000 000 turned into -991 735.54). Suppose that the first amount (-1,000,000) was transferred on 01/31/2010, which means its present value (-991,735.54 \u003d -1,000,000 / (1 + 10% / 12)) was calculated on 12/31/2009. (without much loss of accuracy, we can assume that on 01/01/2010.)
This means that all amounts are shown not at the date of transfer of the first amount, but at an earlier date - at the beginning of the first month (period). Thus, the formula assumes that the first and all subsequent amounts are paid at the end of the period.
If you want all amounts to be shown on the date of the first investment, then you do not need to include it in the arguments of the NPV () function, but you just need to add it to the result (see the example file).
A comparison of the 2 discount options is given in the example file, NPV sheet:
About the accuracy of calculating the discount rate
There are dozens of approaches for determining the discount rate. For calculations, many indicators are used: the weighted average cost of company capital; refinancing rate; average bank deposit rate; annual inflation rate; income tax rate; country risk-free rate; premium for project risks and many others, as well as their combinations. Not surprisingly, in some cases, calculations can be quite time-consuming. The choice of the right approach depends on the specific task, we will not consider them. We only note one thing: the accuracy of calculating the discount rate must correspond to the accuracy of determining the dates and amounts of cash flows. We show the existing dependence (see example file accuracy sheet).
Let there be a project: the implementation period is 10 years, the discount rate is 12%, the cash flow period is 1 year.
NPV was 1,070,283.07 (Discounted at the date of first payment).
Because Since the project is long, everyone understands that the amounts in 4-10 are not determined exactly, but with some acceptable accuracy, say +/- 100,000.0. Thus, we have 3 scenarios: Basic (the average (most “probable”) value is indicated), Pessimistic (minus 100,000.0 from the base) and optimistic (plus 100,000.0 to the base). It should be understood that if the base amount is 700,000.0, then the amounts of 800,000.0 and 600,000.0 are no less accurate.
Let's see how NPV will respond when the discount rate changes by +/- 2% (from 10% to 14%):
Consider a rate increase of 2%. It is clear that with an increase in the discount rate, NPV decreases. If we compare the ranges of the NPV scatter at 12% and 14%, we see that they intersect at 71%.
Is it a lot or a little? Cash flow in 4-6 years is predicted with an accuracy of 14% (100 000/700 000), which is quite accurate. A change in the discount rate of 2% led to a decrease in NPV by 16% (when compared with the base case). Given that the ranges of NPV scatter overlap significantly due to the accuracy of determining the amount of cash income, an increase of 2% in the rate did not significantly affect the NPV of the project (taking into account the accuracy of determining the amount of cash flow). Of course, this cannot be a recommendation for all projects. These calculations are given as an example.
Thus, using the above approach, the project manager should evaluate the costs of additional calculations of a more accurate discount rate, and decide how much they will improve the NPV score.
We have a completely different situation for the same project, if the discount rate is known to us with less accuracy, say +/- 3%, and future flows are known with greater accuracy +/- 50,000.0
An increase in the discount rate of 3% led to a decrease in NPV by 24% (when compared with the base case). If we compare the ranges of the NPV scatter at 12% and 15%, we see that they intersect only 23%.
Thus, the project manager, having analyzed the sensitivity of NPV to the discount rate, must understand whether the calculation of NPV will be significantly refined after calculating the discount rate using a more accurate method.
After determining the amounts and terms of cash flows, the project manager can assess what maximum discount rate the project can withstand (criterion NPV \u003d 0). The next section discusses the Internal Rate of Return - IRR.
Internal rate of returnIRR (VSD)
Internal rate of return internal rate of return, IRR (IRR)) is the discount rate at which the Net Present Value (NPV) is 0. The term Internal Rate of Return (IRR) is also used (see example file, IRR sheet).
The advantage of IRR is that in addition to determining the level of return on investment, it is possible to compare projects of different sizes and various durations.
The IRR () function is used to calculate IRR (the English version is IRR ()). This function is closely related to the NPV () function. For the same cash flows (B5: B14), the Rate of Return calculated by the IRR function () always leads to a Zero Net Present Value. The relationship of functions is reflected in the following formula:
\u003d NPV (VVD (B5: B14); B5: B14)
Note4. IRR can also be calculated without the IRR () function: it is enough to have the NPV () function. To do this, use the tool (the "Set in a cell" field should refer to the formula with the NPV (), set 0 in the "Value" field, the "Changing the cell value" field should contain a link to the cell with the rate).
Calculation of NPV at constant cash flows using the PS function ()
Internal rate of return
By analogy with the NPV (), which has a related function of the IRR (), CHISTNZ () has the function CHISTVDOCH (), which calculates the annual discount rate at which CHISTNZ () returns 0.
Calculations in the function PURPOSE () are performed according to the formula:
Where, Pi \u003d i-th amount of cash flow; di \u003d date of the i-th amount; d1 \u003d date of the 1st amount (the starting date at which all amounts are discounted).
Note5. The NULL () function is used for.
CalculatePresented (to the current moment) costinvestments with various methods of calculating interest: according to the formula of simple interest, compound interest, annuity, and in the case of payments of arbitrary value.
Present value is calculated on the basis of the concept of the value of money over time: the money currently available is worth more than the same amount in the future, due to its potential to provide income. The calculation of the present value is just as important, since payments made at different points in time can only be compared after bringing them to one time point.
The present value is obtained as a result of bringing the Future income and expenses to the initial period of time and depends on what method the interest is calculated:, or (in the example file the solution to the problem for each method is given).
Simple interest
The essence of the method of accrual for simple interest is that interest is accrued over the entire investment period for the same amount (interest accrued for previous periods is not capitalized, i.e., interest is not accrued on them in subsequent periods).
In MS EXCEL, the abbreviation PS is used to refer to the Present Value (PS is used as an argument in the numerous financial functions of MS EXCEL).
Note. MS EXCEL does not have a separate function for calculating the Present Value using the Simple Interest method. The PS function () is used to calculate in case of compound interest and annuity. Although, specifying the value 1 as argument, and i * n as the rate, you can make PS () calculate the Present Value using the simple interest method (see example file).
To determine the Present Value when calculating simple interest, we use the formula for calculating (FV):
FV \u003d PV * (1 + i * n)
where PV is the Present Value (the amount that is currently invested and on which interest is accrued);
i - interest rate over a period interest accrual (for example, if interest is accrued once a year, then annual; if interest is accrued monthly, then per month);
n is the number of time periods during which interest is accrued.
From this formula we get that:
PV \u003d FV / (1 + i * n)
Thus, the procedure for calculating Present Value is the opposite of calculating Future Value. In other words, with its help we can find out how much we need to invest today in order to receive a certain amount in the future.
For example, we want to know how much we need to open a deposit today in order to accumulate 100 000 rubles in 3 years. Let the bank have a deposit rate of 15% per annum, and interest will be accrued only on the principal amount of the deposit (simple interest).
In order to find the answer to this question, we need to calculate the Present value of this future amount by the formula PV \u003d FV / (1 + i * n) \u003d 100000 / (1 + 0.15 * 3) \u003d 68 965.52 rubles. We got that the current (current, real) amount is 68,965.52 rubles. equivalent to the amount after 3 years in the amount of 100 000,00 rub. (at the current rate of 15% and accrual using the simple interest method).
Of course, the Present Value method does not take into account inflation, bank bankruptcy risks, etc. This method works effectively to compare amounts “all other things being equal.” For example, what can you use to answer the question “What is the most profitable proposal to accept in order to receive the maximum amount in 3 years: open a deposit with simple interest at a rate of 15% or with complex interest with a monthly capitalization at a rate of 12% per annum”? To answer this question, we consider the calculation of the Present Value in calculating compound interest.
Compound interest
When using complex interest rates, interest money accrued after each accrual period is added to the amount of debt. Thus, the basis for calculating compound interest, in contrast to use, changes in each accrual period. The addition of accrued interest to the amount that served as the basis for their accrual is called interest capitalization. Sometimes this method is called "percent by percent."
The present value of PV (or PS) in this case can be calculated using.
FV \u003d RV * (1 + i) ^ n
where FV (or S) is the future (or accumulated amount),
i is the annual rate
n is the loan term in years,
those. PV \u003d FV / (1 + i) ^ n
With a capitalization of m once a year, the Present Value formula looks like this:
PV \u003d FV / (1 + i / m) ^ (n * m)
i / m is the rate for the period.
For example, the amount of 100 000 rub. after 3 years on the current account is equivalent to today's amount of 69,892.49 rubles. at the current interest rate of 12% (accrual% monthly; no replenishment). The result is obtained by the formula \u003d 100000 / (1 + 12% / 12) ^ (3 * 12) or by the formula \u003d PS (12% / 12; 3 * 12; 0; -100000).
Answering the question from the previous section, “What is the bank’s best offer to accept in order to receive the maximum amount in 3 years: open a deposit with simple interest at a rate of 15% or with complex interest with a monthly capitalization at a rate of 12% per annum”? we need to compare two Present values: 69 892,49 rub. (compound interest) and 68 965.52 rubles. (simple interest). Because The present value calculated on the proposal of the bank for a deposit with simple interest is less, then this offer is more profitable (today you need to invest less money in order to receive the same amount of 100,000.00 rubles in 3 years)
Compound interest (several amounts)
Define the present value of several amounts that belong to different periods. This can be done using the PS function () or the alternative formula PV \u003d FV / (1 + i) ^ n
By setting the discount rate to 0%, we simply get the amount of cash flows (see example file).
Annuity
If, in addition to the initial investment, additional equal amounts of payments (additional investments) are made through equal periods of time, then the calculation of the Present Value is significantly complicated (see the article for the calculation using the PS () function, as well as the alternative formula).
Here we will analyze another task (see the example file):
The client opened a deposit for a period of 1 year at a rate of 12% per annum with monthly interest accrual at the end of the month. The client also at the end of each month makes additional contributions in the amount of 20,000 rubles. The value of the deposit at the end of the term reached 1,000,000 rubles. What is the initial deposit amount?
The solution can be found using the PS () function: \u003d PS (12% / 12; 12; 20,000; -1000000; 0) \u003d 662 347.68 rub.
Argument Rate indicated for the period of interest calculation (and, accordingly, additional contributions), i.e. per month.
Argument Nper Is the number of periods, i.e. 12 (months), as the client opened a deposit for 1 year.
Argument Fr - this is 20,000 rubles., i.e. amount of additional contributions.
Argument Bs - this is -1000000r., i.e. future value of the contribution.
The minus sign indicates the direction of cash flows: additional contributions and the initial deposit amount of one sign, because client lists these funds to the bank, and the future amount of the client’s deposit will receive from the bank. This very important point applies to everyone, as otherwise, you may get an incorrect result.
The result of the PS function () is the initial amount of the contribution, it does not include the present value of all additional contributions of 20,000 rubles. You can verify this by calculating the present value of additional contributions. Total additional contributions were 12, the total amount of 20,000 rubles. * 12 \u003d 240000 rubles. It is clear that at the current rate of 12% their Present value will be less \u003d PS (12% / 12; 12; 20,000) \u003d -225 101.55 rubles. (accurate to the sign). Because these 12 payments made in different periods of time are equivalent to 225 101.55 rubles. at the time of opening the deposit, they can be added to the initial deposit amount calculated by us 662,347.68 rubles. and calculate their total future value \u003d BS (12% / 12; 12 ;; 225 101.55 + 662 347.68)\u003d -1000000.0 rub., Which was required to prove.
Both concepts from the title of this section, discounted (present) value, PS (presentvalue, or PV), and net present valueNPV (netpresentvalue, or NPV), denote currentthe value of future cash receipts.
As an example, consider the valuation of an investment that promises a return of $ 100 per year at the end of the current and four next years. We assume that this series of five payments of $ 100 each is guaranteed and money will certainly arrive. If the bank paid us an annual interest of 10% for a five-year deposit, then these ten percent would have constituted the opportunity cost of the investment — the benchmark rate of return, with which we would compare the benefits of our investment.
You can calculate the value of the investment by discounting the cash flow from it using the opportunity cost as the discount rate.
Calculation formula inExcel present value (PV) \u003d NPV (C1; B5: B9)
Present value(PS) in the amount of $ 379.08 is the current value of the investment.
Suppose that this investment would sell for $ 400. Obviously, it would not be worth the asking price, because - given an alternative income (discount rate) of 10% - the real value of this investment would be only $ 379.08. appropriate to introduce the concept net present value(NPV). Symbolizing r discount rate for this investment, we get the following nPV formula:
Where CF t - cash flow from the investment at time t; CF 0 - current cash flow (receipt).
Calculation formula inExcel net present value (NPV) \u003d NPV (C1; B6: B10) + B5
Excel terminology for discounted cash flows is somewhat different from standard financial terminology. In Excel, the abbreviation SUR (NPV) stands for present value (not chiflockpresent value) series of cash receipts.
To calculate in Excel net present valueseries of cash receipts in the usual sense of financial theory, you must first calculate present valuefuture cash receipts (using an Excel function such as NPV), and then subtract cash flow from that number at the initial point in time. (This value often coincides with the value of the asset in question.)
In this article we will consider what the net present value (NPV) is, what economic sense it has, how and by what formula to calculate the net present value, we will consider some examples of calculation, including using the MS Exel formulas.
What is net present value (NPV)?
When investing money in any investment project, the key point for the investor is to assess the economic feasibility of such an investment. After all, the investor seeks not only to recoup his investments, but also to earn something else in excess of the amount of the initial investment. In addition, the investor's task is to search for alternative investment options that would, with comparable risk levels and other investment conditions, bring higher returns. One of the methods of such an analysis is to calculate the net present value of an investment project.
Net Present Value (NPV) - This is an indicator of the economic efficiency of the investment project, which is calculated by discounting (bringing to current value, i.e. at the time of investment) the expected cash flows (both income and expenses).
The net present value reflects the investor’s profit (value added of the investment) that the investor expects to receive from the project after the cash inflows cover its initial investment costs and the periodic cash outflows associated with the project.
In domestic practice, the term “net present value” has a number of identical designations: net present value (NPV), net present value (NPV), net present value (NPV), Net Present Value (NPV).
NPV calculation formula
To calculate NPV you need:
- Make a forecast schedule for the investment project in the context of periods. Cash flows should include both income (cash inflows) and expenses (ongoing investments and other project implementation costs).
- Determine the size. In fact, the discount rate reflects the marginal rate of investor capital. For example, if borrowed funds of a bank are used for investment, then the discount rate will be on the loan. If the investor’s own funds are used, then the discount rate can be taken as the interest rate on bank deposits, the rate of return on government bonds, etc.
NPV calculation is carried out according to the following formula:
where
NPV (Net Present Value) - the net present value of the investment project;
CF (Cash Flow) - cash flow;
r - discount rate;
n - total number of periods (intervals, steps) i \u003d 0, 1, 2, ..., n for the entire investment period.
In this formula CF 0 corresponds to the amount of initial investment IC (Invested Capital), i.e. CF 0 \u003d IC. Cash flow CF 0 has a negative value.
Therefore, the above formula can be modified:
If investments in a project are made not at one time, but over a number of periods, then investment must also be discounted. In this case, the NPV formula of the project will take the following form:
Practical application of NPV (net present value)
The NPV calculation allows you to evaluate the feasibility of investing money. There are three possible NPV values:
- NPV\u003e 0. If the net present value has a positive value, then this indicates a full return on investment, and the NPV value shows the total profit of the investor. Investments are advisable due to their economic efficiency.
- NPV \u003d 0. If the net present value is zero, then this indicates a return on investment, but the investor does not make a profit. For example, if borrowed funds were used, then the cash flows from investment investments will make it possible to fully settle with the creditor, including paying interest due to him, but the financial situation of the investor will not change. Therefore, you should look for alternative investment options that would have a positive economic effect.
- NPV< 0 . If the net present value is negative, then the investment does not pay off, and the investor in this case receives a loss. Investment in such a project should be abandoned.
Thus, all projects that have a positive NPV value are accepted for investment. If the investor needs to make a choice in favor of only one of the projects under consideration, then, ceteris paribus, preference should be given to the project that has the highest NPV value.
Calculating NPV with MS Exel
In MS Exel, there is a NPV function that allows you to calculate the net present value.
The NPV function returns the net present value of the investment using the discount rate, as well as the value of future payments (negative values) and receipts (positive values).
NPV function syntax:
NPV (rate; value1; value2; ...)where
Rate - discount rate for one period.
Value1, Value2, ... - from 1 to 29 arguments representing expenses and income.
Value1, value2, ... should be evenly distributed over time, payments should be made at the end of each period.
The NPV uses the order of arguments value1, value2, ... to determine the order of receipts and payments. Make sure your payments and receipts are entered in the correct order.
Consider an example of calculating NPV based on 4 alternative projects.
As a result of the calculations project A should be rejected project B is at the point of indifference for the investor, but projects B and D should be used for investing. Moreover, if you need to select only one project, then preference should be given project Bdespite the fact that the amount of undiscounted cash flows for 10 years it generates less than project G.
Advantages and disadvantages of NPV
The positive aspects of the NPV technique include:
- clear and simple rules for making decisions regarding the investment attractiveness of a project;
- applying a discount rate to adjust the amount of cash flows over time;
- the ability to account for the risk premium as part of the discount rate (for more risky projects, you can apply an increased discount rate).
The disadvantages of NPV include the following:
- difficulty assessing complex investment projects that involve many risks especially in the long term (adjustment of the discount rate is required);
- the difficulty of predicting future cash flows, the calculated value of NPV depends on the accuracy of which;
- nPV formula does not take into account reinvestment of cash flows (income);
- NPV reflects only the absolute amount of profit. For a more correct analysis, it is also necessary to additionally calculate the relative indicators, for example, such as,.