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 value for the owner of capital. In this case, the cost of these values is determined, which exceeds the cost of their acquisition. Of course, the question arises as to whether it is possible to assess them more than their real value. This is available if the final result is more valuable in comparison with the total cost of the individual stages, the implementation of which made it possible to achieve this result. To understand this, you need to know what the net present value is and how it is calculated.
What is present value?
Present or present value is calculated based on the concept of money over 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. Carrying out an appropriate calculation is of great importance, since payments that are made in a different period can be compared only after they have been brought to the same time interval.
The present value is formed as a result of bringing to the initial period of future receipts and expenditures of funds. It depends on how the interest is calculated. For this, simple or compound interest, as well as annuity, are used.
What is Net Present Value?
Net present value NPV is the difference between the market price of a particular project and the cost of its implementation. The abbreviation that is used to designate 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 challenge is to implement projects that have a positive net present value. However, first you need to learn how to define it, which will help you make the most profitable investments.
Basic rule of NPV
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 project to be considered. It should be rejected if a negative value is received.
It should be noted that the calculated value is rarely zero. However, upon receiving such a value, it is also advisable for the investor to reject the project, since it will not have economic sense... This is due to the fact that the profit from the investment will not be received in the future.
Calculation accuracy
When calculating NPV, it is worth remembering that the discount rate and revenue projections have a significant impact on the present value. The end result may be inaccurate. This is due to the fact that a person cannot make a forecast for future profit with absolute accuracy. Therefore, the resulting figure is only a guess. He is not immune to fluctuations in different directions.
Of course, an investor needs to know how much profit he will receive even before investing. To keep variances as low as possible, the most accurate methods should be used to determine performance in conjunction with net present value. The general use of different methods will allow you to understand whether an investment in a particular project will be profitable. If the investor is confident in the correctness of his calculations, a decision can be made that will be reliable.
Calculation formula
When looking for programs to determine net present value, one may come across the concept of "net present value", which has a similar definition. It can be calculated using MS EXCEL, where it is found under the abbreviation NPV.
The formula used uses the following data:
- CFn - sum of money for period n;
- N is the number of periods;
- i - discount rate, which is calculated from the annual interest rate
In addition, cash flow for a certain period may be zero, which is equivalent to no cash flow at all. When determining income, the amount of money is recorded with a "+" sign, for expenses - with a "-" sign.
As a result, the calculation of the net present value leads to the possibility of assessing the effectiveness of investments. If NPV> 0, the investment will pay off.
Limitations in use
When trying to determine what the net present value of the NPV will be, using the proposed method, you should pay attention to some conditions and restrictions.
First of all, it is assumed that the indicators of the investment project will be stable throughout its implementation. However, the probability of this may approach zero, since a large number of factors affect the value of cash flows. After a certain time, the cost of capital allocated for financing may change. It should be noted that the figures obtained may change significantly in the future.
An equally important point is the choice of the discount rate. As it, you can apply the cost of capital attracted for investment. Taking into account the risk factor, the discount rate can 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 only taking a loss is considered by the investor in the first place. He may mistakenly reject a lucrative project. The discount rate can also be the return on alternative investments. For example, if the capital used for investment will be invested in another case at a rate of 9%, it can be taken as the discount rate.
Benefits of using the technique
The net present value calculation has the following advantages:
- the indicator takes into account the discount factor;
- clear criteria are used when making a decision;
- the possibility of using it when calculating the risks of the project.
However, it should be borne in mind that this method has more than just advantages.
Disadvantages of using the technique
The net present value of an 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.
- Although cash flows are predicted, the formula cannot calculate the likelihood of an event occurring. The applied coefficient can take into account inflation, but basically it is the rate of return that is included in the calculation project.
After a detailed acquaintance with the concept of "net present value" and the calculation procedure, the investor can conclude whether it is worth using the method under consideration. To determine the effectiveness of investments, it is advisable 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.
Let's calculate the Net Present Value and Internal norm yield using formulasMSEXCEL.
Let's start with the definition, more precisely, with the definitions.
Net present value (NPV) is called the sum of the discounted values of the flow of payments reduced to today
(taken from Wikipedia).
Or like this: Net present value is the present value of the future cash flows of an investment project, calculated taking into account discounting, less investments (websitecfin.ru)
Or like this: Currentthe value of a security or investment project, determined by taking into account all current and future receipts and expenses at an appropriate interest rate. (Economy .
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Note1... Net Present Value is also often referred to as Net Present Value, Net Present Income (NPV). But since 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 as payments of arbitrary size, made at regular intervals.
Advice: at the first acquaintance 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 since this method can be used to estimate cash flows of any nature (although, in fact, the NPV method is often used to assess the effectiveness of projects, including for comparing projects with different cash flows).
Also, the definition does not include the concept of discounting, since the discounting procedure is, in essence, the computation of the present value using the method.
As mentioned, 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 (amount of money) in period n. The total number of periods is N. To show whether the cash flow is an income or an expense (investment), it is written with a certain sign (+ for income, minus for expenses). The amount of cash flow in certain periods can be = 0, which is equivalent to no cash flow in a certain period (see note 2 below). i is the discount rate for the period (if an annual interest rate(let 10%), and the period is equal to a month, then i = 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 as payments of arbitrary size, made at intervals of time, multiples of a certain period (month, quarter or year)... For example, the initial investments were made in the 1st and 2nd quarters (indicated with a minus sign), there were no cash flows in the 3rd, 4th and 7th quarters, and in the 5-6th and 9th quarters the proceeds from the project have been received (indicated with a plus sign). For this case, NPV is calculated in the same way as for regular payments (amounts in the 3rd, 4th and 7th quarter must be specified = 0).
If the sum of the present cash flows representing income (those with a + sign) is greater than the sum of the present cash flows representing investments (expenses, with a minus sign), then NPV> 0 (the project / investment pays off). Otherwise NPV<0 и проект убыточен.
Selecting the discount period for the NPV () function
When choosing a discount period, you need to ask yourself the question: "If we forecast for 5 years ahead, can we predict cash flows with an accuracy of up to a month / up to a quarter / up to a year?"
In practice, as a rule, the first 1-2 years of receipts and payments 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 should determine the most likely dates for the receipt of amounts based on current realities.
Having decided on 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 the receipts are planned monthly, and in the 2nd - quarterly, then the period should be chosen equal to 1 month. In the second year, the sums of cash flows in the first and second month of the quarters will be equal to 0 (see. example file, NPV sheet).
In the table, NPV is calculated in two ways: through the NPV () function and by 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, so its present value (-991,735.54 = -1,000,000 / (1 + 10% / 12)) was calculated as of 12/31/2009. (without much loss of accuracy, we can assume that as of 01.01.2010)
This means that all amounts are shown not as of 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 the amounts to be given as of the date of the first investment, then it does not need to be included in the arguments of the NPV () function, but you just need to add it to the resulting result (see the example file).
A comparison of the 2 discounting options is given in the example file, NPV sheet:
On the accuracy of calculating the discount rate
There are dozens of approaches to determining the discount rate. Many indicators are used for calculations: the weighted average cost of capital of the company; refinancing rate; average bank rate on a deposit; annual inflation rate; income tax rate; country risk-free rate; project risk premium and many others, as well as their combinations. It is not surprising that in some cases the calculations can be quite laborious. The choice of the necessary approach depends on the specific task, we will not consider them. We only note one thing: the accuracy of calculating the discount rate should correspond to the accuracy of determining the dates and amounts of cash flows. Let's show the existing dependence (see. example file, sheet Accuracy).
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 the first payment).
Because the project is long, then everyone understands that the amounts in 4-10 years are not determined precisely, but with some acceptable accuracy, say +/- 100,000.0. Thus, we have 3 scenarios: Baseline (the average (most "probable") value is indicated), Pessimistic (minus 100,000.0 from the baseline) and optimistic (plus 100,000.0 to the baseline). It should be understood that if the base amount is 700,000.0, then the amounts 800,000.0 and 600,000.0 are no less accurate.
Let's see how NPV reacts when the discount rate changes by +/- 2% (from 10% to 14%):
Consider a 2% rate increase. 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%, it can be seen that they overlap by 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. The change in the discount rate by 2% led to a decrease in NPV by 16% (when compared with the base case). Taking into account that the ranges of NPV scatter overlap significantly due to the accuracy of determining the amounts of cash income, an increase of 2% in the rate did not have a significant effect on the NPV of the project (taking into account the accuracy of determining the amounts of cash flows). 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 must estimate the costs of additional calculations for a more accurate discount rate, and decide how much they will improve the NPV estimate.
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 a higher accuracy +/- 50,000.0
A 3% increase in the discount rate resulted in a 24% decrease in NPV (compared to the base case). If we compare the ranges of the NPV scatter at 12% and 15%, it can be seen that they intersect only 23%.
Thus, the project manager, having analyzed the sensitivity of NPV to the value of the discount rate, should understand whether the calculation of NPV will be significantly improved after calculating the discount rate using a more accurate method.
After determining the amounts and timing of cash flows, the project manager can estimate what the maximum discount rate the project can withstand (criterion NPV = 0). The next section discusses the Internal Rate of Return - IRR.
Internal rate of returnIRR(VSD)
Internal rate of return (eng. internal rate of return, IRR (IRR)) is the discount rate at which the Net Present Value (NPV) is equal to 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 durations.
To calculate the IRR, the IRR () function is used (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 results in zero NPV. The relationship of functions is reflected in the following formula:
= NPV (IRR (B5: B14); B5: B14)
Note4... IRR can be calculated without the IRR () function: it is enough to have the NPV () function. To do this, you need to use a tool (the "Set in a cell" field must refer to the formula with NPV (), set the "Value" field to 0, the "Changing the cell value" field must contain a link to the cell with the rate).
Calculating NPV at constant cash flows using the PS () function
Internal rate of return PIR ()
By analogy with NPV (), which has a related function, IRR (), NETWORK () has a NETWORK () function that calculates the annual discount rate at which NETWORK () returns 0.
Calculations in the PERFORMANCE function () are made according to the formula:
Where, Pi = i-th amount of cash flow; di = date of the i-th amount; d1 = date of 1st amount (starting date on which all amounts are discounted).
Note5... The CLEAR () function is used for.
Let's calculatePresent (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 an arbitrary amount.
Present Value is calculated based on the concept of the value of money in time: the money currently available is worth more than the same amount in the future due to its potential to generate income. The calculation of the Present value is also important, since payments made at different points in time can be compared only after bringing them to one time point.
The present value is obtained as a result of bringing Future income and expenses to the initial period of time and depends on which method the interest is calculated by:, or (the example file contains a solution to the problem for each of the methods).
Simple interest
The essence of the simple interest accrual method is that interest accrues 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 denote the Present Value (PS appears as an argument in numerous financial functions of MS EXCEL).
Note... In MS EXCEL there is no separate function for calculating the Present Value using the Simple Interest method. The PS () function is used to calculate compound interest and annuity. Although, specifying the value 1 as the Nper argument, and specifying i * n as the rate, you can force the PS () to calculate the Present Value using the simple interest method (see the example file).
To determine the Present Value when calculating simple interest, use the formula for calculating (FV):
FV = PV * (1 + i * n)
where PV is the Present Value (the amount that is being invested at the moment and on which interest is charged);
i - interest rate over a period accrual of interest (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 calculated.
From this formula we get that:
PV = FV / (1 + i * n)
Thus, the procedure for calculating the Present Value is the opposite of calculating the 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 in 3 years the amount of 100,000 rubles. Let the bank apply a rate of 15% per annum on deposits, and only the principal amount of the deposit (simple interest) is charged.
In order to find the answer to this question, we need to calculate the Present Value of this future amount using the formula PV = FV / (1 + i * n) = 100,000 / (1 + 0.15 * 3) = 68,965.52 rubles. We got that today's (current, real) amount is 68,965.52 rubles. is equivalent to the amount after 3 years in the amount of 100,000.00 rubles. (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 for comparing amounts “all other things being equal”. For example, that with the help of it you can answer the question "Which offer of the bank is more profitable to accept in order to get the maximum amount in 3 years: open a deposit with simple interest at a rate of 15% or with compound interest with a monthly capitalization at a rate of 12% per annum"? To answer this question, consider the calculation of the Present Value when calculating compound interest.
Compound interest
When compound interest rates are used, interest accrued after each accrual period is added to the amount owed. Thus, the basis for compounding, as opposed 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. This method is sometimes referred to as "percentage by percentage".
The present value of PV (or PS) in this case can be calculated using.
FV = PV * (1 + i) ^ n
where FV (or S) is the future (or accrued amount),
i - annual rate,
n - loan term in years,
those. PV = FV / (1 + i) ^ n
With capitalization m times a year, the Present Value formula looks like this:
PV = FV / (1 + i / m) ^ (n * m)
i / m is the rate for the period.
For example, the amount of 100,000 rubles. on the current account in 3 years 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 = 100000 / (1 + 12% / 12) ^ (3 * 12) or by the formula = PS (12% / 12; 3 * 12; 0; -100000).
Answering the question from the previous section "Which offer of the bank is more profitable to accept in order to get the maximum amount in 3 years: open a deposit with simple interest at a rate of 15% or with compound interest with a monthly capitalization at a rate of 12% per annum"? we need to compare two Present Values: 69 892.49 rubles. ( compound interest) and 68 965.52 rubles. (simple interest). Because The present value, calculated according to the bank's proposal for a deposit with simple interest, is less, then this offer is more profitable (today you need to invest less money in order to get the same amount of 100,000.00 rubles in 3 years.)
Compound interest (several amounts)
Let's determine the present value of several amounts that belong to different periods. This can be done using the PS () function or the alternative formula PV = FV / (1 + i) ^ n
By setting the value of the discount rate to 0%, we simply get the sum of the cash flows (see the example file).
Annuity
If, in addition to the initial investment, after equal periods of time, additional equal payments (additional investments) are made, then the calculation of the Present Value becomes significantly more complicated (see the article, where the calculation using the PS function () is given, as well as the derivation of an 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 at the end of the month. The client also makes additional contributions in the amount of 20,000 rubles at the end of each month. 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: = PS (12% / 12; 12; 20,000; -1000000; 0)= 662 347.68 rubles.
Argument Bid indicated for the period of interest accrual (and, accordingly, additional contributions), i.e. per month.
Argument Nper Is the number of periods, i.e. 12 (months), because the client opened a deposit for 1 year.
Argument Plt- this is 20,000 rubles, i.e. the amount of additional contributions.
Argument Bs- this is -1000000 rubles, i.e. the future value of the contribution.
The minus sign indicates the direction of cash flows: additional contributions and the initial amount of the deposit are of one decimal place, since customer enumerates these funds to the bank, and the client's future deposit amount will receive from the bank. This is a very important note for everyone, because otherwise, you may get an incorrect result.
The result of the PS () function is the initial amount of the deposit, it does not include the present value of all additional contributions of 20,000 rubles. This can be verified by calculating the Present Value of Additional Contributions. There were 12 additional contributions in total, the total amount of 20,000 rubles. * 12 = 240000 rubles. It is clear that at the current rate of 12%, their present value will be less = PS (12% / 12; 12; 20,000) = -225 101.55 rubles. (up to a sign). Because these 12 payments made in different periods of time are equivalent to 225,101.55 rubles. at the time of opening a deposit, then they can be added to the initial deposit amount calculated by us 662 347.68 rubles. and calculate their total Future value = BS (12% / 12; 12 ;; 225 101.55 + 662 347.68)= -1000000,0 rubles, which was required to prove.
Both concepts from the title of this section, discounted (present) value, PS (presentvalue, or PV), and net present value, NPV (netpresentvalue, or NPV), denote the current the value of expected future cash flows.
As an example, consider the valuation of an investment that promises a return of $ 100 a year at the end of this year and four more years to come. We assume that this series of five payments of $ 100 each is guaranteed and the money will certainly come. If the bank paid us an annual interest of 10% on a deposit for five years, then this ten percent would just constitute 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 an investment by discounting the cash receipts from it using the opportunity cost as the discount rate.
Calculation formula inExceldiscounted (present) value (PV)= NPV (C1; B5: B9)
Present value(PS) in the amount of $ 379.08 is the present value of the investment.
Suppose that this investment would sell for $ 400. Obviously, it would not be worth the asking price, because - assuming an alternative income (discount rate) of 10% - the real value of this investment would be only $ 379.08. it is appropriate to introduce the concept net present value(NPV). By symbol r discount rate for this investment, we get the following NPV formula:
Where СF t is the cash flow from the investment at the moment t; CF 0 - the flow of funds (receipt) at the current moment.
Calculation formula inExcel net present (present) value (NPV)= NPV (C1; B6: B10) + B5
Excel terminology for discounted flows Money is somewhat different from standard financial terminology. In Excel, the abbreviation MUR (NPV) stands for present value (not chistop present value) of a series of cash receipts.
To calculate in Excel net present value series of cash receipts in the usual sense of financial theory, you must first calculate present value future cash flows (using an Excel function such as NPV), and then subtract from that number the cash flow at the start. (This amount is often the same as 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, consider some examples of calculation, including using MS Excel formulas.
What is Net Present Value (NPV)?
When investing money in any investment project, the key point for an 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 find alternative investment options that would bring higher returns with comparable levels of risk and other investment conditions. One of the methods of such analysis is the calculation of the net present value of an investment project.
Net Present Value (NPV) Is an indicator of the economic efficiency of an investment project, which is calculated by discounting (bringing to the present 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 (added value of investments) that the investor expects to receive from the project, after the cash inflows have recouped their initial investment costs and the periodic cash outflows associated with the implementation of such a 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).
Formula for calculating NPV
To calculate NPV you need:
- Draw up a forecast schedule for an investment project in terms of periods. Cash flows should include both revenues (inflows of funds) and expenses (ongoing investments and other costs of the project).
- Determine the size. In essence, the discount rate reflects the marginal rate of the investor's cost of capital. For example, if for investment will be used borrowed funds bank, then the discount rate will be on the loan. If the investor's own funds are used, then the rate of interest on a bank deposit, the rate of return on government bonds, etc. can be taken as the discount rate.
NPV is calculated using 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- the total number of periods (intervals, steps) i = 0, 1, 2, ..., n for the entire investment period.
In this formula CF 0 corresponds to the volume of the initial investment IC(Invested Capital), i.e. CF 0 = IC... At the same time, the cash flow CF 0 has a negative value.
Therefore, the above formula can be modified:
If investments in a project are made not at once, but over a number of periods, then the 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)
Calculating NPV allows you to assess the feasibility of investing funds. There are three possible NPV values:
- NPV> 0... If the net present value has positive value, then this indicates a full return on investment, and the NPV value shows the final size of the investor's profit. Investments are advisable due to their economic efficiency.
- NPV = 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 cash flows from investment investments will allow you to pay the creditor in full, including to pay the interest due to him, but financial position the investor will not change. Therefore, you should look alternative options investment of funds 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. Investments 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, all other things being equal, preference should be given to the project that has the highest NPV value.
Calculating NPV using MS Excel
MS Excel has a NPV function that allows you to calculate the net present value.
The NPV function returns the net present value of an investment using the discount rate and the value of future payments (negative values) and receipts (positive values).
The syntax for the NPV function is:
NPV (rate; value1; value2; ...)where
Bid- discount rate for one period.
Value1, value2, ...- 1 to 29 arguments representing expenses and income.
Value1, value2, ... must be evenly distributed over time, payments must be made at the end of each period.
NPV uses the order of the arguments value1, value2,… to determine the order of receipts and payments. Make sure your payments and receipts are entered in the correct order.
Let's consider an example of NPV calculation 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 C and D should be used for investment. Moreover, if it is necessary to select only one project, then preference should be given project B, despite the fact that the amount of undiscounted cash flows for 10 years it generates less than project D.
Advantages and Disadvantages of NPV
The positive aspects of the NPV method include:
- clear and simple rules to make decisions about investment attractiveness project;
- applying a discount rate to adjust the amount of cash flows over time;
- the ability to take into account the risk premium as part of the discount rate (for more risky projects, you can apply a higher discount rate).
The disadvantages of NPV include the following:
- difficulty of assessment for complex investment projects, which include many risks, especially in the long term (adjustment of the discount rate is required);
- the complexity of forecasting future cash flows, on the accuracy of which the estimated value of NPV depends;
- the NPV formula does not take into account the 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 and relative indicators, for example such as,.