Payback period of investments – theory and practice. Discounted payback period of DPP investments

When investing in production or services, an entrepreneur wants to know when his money will return to him and begin to generate additional income. In order to obtain such information, the payback period of the project is calculated. However, taking into account the dynamics of the value of money over time, all indicators should be reduced to the current value. Accordingly, a more accurate estimate is given by discounted term payback.

The payback period (PP) is the shortest period after which invested funds will come back and start making a profit. For short-term projects, a simple method is often used, which consists in taking as a basis the value of the period at which the net start-up (excluding taxes and operating costs) exceeds the amount of invested funds.

The payback period for investments is expressed by the following formula:

IC – investments in the initial phase investment project;
CFi is the flow of money in time period i, consisting of net profit and accrued depreciation.

For example, an investor invested 4,000 thousand rubles in one payment into a five-year project. He receives an annual income of 1,200 thousand rubles, taking into account depreciation. Based on the above conditions, you can calculate when the investment will pay off.

The amount of income for the first three years of 3600 (1200 + 1200 + 1200) does not cover the initial investment, but the amount for four years (4800 thousand rubles) exceeds the investment, which means that the initiative will pay off in less than 4 years. This value can be calculated more accurately if we assume that the influx of money occurs evenly throughout the year:

Remaining = (1 – (4800 – 4000 / 1200) = 0.33, that is, 4 months.

Therefore, the payback period for investments in our case will be 3 years and 4 months. It would seem that everything is simple and very clear. However, we should not forget that our undertaking is designed for a five-year implementation period, and in conditions of declining purchasing power money, such a period will lead to a serious error. Besides, in in a simple way flows not taken into account Money, which are generated after the payback period.

To get a more accurate forecast, use the discounted payback period (DPP). This criterion can be considered as the time period during which the investor will receive the same income, reduced to the current period, as in the case of the investment financial capital into an alternative asset.

The indicator can be calculated using the following formula:

DPP – discounted payback period;
CF is the cash flow generated by the investment;
IC – costs at the initial stage;
n – duration of the initiative (in years);
r – barrier rate (discount rate).

From the formula you can see that the discounted payback period is calculated by multiplying the expected cash flows by a reduction factor, which depends on the established one. The discounted payback rate is always higher than that obtained by the simple method.

Situations often arise when, after the end of an investment project, there remains a significant amount of assets (vehicles, structures, buildings, equipment, materials) that can be sold at residual value, increasing the incoming cash flow. In such cases, they use the calculation of the refund period taking into account the liquidation value (Bail-Out Payback Period, BOPP). Its formula is:

where RV is the liquidation value of the project assets.

With this method of calculation, the liquidation value of the assets, calculated at the end of the life cycle of the initiative, is added to the incoming flows from the main activity. Most often, such projects have a shorter payback period than standard ones.

In unstable economies with rapidly changing conditions, the discount rate may change during the life cycle of the venture. The reason for this is most often high level inflation, as well as changes in the cost of resources that can be attracted.

DPP allows you to take into account the dynamics of the value of money, as well as use different discount rates for different periods. At the same time, it has its drawbacks. These include the inability to take into account flows of funds after reaching the break-even point, as well as incorrect results when calculating flows with different signs (negative and positive).

Determination of DPP during assessment investment proposal helps reduce the risk of losses invested money and generally assess the liquidity of the initiative. At the same time, far-reaching conclusions should not be drawn based on this criterion alone; it is best to evaluate the proposed project according to a number of indicators and draw a conclusion based on the entire complex of data obtained.

Examples of indicator calculations with different flow dynamics

Let's consider an example of calculating the DPP indicator for the case we described. To apply the formula to our example, we must first set the discount rate. Let's take it as average the interest rate on long-term deposits is 9%.

PV1 = 1200 / (1 + 0.09) = 1100.9;

PV2 = 1200 / (1 + 0.09)2 = 1010.1

PV3 = 1200 / (1 + 0.09)3 = 926.6

PV4 = 1200 / (1 + 0.09)4 = 844.5

PV5 = 1200 / (1 + 0.09)5 = 780.2

Now let's calculate when the payback time will come. Considering that the amount of receipts for the first 2 (2111 thousand rubles), 3 (3037.6 thousand rubles) and 4 years of implementation of the initiative (3882.1 thousand rubles) is less than the starting investment, and the amount for 5 years (4662.3 thousand rubles) - more than it, then the payback period is between four and five years. Let's find the remainder:

Remaining = (1 - (4662.3 - 4000) / 780.2) = 0.15 years (2 months).

We get the result. The investment, when bringing cash flows to the present, will pay off in 4 years and 2 months, which exceeds the PP indicator (3 years and 4 months).

The payback period of an investment in an investment project can be influenced by various indicators. In particular, it depends on the size of the inflow of funds by period. Let's try to solve two problems by slightly modifying our example. Life cycle project (5 years) and the initial investment (4,000 thousand rubles), the barrier rate (9%) and the nominal amount of income (6,000 thousand rubles) remain unchanged, but the inflows vary from year to year.

So, in option A, revenues begin with small amounts and increase every year, and in option B, large amounts are initially received, decreasing towards the end of the implementation of the initiative.

Option A:

1 year – 800 thousand rubles;

2 year – 1000 thousand rubles;

3rd year – 1200 thousand rubles;

4 year – 1300 thousand rubles;

5 year – 1700 thousand rubles.

We discount revenues by year of option A:

PV1 = 800 / (1 + 0.09) = 733.9;

PV2 = 1000 / (1 + 0.09)2 = 841.7;

PV4 = 1300 / (1 + 0.09)4 = 921.3;

PV5 = 1700 / (1 + 0.09)5 = 1105.3.

Adding up the profits, we see the following picture. Income for 2 years (1575.6 thousand rubles), 3 years (2502.2 thousand rubles) and 4 years (3423.5 thousand rubles) do not provide a return on investment, and the amount of income for 5 years (4528 .8 thousand rubles) – provides. This means the payback period is more than 4 years. Looking for the remainder:

Remaining = (1 - (4528.8 - 4000) / 1105.3) = 0.52 years (rounded to 7 months).

The discounted payback period in option A is 4 years and 7 months. This is 5 months longer than in the example with uniform receipts.

Option B:

1 year – 1700 thousand rubles;

2 year – 1300 thousand rubles;

3rd year – 1200 thousand rubles;

4 year – 1000 thousand rubles;

5 year – 800 thousand rubles.

Let's calculate inflows by year taking into account the discount rate:

PV1 = 1700 / (1 + 0.09) = 1559.6;

PV2 = 1300 / (1 + 0.09)2 = 1094.3;

PV3 = 1200 / (1 + 0.09)3 = 926.6;

PV4 = 1000 / (1 + 0.09)4 = 708.7;

PV5 = 800 / (1 + 0.09)5 = 520.2

We find the required value of the indicator. The total income for 2 years (2653.9 thousand rubles) and for 3 years (3850.5 thousand rubles) is less than the initial investment, but after 4 years of work (4289.2 thousand rubles) it is fully returned . Let's calculate the exact indicator:

Remaining = (1 - (4289.2 - 4000) / 708.7) = 0.59 years (rounded to 8 months).

In option B, the discounted payback period is 3 years and 8 months, which is much more attractive for the investor than receiving income evenly or increasing it by the end of the project. Thus, we can conclude that the return large sums at the beginning of the implementation of an investment project makes it much more promising from a financial point of view.

In order not to make mistakes, it is advisable to use specialized computer programs. In particular, DPP is most often calculated in MS Excel.

The discounted payback period of a project is the duration of the period from the start of investments to the moment of their payback, taking into account discounting. The meaning of the method is to discount all cash flows generated by the project and sum them up in a sequential order until they cover the initial investment costs.

In a general sense, the discount formula determines the present that relates to future periods, and shows future income determined today. To make a correct assessment of future income, you should have information about the forecast values of revenue, investments, expenses, property, discount rate, and capital structure.

The discounted payback period reflects a more objective and more conservative characteristic of project evaluation than the usual payback period. This indicator partially takes into account the risks inherent in the project, which include increased costs, decreased income, and the emergence of alternative, more profitable investment opportunities.

The discount rate is equal to the sum of the risk-free investment rate and adjustments for the risks of a specific specific project. In the second case this indicator reflects the internal nature of an alternative project that is similar in risk.

In addition, there are the following methods that determine the discounted payback period and the discount rate.

The calculation is made based on the weighted average cost of capital when using your own investments. This method has both advantages and a number of disadvantages. The positive aspects are that the cost of capital can be calculated accurately and then determined possible options alternative use of resources. The disadvantage is that the calculations are based on dividends and interest on borrowed funds However, these criteria include adjustments for risk, which, when discounting, are taken into account when determining compound interest, which causes a uniform increase in risk over time.

The discounted payback period and the rate are calculated based on interest on B in this case This refers to the percentage at which an enterprise can currently borrow funds. Given the opportunity to invest or return capital to lenders, the interest rate on borrowed funds will be equal to the opportunity cost of capital. It is worth noting that to determine the discount rate, only the effective one other than the nominal one should be used, since the capitalization period may vary.

Calculations are also made based on the safe investment rate; it is also considered as the alternative cost of funds. The next method includes the same rate, but adjusted for various risk factors - the possibility of shortfall in income provided for by the project, unreliability of project participants,

The discount rate and then the discounted payback period are determined by taking into account the cost of debt and risk adjustments. As a result, the difference in risks between the company's investment projects is leveled. A possible approach is to discount the cash flows at a rate that reflects only the risk of the project itself and does not take into account the effect of financing.

To determine the discount rate, an alternative one is used, which is taken to be the internal rate of return of the marginal accepted and unaccepted projects. The disadvantage of the method is the practical difficulty of determining this value; moreover, confusion arises in the calculations due to the difference interest rates by projects.

The payback period (PP) is the shortest period within which the invested funds will return and begin to generate profit. For short-term projects, a simple method is often used, which consists in taking as a basis the value of the period in which the net cash flow of the undertaking (excluding taxes and operating costs) will exceed the amount of invested funds.

The payback period for investments is expressed by the following formula:

IC – investments at the initial phase of the investment project;
CFi is the cash flow in time period i, consisting of net profit and accrued depreciation.

Remaining = (1 – (4800 – 4000 / 1200) = 0.33, that is, 4 months.

Therefore, the payback period for investments in our case will be 3 years and 4 months. It would seem that everything is simple and very clear. However, we should not forget that our undertaking is designed for a five-year implementation period, and in conditions of declining purchasing power of money, such a period will lead to a serious error. In addition, the simple method does not take into account cash flows that are generated after the payback period.

To get a more accurate forecast, use the discounted payback period (DPP). This criterion can be considered as the time period during which the investor will receive the same income, reduced to the current period, as in the case of investing financial capital in an alternative asset.

The indicator can be calculated using the following formula:

DPP – discounted payback period;
CF is the cash flow generated by the investment;
IC – costs at the initial stage;
n – duration of the initiative (in years);
r – barrier rate (discount rate).

From the formula you can see that the discounted payback period is calculated by multiplying the expected cash flows by a reduction factor, which depends on the established discount rate. The discounted payback rate is always higher than that obtained by the simple method.

where RV is the liquidation value of the project assets.

In unstable economies with rapidly changing conditions, the discount rate may change during the life cycle of the venture. The reason for this is most often the high level of inflation, as well as changes in the cost of resources that can be attracted.

Determining the DPP indicator when assessing an investment proposal allows you to reduce the risk of loss of invested money and generally assess the liquidity of the initiative. At the same time, far-reaching conclusions should not be drawn based on this criterion alone; it is best to evaluate the proposed project according to a number of indicators and draw a conclusion based on the entire complex of data obtained.

Examples of indicator calculations with different flow dynamics

Let's consider an example of calculating the DPP indicator for the case we described. To apply the formula to our example, we must first set the discount rate. Let's take it as the average interest rate on long-term deposits - 9%.

PV1 = 1200 / (1 + 0.09) = 1100.9;

PV2 = 1200 / (1 + 0.09)2 = 1010.1

PV3 = 1200 / (1 + 0.09)3 = 926.6

PV4 = 1200 / (1 + 0.09)4 = 844.5

PV5 = 1200 / (1 + 0.09)5 = 780.2

Remaining = (1 - (4662.3 - 4000) / 780.2) = 0.15 years (2 months).

We get the result. The investment, when bringing cash flows to the present, will pay off in 4 years and 2 months, which exceeds the PP indicator (3 years and 4 months).

The payback period of an investment in an investment project can be influenced by various indicators. In particular, it depends on the size of the inflow of funds by period. Let's try to solve two problems by slightly modifying our example. The life cycle of the project (5 years) and the initial investment (4,000 thousand rubles), the barrier rate (9%) and the nominal amount of income (6,000 thousand rubles) remain unchanged, but the inflows vary from year to year.

So, in option A, revenues begin with small amounts and increase every year, and in option B, large amounts are initially received, decreasing towards the end of the implementation of the initiative.

Option A:

1 year – 800 thousand rubles;

2 year – 1000 thousand rubles;

3rd year – 1200 thousand rubles;

4 year – 1300 thousand rubles;

5 year – 1700 thousand rubles.

We discount revenues by year of option A:

PV1 = 800 / (1 + 0.09) = 733.9;

PV2 = 1000 / (1 + 0.09)2 = 841.7;

PV4 = 1300 / (1 + 0.09)4 = 921.3;

PV5 = 1700 / (1 + 0.09)5 = 1105.3.

Remaining = (1 - (4528.8 - 4000) / 1105.3) = 0.52 years (rounded to 7 months).

The discounted payback period in option A is 4 years and 7 months. This is 5 months longer than in the example with uniform receipts.

Option B:

1 year – 1700 thousand rubles;

2 year – 1300 thousand rubles;

3rd year – 1200 thousand rubles;

4 year – 1000 thousand rubles;

5 year – 800 thousand rubles.

Let's calculate inflows by year taking into account the discount rate:

PV1 = 1700 / (1 + 0.09) = 1559.6;

PV2 = 1300 / (1 + 0.09)2 = 1094.3;

PV3 = 1200 / (1 + 0.09)3 = 926.6;

PV4 = 1000 / (1 + 0.09)4 = 708.7;

PV5 = 800 / (1 + 0.09)5 = 520.2

Remaining = (1 - (4289.2 - 4000) / 708.7) = 0.59 years (rounded to 8 months).

In option B, the discounted payback period is 3 years and 8 months, which is much more attractive for the investor than receiving income evenly or increasing it by the end of the project. Thus, we can conclude that the return of large sums at the beginning of the implementation of an investment project makes it much more promising from a financial point of view.

In order not to make mistakes in calculating the economic efficiency indicators of a project, it is advisable to use specialized computer programs for these purposes. In particular, DPP is most often calculated in MS Excel.

To make an informed decision on financing an investment project, several performance indicators are used:

Term payback;
Internal norm profitability;
Net reduced price;
Discounted economic effect and others.

One of the key indicators is payback period of the investment project.

The payback period is a period of time that shows how long it will take to return the investment in the project, taking into account the financing of all associated operating costs.

The shorter this period, the more attractive the project is for a potential investor.. You can determine in several ways.

Project payback period (PP)

The simplest calculation method is payback period(from English paybackperiod).

This is an indicator equal to the period when the total net financial flow from the project (income minus operating costs and tax payments) will exceed the amount of invested funds.

on a cumulative basis.
The total cash flow can now be compared with the amount of investment. The period in which the first value exceeds the second is the payback period for the investment.

Dignity This method of calculation is its relative simplicity.

Disadvantages of the method:

Changes in cost are not taken into account capital over time.
Cash flow is not taken into account and after payback.

This period is good to use for projects that provide for a relatively quick return of funds (for example, the project is designed for 10 years, and the approximate payback period is 1-2 years). In other cases, it is better to use more complex coefficients.

Discounted payback period

Important factor, which must be taken into account when considering long-term investment projects – change in the cost of capital over time.

Discounting- this is a cast future cash flows to present period, taking into account changes in the value of capital over time.

Discounting is done by multiplying values future flows by a reduction factor depending on the discount rate.

Discount rate is a special rate used to convert future income streams into a single present value.

The choice of discount rate is determined by:

the cost of the attracted investor capital;
forecast inflation;
risk premium project.

Basic rate definition– the rate that can be received by saving money in risk-free assets, such as bank deposit.

Based on discounting, it is calculated discounted payback period(Discounted Payback Period, DPP).

The scheme for calculating it is similar to the usual payback period, except that it is not just the total financial flow that is summed up, but the discounted one. This indicator is also called payback period of discounted income (DPB, Discounted Pay-Back Period).

This indicator is more accurate than the PP indicator, since it takes into account changes in cost over time and allows us to cut off unprofitable projects. There remains a disadvantage associated with ignoring financial flows beyond profitability.

Calculation of discounted payback period

Formula for calculating discounted financial flow in a separate period:

CF (discounted) = CF/(1+r)^n,

CF– value of undiscounted total cash flow during this period;
r- discount rate;
n– period number.

The calculation scheme for the indicator is as follows:

A table of financial flows is compiled(for each period, cash flows associated specifically with this investment project are calculated - relevant income and expenses).
For all periods, the incoming amounts are filled in and outgoing cash flows.
The total cash flow is calculated for a period as the difference between incoming and outgoing flows.
according to the above formula.
The total cash flow is calculated on a cumulative basis.
The total cash flow can now be compared with the amount of investment. The period in which the first value exceeds the second is the payback period for the investment.

Calculation of payback period in MS Excel

Since the discounted payback period formula is much more complex than the PP formula, it is more convenient to do the calculations in a spreadsheet program such as MS Excel.

The program creates a table of columns:

column A– period number;
column B- amount of investment;
column C– total incoming financial flow in the period (income);
column D– total outgoing flow in the period (expenses);
column E– total cash flow for the period CF (=income – expenses);
column F– discounted cash flow for the period;
column G– cumulative discounted cash flow on an accrual basis;
column H– difference between column B and column G.

Column A filled in with numbers from 1 to the planned end of the project period.

Columns B, C and D filled in manually.

To Column E entered simple formula(difference between columns D and C).

Column F also filled in with formulas. For example, if the cash flow table begins on line 11, and the discount rate value is in cell A5, then you need to enter the formula in cell F11 «= E11/(1+$A$5)^A11", and then copy it and paste it into the remaining cells of column F.

According to the above formula for calculating discounted flow, this Excel formula takes the value of the undiscounted flow and divides it by the value (1 + discount rate) raised to the power equal to the period number from cell A11. Notice the absolute addressing of cell A5 in the formula.

Column G sums up the cumulative discounted flow: in cell G12 there will be a formula “=G10+F11”. In cell H11 – the formula “=G11-B11”. As soon as there is a non-negative value in this column, the payback period has been found. You can use conditional formatting to highlight non-negative values in this column.

Payback period of investments taking into account liquidation value

The above indicators do not in any way consider the value of the invested assets at the end of the payback period.

There are often investment projects in which, by the end of the project, there remains enough a large number of assets that the investor can sell at residual value (buildings, structures, vehicles, etc.) and thereby increase incoming cash flow.

To take this factor into account, another indicator for calculating the payback period is used: Withpayback period taking into account liquidation value (English Bail-out Payback Period) .

Its essence is that not only the total cash flow is compared with the amount of investment investments, but the liquidation value of assets at the end of the period is added to the latter amount.

At the same time, the liquidation value may change during the course of the project: it may decrease due to depreciation, or it may increase if assets are created during the project.

In most cases, the payback period of an investment project calculated in this way will be less than the usual payback period.

Salvage value accounting may be used as in option with discounted term payback, and for undiscounted term.

The indicator calculation scheme is as follows (discounting option):

A table of financial flows is compiled(for each period, cash flows associated specifically with this investment project are calculated - relevant income and expenses).
For all periods, the incoming amounts are filled in and outgoing cash flows.
The total cash flow is calculated for a period as the difference between incoming and outgoing flows.
For each period, discounted cash flow is calculated according to the above formula.
The liquidation value is calculated for each period.
The total cash flow is calculated on a cumulative basis.
TO the liquidation value is added to the amount of cash flow and is compared with the amount of investment. The period in which the first value exceeds the second is the payback period for the investment.

The Importance of Internal Rate of Return

The payback period, calculated by any of the methods considered, tells us when the project will begin to make a profit (and whether it will make a profit at all), but says absolutely nothing about how much an investor can earn from this project, and whether it makes sense to invest in the project at all .

To calculate the effectiveness of an investment project, an additional indicator is used, called internal rate of return (VND, from English.IRR – internal rate of return).

The rate of return for an investment project is the rate at which the costs of the initial investment are equal to the discounted income from these investments.

This minimum bid, at which investments in the project pay off.

This indicator is used when comparing the profitability of an investment project with a risk-free placement of money (for example, a bank deposit or government bonds), as well as for comparison different options investment projects.

The internal rate of return should be higher average cost investments (discount rates), otherwise there is no point in investing in the project.

Why is a short payback period better than a longer one?

Any investment project carries with it risks for the investor. This is not a bank deposit or a blue chip stock that has sufficient reliability over the long term.

When investing in an investment project, the investor bears the risk of loss of investment as a result of changes external environment(exchange rates, changes in legislation, and as a result of ineffective work of the company (marketing miscalculations, inefficient production, cost overruns, non-payments by customers, etc.).

The faster the investor will “recoup” the invested funds and the faster the project begins to make a profit, the less damage the investor can receive.

That's why when comparing investment projects of equal efficiency(with the same rate of internal return) the investor will most likely choose a project with a shorter payback period.

Conclusion

Before deciding to invest money in a project, an investor must conduct a comprehensive assessment of investment options using various indicators.

The indicator is suitable for quickly assessing the payback of non-capital-intensive projects PP– undiscounted payback period.

For more detailed consideration and comparison of different investment projects, the discounted payback period is suitable. For a more complete assessment, other indicators should be used: internal rate of return and net present value of the project.

In economics, it is common to use the term "Pay-Back Period", abbreviated as "PP". In Russian we say “term” or “recoupment period of investment”. There are two similar indicators: simple payback period; discounted payback period of investment. The first indicator allows the investor to estimate the time it will take for the project to fully recoup the investment, but without taking into account changes in the value of money.

The method for determining the payback period of an investment may also include the use of net present value (NPV). In the second case, we are talking about a discounted payback period, which allows us to include discount rates in the calculation and more accurately assess risks.

Internal investment activities enterprises for one annuity (year) can often be reflected in a simpler form with a PP calculation. Internal investment policy economic object includes real investment with the expectation of a certain net income.

2 Calculation of the payback period

At the initial stage of evaluating an investment project, it is important for the investor to imagine the effectiveness of future investments in general outline to understand whether the project has potential or not. Often, for greater objectivity of the analysis, the indicator “rate of return” or project profitability is also used. The formula for calculating the ROR (Rate of Return) indicator is quite simple. We have already talked about this indicator in the investment article.

The formula for calculating PP includes static indicators - actual or expected profitability for specified period time (usually a year) and total amount investments.

As an example, we will give a solution to a simple problem. In our case, we will use short time periods (1 week), and as an investment object we will use a stable PAMM account with an expected return of $300 weekly. Example 1. The initial investment amount is $3,000. Expected monthly income – $300. What is the simple payback period? Following the formula, we get: PP=3000/300=10. 2 months and 2 weeks or 70 days.

Let's complicate the task a little and add analytics. We will need a formula that can be used to calculate the “rate of return” indicator, as well as a calculation formula compound interest which looks like this. The task is to identify best project for a profitability of 100%.

Example 2. There are 2 projects, each worth $3000, a PAMM account with an expected return of $300 weekly and a deposit with 10% per month with monthly capitalization. What is the rate of return for both projects over their respective payback periods? For the first project, PP 1 has already been calculated.

Everything is very simple here, you need to determine the number of periods (n) required to obtain an amount equal to 2x "investment amount". You can count sequentially or use the logarithm formula: n=log 1.1 2=~7.2. To calculate the number of days, we reduce the decimal remainder to the proportion and get: 1/5*30=6. PP 2 is equal to more than 7 months or ~246 days. The investor should choose the first project due to the fact that PP 1

3 Discounted project payback period or DPBP

Discounted Pay-Back Period is a more complex calculation of the period of full payback of the initial investment, taking into account the changing value of money and financial risks. The longer the project, the greater the number of risks affecting it. We have already talked about how to calculate NPV, so we will not dwell on this in detail.

We will need to calculate the NPV of the project in order to understand how profitable the project will actually be, taking into account inflation, taxes, and depreciation costs. Companies resort to this technique when their internal investment policy requires long-term investments (expansion of production facilities, for example), or when money is invested in an investment instrument for several years.

A private capitalist's short-term investments are less affected by discount rates. On the contrary, the internal investment activities of enterprises almost always require attention to depreciation charges. It is more difficult to do without discounting. The formula for calculating DPBP is quite simple in nature; the difficulty always becomes the calculation of NPV for a single project.

Example 3. An enterprise has an average annual income of $5,000 per annum with annual capitalization. What would be the DPBP for $20,000, taking into account 8% inflation and without selling the business? Let's take a slightly simpler path and find the amounts of net present value in each reporting period for 6 years. The data is summarized in the table below. Using the data from the table, we find that DPBP = 4 years and 211 days.

The PP for the same company is only 4 years. Taking into account inflation alone, DPBP is longer than PP by 211 days. The advantages of DPBP are: greater attention to likely risks; use of dynamic data in calculations.

4 The importance of internal rate of return

When analyzing financial performance, it is also necessary to use the indicator “internal rate of return” or IRR (Internal Rate of Return), this value allows the investor to determine whether the investment project can be accepted for execution or not by comparing the IRR for the selected payback period and the discount rate.

IRR can be determined using the formula we provide below.

This method is also suitable for analyzing short-term investments, where discount rates are much lower. For example, our profit reports are weekly. Theoretically, an investor can deposit and withdraw money every day, the number of settlement periods increases, but the discount rate does not.

To calculate this indicator, it is recommended to use special programs or the MS Excel application, which has a special function “IRR” that allows you to calculate IRR. The IRR is usually chosen so that the discounted cash flows are equal to zero. If the discount rate is less than the internal rate of return, then the project will be profitable.