Discounted term project payback is the duration of the period from the beginning 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 risk adjustments, 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 rate for a safe investment, it is also considered as an alternative cost Money. 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.

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 invested funds.

• on a cumulative basis.
• Total cash flow can now be compared with the investment amount. 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– the value of the undiscounted cumulative cash flow in a given 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.

Not uncommon 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 is the minimum rate 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.

Discounted payback period ( English Discounted Payback Period, DPP) is one of the parameters used in the evaluation of investment projects, which represents the period of time during which the initial investment will be fully recovered. In other words, it is the break-even point of the project. For investment managers, this parameter is a measure of the overall risk of the project.

When making long-term investment decisions, the discounted payback period is a more reliable parameter than the conventional payback period because it takes into account the concept of the time value of money.

Formula

To calculate the discounted payback period, use the following formula.

where p is the number of the period in which the last negative cumulative discounted net cash flow was observed;

CDNCF p – the value of the last negative cumulative discounted net cash flow (substituted modulo);

CDNCF p+1 is the value of the cumulative discounted net cash flow at the end of the next period.

Example

The company is considering the possibility of launching a new production line. The cost of purchasing and installing new equipment is CU 200,000, and the planned need for net working capital is CU 180,000. The life of this investment project is 5 years, during which the equipment will be depreciated using the straight-line method, subject to zero salvage value. The after-tax cost of capital raised for the implementation of the project is 15.7% per annum, and the income tax rate is 30%. Other indicators are presented in the table.

To calculate the discounted payback period, it is necessary to determine the amount of net cash flow ( English Net Cash Flow, NCF) of the project by year, which is the amount depreciation charges (English Depreciation) and net profit ( English Net Profit). The results of calculations by year are summarized in a table.

Revenue from product sales by year will be:

S 1 = 20,000 × 35 = 700,000 USD

S 2 = 22,000 × 36 = 792,000 USD

S 3 = 27,000 × 38 = 1,026,000 c.u.

S 4 = 25,500 × 41 = 1,045,500 USD

S 5 = 23,000 × 45 = 1,035,000 USD

Aggregate variable costs by year will be:

TVC 1 = 20,000 × 22 = 440,000 USD

TVC 2 = 22,000 × 22 = 484,000 USD

TVC 3 = 27,000 × 23 = 621,000 USD

TVC 4 = 25,500 × 25 = 637,500 USD

TVC 5 = 23,000 × 28 = 644,000 USD

Since the company uses the straight-line depreciation method, the amount of depreciation charges for each year will be the same and amount to CU 40,000. (200,000 ÷ 5).

To calculate the amount of operating income, you must use the following formula.

where S i is revenue from sales in i-th period; TVC i – total variable costs in i-th period; FC i – fixed costs minus depreciation charges in i-th period; D i – the amount of depreciation charges in i-th period.

Thus, the amount of operating profit by year will be:

EBIT 1 = 700,000 - 440,000 - 100,000 - 40,000 = $120,000

EBIT 2 = 792,000 - 484,000 - 102,000 - 40,000 = $166,000

EBIT 3 = 1,026,000 - 621,000 - 105,000 - 40,000 = $260,000

EBIT 4 = 1,045,500 - 637,500 - 109,000 - 40,000 = $259,000

EBIT 5 = 1,035,000 - 644,000 - 115,000 - 40,000 = $236,000

Provided that the income tax rate is 30%, net profit by year will be.

NP 1 = 120,000 × (1-0.3) = 84,000 c.u.

NP 2 = 166,000 × (1-0.3) = 116,200 c.u.

NP 3 = 260,000 × (1-0.3) = 182,000 c.u.

NP 4 = 259,000 × (1-0.3) = 181,300 c.u.

NP 5 = 236,000 × (1-0.3) = 165,200 c.u.

The data required to calculate the discounted payback period is summarized in a table.

The net cash flow (NCF) by year will be:

NCF 1 = 84,000 + 40,000 = 124,000 c.u.

NCF 2 = 116,200 + 40,000 = 156,200 c.u.

NCF 3 = 182,000 + 40,000 = 222,000 c.u.

NCF 4 = 181,300 + 40,000 = 221,300 c.u.

NCF 5 = 165,200 + 40,000 = 205,200 c.u.

Cumulative net cash flow is the sum of net cash flows by year on a cumulative basis. For this investment project, the amount of the initial investment (the so-called zero cash flow) is 380,000 USD. (the amount of costs for the purchase of equipment is 200,000 USD and financing of clean working capital 180,000 USD). Thus, the cumulative net cash flow by year will be:

CNCF 1 = -380,000 + 124,000 = -256,000 c.u.

CNCF 2 = -256,000 + 156,200 = -99,800 c.u.

CNCF 3 = -99,800 + 222,000 = 122,200 c.u.

CNCF 4 = 122,200 + 221,300 = 343,500 c.u.

CNCF 5 = 343,500 + 205,200 = 548,700 USD

To determine the discounted payback period, it is necessary to calculate the present value ( English Present Value, PV) net cash flows by year using the following formula.

where FV – future value cash flow, i – discount rate, N – number of periods.

Thus, the value of discounted net cash flow (DNCF) by year will be:

DNCF 0 = -380,000 ÷ (1+0.157) 0 = -380,000 c.u.

DNCF 1 = 124,000 ÷ (1+0.157) 1 = 107,173.73 c.u.

DNCF 2 = 156,200 ÷ (1+0.157) 2 = 116,684.81 c.u.

DNCF 3 = 222,000 ÷ (1+0.157) 3 = 143,335.21 c.u.

DNCF 4 = 221,300 ÷ (1+0.157) 4 = 123,494.60 c.u.

DNCF 5 = 205,200 ÷ (1+0.157) 5 = 98,971.59 c.u.

In this case, the cumulative discounted net cash flow (CDNCF) will be.

CDNCF 1 = -380,000 + 107,173.73 = -272,826.27 c.u.

CDNCF 2 = -272826.27 + 116,684.81 = -156,141.47 c.u.

CDNCF 3 = -156,141.47 + 143,335.21 = -12,806.25 c.u.

CDNCF 4 = -12,806.25 + 123,494.60= 110,688.35 c.u.

CDNCF 5 = 110,688.35 + 98,971.59 = 209,659.94 USD

The calculations carried out allow us to calculate the discounted payback period using the above formula. For the conditions of this example, the last negative cumulative discounted net cash flow was observed at the end of year 3, therefore, the discounted payback period will be 3.1 years.

DPP = 3 + |-12,806.25| ÷ (110,688.35 + |-12,806.25|) = 3.1 years

To compare this parameter of an investment project with the usual payback period (PP), we calculate the latter using the following formula.

where p is the number of the period in which the last negative cumulative net cash flow was observed; CNCF p – the value of the last negative cumulative net cash flow (substituted modulo); CNCF p+1 – the value of the cumulative net cash flow in the next period.

For the conditions of this example, the last negative cumulative net cash flow was observed at the end of year 2, which means the usual payback period will be 2.5 years.

PP = 2 + |-99 800| ÷ (122,200 + |-99,800|) = 2.5 years

Schedule

Graphically, the difference between the discounted payback period and the normal payback period is as follows (the graph is based on the example condition).

Advantages and disadvantages

Advantages

• The main advantage of the discounted payback period over the regular payback period is that its calculation takes into account the concept of the time value of money.


• It allows you to assess whether the initial investment will be returned or not.


• This design parameter can be used as a measure of risk. The shorter its duration, the lower the risk and vice versa.

Flaws

• The main disadvantage of using a discounted payback period is that on its basis it is impossible to make a decision on whether to implement or abandon an investment project, since it does not give an idea of ​​​​the increase in the value of the company. Therefore, when making a decision, the main parameter of the project is the net present value.


• Cash flows that will be received after the project payback occurs are not taken into account.


• The assumption is that all cash flows are reinvested at the discount rate. If intermediate cash flows are reinvested at a rate lower than the discount rate, the actual payback period of the project will be higher than the estimated one.

Before making any investment, investors in mandatory trying to find out when investments will start to make a profit.

For this purpose the following is used financial ratio as the payback period.

Concept

Depending on your goals financial investments can be distinguished several basic concepts of payback period.

For investment

The payback period is the period of time after which the amount of invested funds is equal to the amount of income received. In other words, in this case the coefficient shows what time will be required in order to return the invested money and start making a profit.

Often the indicator is used to select one of alternative projects for investment. For an investor, the project with a lower coefficient value will be more preferable. This is due to the fact that it will become profitable faster.

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For capital investments

This indicator allows you to evaluate efficiency reconstruction, modernization of production. In this case, this indicator reflects the period over which the resulting savings and additional profits will exceed the amount spent on capital investment.

Often such calculations are used to assess the effectiveness and feasibility of capital investments. If the coefficient is too high, you may have to abandon such investments.

Equipment

The payback period of equipment allows you to calculate how long it will take for the funds invested in a given production unit to be returned from the profit received from its use.

Calculation methods

Depending on whether the change in the value of funds over time is taken into account when calculating the payback period or not, they are traditionally divided into 2 calculation methods this coefficient:

1. simple;
2. dynamic (or discounted).

Easy way to calculate represents one of the oldest. It allows you to calculate the period that will pass from the moment of investing funds to the moment of their payback.

Using in process financial analysis this indicator, it is important to understand that it will be quite informative only if following conditions:

• in the case of comparing several alternative projects, they must have an equal lifespan;
• investments are made one-time at the beginning of the project;
• income from invested funds comes in approximately equal parts.

The popularity of this calculation method is due to its simplicity, as well as complete clarity for understanding.

In addition, the simple payback period is quite informative in terms of quality investment risk indicator. That is, its greater value allows us to judge the riskiness of the project. At the same time, a lower value means that immediately after the start of its implementation, the investor will receive consistently large income, which allows maintaining the level of the company at the proper level.

However, in addition to these advantages, a simple calculation method has a number of disadvantages. This is due to the fact that in this case are not taken into account the following important factors:

• the value of funds changes significantly over time;
• After the project has achieved payback, it can continue to generate profits.

That is why the calculation of the dynamic indicator is used.

Dynamic or discounted payback period project is the duration of the period that passes from the beginning of investments to the time of its payback, taking into account discounting. It is understood as the onset of a moment when the net present value becomes non-negative and remains so in the future.

It is important to know that the dynamic payback period will always be longer than the static one. This is because in this case the change in the value of funds over time is taken into account.

Next, we will consider the formulas used to calculate the payback period in two ways. However, it is important to remember that if the cash flow is irregular or the amounts of income vary in size, it is most convenient to use calculations using tables and graphs.

Method for calculating simple payback period

When calculating, a formula of the form is used:

Example 1

Let's assume that a certain project requires an investment of 150,000 rubles. It is expected that annual revenues from its sale will amount to 50,000 rubles. It is necessary to calculate the payback period.

Let's substitute the data we have into the formula:

RR = 150,000 / 50,000 = 3 years

Thus, the investment is expected to pay off within three years.

The formula proposed above does not take into account that during the implementation of the project, not only an influx of funds may occur, but also an outflow. In this case, it is useful to use a modified formula:

РР = К0 / ПЧсг, where

PChsg - received on average per year. It is calculated as the difference between average income and expenses.

Example 2

In our example, we will additionally introduce the condition that during the implementation of the project there are annual costs in the amount of 20,000 rubles.

Then the calculation will change as follows:

RR = 150,000 / (50,000 – 20,000) = 5 years

As you can see, the payback period when taking into account costs turned out to be longer.

Such calculation formulas are acceptable in cases where revenues are the same over the years. In practice this rarely happens. Much more often the amount of inflow changes from period to period.

In this case, the calculation of the payback period is carried out somewhat differently. There are several steps in this process:

1. there is a whole number of years for which the amount of income will be as close as possible to the amount of investment;
2. find the amount of investments that are not yet covered by inflows;
3. Assuming that investments go evenly throughout the year, find the number of months required to achieve full payback of the project.

Example 3

The amount of investment in the project is 150,000 rubles. During the first year, an income of 30,000 rubles is expected, the second - 50,000, the third - 40,000, and the fourth - 60,000.

Thus, for the first three years the amount of income will be:

30 000 + 50 000 + 40 000 = 120 000

Over 4 years:

30 000 + 50 000 + 40 000 + 60 000 = 180 000

That is, the payback period is more than three years, but less than four.

Let's find the fractional part. To do this, we calculate the uncovered balance after the third year:

150 000 – 120 000 = 30 000

30,000 / 60,000 = 0.5 years

We find that the return on investment is 3.5 years.

Calculation of dynamic payback period

Unlike the simple one, this indicator takes into account changes in the value of funds over time. To do this, the concept of a discount rate is introduced.

The formula takes the following form:

Example

In the previous example, we introduce one more condition: the annual discount rate is 1%.

Let's calculate discounted revenues for each year:

30,000 / (1 + 0.01) = 29,702.97 rubles

50,000 / (1 + 0.01)2 = 49,014.80 rubles

40,000 / (1 + 0.01)3 = 38,823.61 rubles

60,000 / (1 + 0.01)4 = 57,658.82 rubles

We get that for the first 3 years the income will be:

29,702.97 + 49,014.80 + 38,823.61 = 117,541.38 rubles

Over 4 years:

29,702.97 + 49,014.80 + 38,823.61 + 57,658.82 = 175,200.20 rubles

As with simple payback, the project pays off in more than 3 years, but less than 4. Let's calculate the fractional part.

After the third year, the outstanding balance will be:

150 000 – 117 541,38 = 32 458,62

That is, the full payback period is not enough:

32,458.62 / 57,658.82 = 0.56 years

Thus, the return on investment will be 3.56 years. In our example, this is not much more than with the simple payback method. However, the discount rate we adopted was too low: only 1%. In practice it is about 10%.

Payback period is important financial indicator. It helps the investor assess how feasible it is to invest in a particular project.

The following video lecture is devoted to the basics of financial planning, investment plan and payback period:

Discounted payback period is one of the top 10 indicators used by investment analysts to determine the effectiveness of investments. In the article we will look at it economic essence and the calculation formula, we will follow the calculation of the indicator using an example and analyze the results. Let us note the pros and cons of the method and draw conclusions.

The discounted payback period (DPP) is the period during which the profits received from the project will cover the investments made in it. Both indicators - profit and investment - are calculated taking into account the discount rate (barrier rate).

When calculating the discounted payback period, we determine discounted cash flows from the project. Negative flows are initial investments, positive flows are income. Next, income in each period is sequentially subtracted from the investment amount until payback occurs. The payback period will be the calculated DPP indicator. Let's take a closer look.

Formula for calculating discounted payback period

The discounted payback period of an investment project is calculated using the formula:

where DPP is the discounted payback period,

n – number of periods,

t – serial number of the period,

CF t – net cash flow in period t,

r – barrier rate, also known as ,

I 0 – initial investment.

How to calculate the barrier rate

The barrier rate is the minimum amount of profit per invested ruble that the investor agrees to, taking into account all the risks. In fact, for an investor, the barrier rate indicator means the cost of his capital, so each investor has his own expectations for profitability. In addition, the barrier rate can be either constant throughout the entire calculation period or vary from period to period.

There are several approaches to determining the barrier rate:

1. Taking into account only the inflation rate. This approach works mainly for risk-free and low-risk investments and is rarely used.
2. Equating the barrier rate to the investor's cost of capital (). In essence, this method means that the investor compares the profitability of the project under consideration with the profitability of investments already made or considers investing with the involvement of external sources.
3. Calculate the barrier rate based on historical periods using trend line forecasting. It only works if there are accumulated statistics on similar investments.
4. For unique investments for which there is no accumulated experience yet and the risks are high, the risk-based calculation method is used. Let's look at it in our article.

where r is the barrier rate,

r b – risk-free rate, the minimum profit that an investor wants to receive in the absence of risks,

n – number of periods,

i – serial number of risk,

Ri – premium for the i-th risk number.

For the calculation, all project risks are listed and weighed: production, commercial, financial, currency and others.

Calculation of initial investment

The initial investments in the project can be as in the “zero” period, then to calculate I 0 the amount of investments in the project before its start is taken. Investments can continue during the first months (years) of the project, then to calculate I o a formula similar to the DPP formula is used:

where I 0 is the initial investment in the project,

n – number of periods,

t – serial number of the period,

I t – net cash flow in period t,

r – barrier rate, also known as the discount factor.

An example of calculating the discounted payback period

Analyst investment fund evaluates which of the proposed projects to invest money in.

In front of him are business plans for two projects (Table 1 and Table 2).

Table 1. Project "A"

	Net Cash Flow (NCF)

table 2. Project "B"

	Net Cash Flow (NCF)

At the same time, the analyst calculated barrier rates for each project taking into account risks. For project "A" discount rate equal to 21%, for project “B” – 19%. For both projects, the rate remains the same in each billing period.

Most in a simple way Calculating payback taking into account discounting involves filling out a table in Excel. In addition to ease of calculation, providing information in a table provides maximum clarity. Let's follow the calculations for projects “A” and “B”.

Please note that project “A” will require investing money not only at the “zero” stage, but also in the first year of the project. Therefore, to calculate the initial investment, we apply the discounted amount formula described above.

Table 3. Calculation of DPP calculation in Excel for project “A”

	Net Cash Flow (NCF)	Discount rate		DDP is cumulative
			NPV/(1+r) year	Amount(DDC)

Table 4. Calculation of DPP calculation in Excel for project “B”

	Net Cash Flow (NCF)	Discount rate	Discounted Cash Flow (DCF)	DDP is cumulative
			NPV/(1+r)year	Amount(DDC)

From the tables it is clear that:

• DPP for project “A” is 5 years,
• DPP for Project B is 4 years.

You can even more clearly present the calculation result in a diagram.

Diagram

Based on the calculation of the discounted period, it is more profitable to invest money in project “B”, it will pay off faster. But it's not that simple.

Pros and cons of the DPP indicator

The DPP indicator is very effective when calculating high-risk projects when working in developing countries and in dynamically changing markets, as it allows us to take into account possible depreciation of money in future periods. It compares favorably with a similar indicator - the payback period of the project (PP) in that it takes into account the dynamics of depreciation money supply and allows you to take into account the risks of the project. Another advantage of DPP is the ability to calculate different rates discounting for different periods.

But the DPP calculation method also has disadvantages. The first and main thing is the fact that the discounted payback period does not take into account the income and expenses that the project will bring after the payback period has passed.

In our example, project “A”, although it will pay off 1 year later than “B”, will bring more profit to the investor in the future:

• The cumulative DCF in the sixth year for project “A” is 4,140,174;
• The cumulative DCF in the sixth year for project “B” is 3,288,506.

Also investment projects with long term operation will bring the investor in total more profit than those with a short period.

It is possible that the project will begin to generate losses after the payback period; this option also does not take into account the DPP calculation method.

The discounted payback period should only be analyzed in conjunction with:

1. .
2. Profitability index PI.
3. Return on Investment Ratio ARR.
4. .
5. Modified internal rate of return MIRR.

The second disadvantage of the method of calculating the discounted payback period is the fact that its calculation is influenced by the duration of the “pre-operational” period. We will call pre-operational the period between the first investments in the project and the beginning of its operation and receipt of profit from the project. The larger the gap between investment and return, the longer the payback period, which does not always reflect the real effectiveness of the investment.

The third significant disadvantage will be the inability to calculate the indicator with multidirectional cash flows for the project during the payback period.

Let’s say we have project “C”, the net cash flows for which look like this

Table 5. Calculation of discounted cash flow for project “C”

	Net Cash Flow (NCF)	Discount rate	Discounted Cash Flow (DCF)	DDP is cumulative
TOTAL	4 294 000

The calculation shows that the payback period is 3 years. But after three years, money needs to be invested in the project again (additional purchase of equipment, expansion of the range, etc.), the cumulative discounted cash flow again becomes negative. However, DPP no longer takes this fact into account.

And finally, the fourth feature of the calculation will be a certain degree of subjectivity in choosing the method for determining the barrier rate. To level out this subjectivity, we recommend calculating the barrier rate using two different methods. It is desirable that the calculation methodology be recorded in the company’s regulatory documentation.

Let's sum up all the pros and cons of the method and draw a conclusion. Calculation of the discounted payback period is necessary first of all:

• investors working with high-risk investments;
• companies entering new markets, especially in countries with unstable economies;
• analysts in business planning. The payback period in a business plan indicates the period in which income and expenses must be calculated especially carefully.