Payback period of the investment project— the period of time for which net income on an accrual basis becomes equal to zero.
Please note that exactly net income, i.e. income minus expenses. On the Internet you can find many incorrect definitions like this:
The payback period is the period of time after which the amount of investment is equal to the amount of income received. (*)
Several times I had rather lengthy correspondence with buyers of my table for calculating investment projects, who claimed that the table incorrectly calculated the payback period. They argued that the payback period is when [investment] = [amount of income], and referred to carelessly worded definitions similar to definition (*).
This is what one of the table buyers writes to me:
Vladimir, you write that your payback period is the number of the step at which the cash flow cumulatively becomes positive. Those. when the project begins to make a profit. and I say that, as it seems to me, the payback period occurs at the moment when the income from the investment becomes equal to the initial investment.
Let's see why the definition (*) is wrong. Let's consider a simple investment project that allows you to perform mental calculations.
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Examples of calculating the payback period of an investment project
Let's say a certain Mr. X buys a car worth 1 million rubles. in order to earn money using taxi services. Let’s also assume that what Mr. X earns as a taxi driver, he puts in a special envelope. Well, of course, minus the expenses associated with his taxi: minus gasoline, minus fines, etc. When this envelope accumulates 1 million rubles. the payback period will come.
Example 1. Payback period 10 months
Let the monthly revenue (income) be 100 thousand rubles. Mr. X puts 100 thousand rubles in a special envelope every month.
1 000 000: 100 000 = 10
Calculations show that 1 million will be reached in 10 months.
The investment project step (the period following which an interim summing up of results is carried out) is 1 month.
Cash flow table.
Example 2. Payback period 12.5 months
Mr. X must also have expenses associated with his investment project: gasoline, etc. Let the expenses be 20 thousand rubles. per month. Now Mr. X puts only 80 thousand rubles in a special envelope every month.1 000 000: 80 000 = 12.5
Calculations show that 1 million will be reached in 12.5 months.
Please note that the income did not change.
Cash flow table
Example 3. Payback period...
Well, and the extreme case: expenses amount to 100 thousand rubles. per month. Now Mr. X doesn't put anything in his special envelope. When will Mr. X make a million? Never.Please note that the income again remained the same.
Cash flow table
conclusions
- To calculate the payback period of a project, it is not the income itself that is important, but the net income. That is, income minus expenses. The higher the income, the shorter the payback period; the higher the expenses, the longer the payback period.
- The payback period of an investment project is the period of time during which the net income on an accrual basis will become zero. Among other things, this method is very visual - we build a schedule and visually determine this period from the schedule with sufficient accuracy.
- Before the payback period was reached, the net income on an accrual basis was negative, and after this point it will become positive. In other words, when the payback period is reached, the investor returns his investment and begins to receive profit for the sake of which the investment project is carried out.
- In real investment projects, net income is not a constant value and it is impossible to calculate the payback period using simple division, as was done in examples 1 and 2.
Payback period PP
The payback period of an investment is the time it takes for an investment to provide sufficient cash flow to repay investment costs. Together with Net Present Value (NPV) and Internal Return Rate (IRR), it is used as an investment evaluation tool.
The payback period on an investment is an excellent metric that provides you with a simplified way to know how long it will take a firm to recoup its initial costs. This is of particular importance for businesses located in countries with unstable financial systems, or businesses associated with advanced technology, where rapid product obsolescence is the norm, making rapid recovery of investment costs an important issue.
General formula for calculating the payback period of investments:
Current (PP) - payback period of investments;
n - number of periods;
CFt - cash inflow in period t;
Io is the value of the initial investment in the zero period.
Defined by: as the time it takes for an investment to generate sufficient cash flows to repay investment expenses.
Characterizes: financial risk.
Depending on the goal, it is possible to calculate the payback period of investments with varying accuracy (example No. 1). In practice, a situation often occurs when in the first periods there is an outflow of funds and then the amount of cash outflows is put on the right side of the formula instead of Io.
Example No. 1. Calculation of the payback period of investments.
The investment amount is $115,000.
Investment income in the first year: $32,000;
in the second year: $41,000;
in the third year: $43,750;
in the fourth year: $38,250.
Let us determine the period after which the investment pays off.
Amount of income for 1 and 2 years: 32,000 + 41,000 = $73,000, which is less than the investment size of $115,000.
The amount of income for 1, 2 and 3 years: 73,000 + 43,750 = 116,750 more than 115,000, this means that reimbursement of initial expenses will occur before 3 years.
If we assume that cash inflows are received evenly throughout the entire period (the default is that cash is received at the end of the period), then the balance from the third year can be calculated.
Remaining = (1 - (116750 - 115000)/43750) = 0.96 years
Answer: the payback period is 3 years (more precisely 2.96 years).
Example No. 2. Calculation of the payback period of investments.
Investment size - $12800.
First year investment income: $7,360;
in the second year: $5185;
in the third year: $6270.
Calculate the payback period of the investment.
Let us determine the period after which the investment pays off.
The amount of income for 1 and 2 years: 7360 + 5185 = $12545, which is less than the investment amount of $12800.
The amount of income for 1, 2 and 3 years: 12545 + 6270 = 18815 is more than 12800, this means that reimbursement of initial expenses will occur before 3 years.
If we assume that cash inflows are received evenly throughout the entire period, then the balance from the third year can be calculated.
Remaining = (1 - (18815 - 12800)/6270) = 0.04 years.
Answer: the payback period is 3 years (more precisely 2.04 years).
You can easily calculate the payback period of your project using the formula: A = B / C, where A is the project payback indicator; B – the amount invested in the project; C – net annual profit from the project. As we can see, with the help of simple mathematical calculations you will receive a specific period that will be necessary to return the funds you invested in the project.
It is important to consider that this calculation formula only works if the following requirements are met, namely:
In all investment cases, investments must be made once;
All businesses in which funds were invested must have the same period of economic existence;
After investing funds, each year the investor will receive the same amounts of money throughout the entire period of operation of the investment project.
An example of calculating the payback period of an investment project
An example of renting an apartment, room or house. Let's say you invested in real estate and purchased a house for $100,000 in order to rent it out. You expect to receive $600 in rent each month. What will be the payback period for such a project? It is very easy to calculate this by referring to our formula.
B = $100,000 / C = $600 / month. ($7200/year), therefore A = 100000 / 7200 = 14 years. That is, after 14 years you will fully return the invested funds and begin to receive net profit.
(PP is the return on investment project; Io is the size of the initial investment; P is the net annual cash flow from the implementation of the business).
Calculation of the payback period of investments using the formula.
For a more complete understanding of how to calculate the payback period, you should consider an example. Let's say an enterprise made a one-time investment, the amount of which was 50 million tenge. Annual net income – 20 million tenge. To determine the payback period, you must perform the following steps:
Thus, the investment will pay off in 2.5 years.
Coefficient of overall economic efficiency of capital investments (E)
where P is annual profit,
K - capital investments.
Payback period (T)
Profit is:
Profit - the difference between revenues and costs.
Profit on services sold (P) is calculated using the formula:
where B is the planned revenue from the sale of goods or services at current prices (excluding VAT, excise taxes, trade and sales discounts);
C is the full cost of goods or services sold in the coming period.
General formulas for calculating profit.
Gross profit= revenue - cost of products or services sold
Profit/loss from sales (sales)= gross profit - costs * costs in this case - selling and management expenses
Profit/loss before tax= sales profit ± operating income and expenses ± non-operating income and expenses.
Net income (loss= revenue - cost of goods - expenses (administrative and commercial) - other expenses - taxes
Income= revenue (turnover) - cost (or purchase price) of goods or services
Operating profit= gross profit - operating costs*operating costs - company costs for processing raw materials and components into finished goods or services
Payback period of the investment project— the period of time for which net income (income minus expenses) on an accrual basis becomes equal to zero. The notation often used PBP from English Pay Back Period.
Before this, the cumulative net income was negative, but after this it will become positive. It is from this moment that the investor, having recouped his investment, begins to receive the profit for which the investment project was started.
Please note that exactly net income, i.e. income minus expenses. On the Internet you can find many incorrect definitions like this: “The payback period is the period of time after which the amount of investment is equal to the amount of income received.” Here is a showing that this definition is wrong.
Payback period on a cash flow chart
The cash flows for which the graph was constructed are shown in Table 1. The payback period of the project is approximately 10.5 steps of the investment project.
Mathematical formulation of the payback period of an investment project
Typically, the implementation period of an investment project is divided into steps of the investment project, periods (month, quarter, year) based on the results of which an interim summing up of costs incurred and income received is carried out.
Then the net income on an accrual basis for k steps can be written as follows.
NCF k = (CF 1+ - CF 1-)+ (CF 2+ - CF 2-)+…+ (CF k+ - CF k-)
If the payback period is n steps of the investment project, equality will be satisfied
NCF n = (CF 1+ - CF 1-)+ (CF 2+ - CF 2-)+…+ (CF n+ - CF n-) = 0 (*)
Just in case, I’ll clarify that expression (*) is not a formula for calculating the payback period of a project, but a mathematical formulation of the definition from the first paragraph. There is no formula by which in general the payback period can be calculated.
In fact, such a formula is not really needed. If calculations are made to determine the standard indicators of an investment project, the payback period is determined very simply.
Table 1
In the table above, the investment project step is 1 quarter (3 months). It can be seen that the payback period occurs somewhere at the 11th step, which is approximately two and a half years.
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Typically, the payback period is not achieved in an integer number of steps, but the following situation occurs:
NCF n< 0
NCF n+1 > 0
If you want to more accurately determine the part of the step after which the payback period begins, you can proceed as follows. Suppose that at a step of an investment project, net income grows linearly on an accrual basis, then we can compose and solve a proportion to determine part of the step:
Ш - /Ш + = NCF na /NCF n+1
Considering that
can be written down
Ш - /(1-Ш -) = NCF na /NCF n+1
Solving for Ш - , we get
Ш - = NCF na /(NCF na + NCF n+1)
Thus, the payback period measured in steps: n whole steps and plus NCF na /(NCF na + NCF n+1) part of the step.
PBP= n + NCF na /(NCF na + NCF n+1) steps.
We determine the integer number of steps using the table of net income, and calculate the fractional part.
Let's check the resulting formula for calculating the payback period
1.
NCF na =0, i.e. exact payback period n steps.
Substitute into the formula.
Payback period in steps = n + 0/(0+ NCF n+1) = n
2.
NCF n+1 =0, i.e. exact payback period n+1 steps.
Substitute into the formula.
PBP= n + NCF na /(NCF na + 0) = n + 1
3.
NCF na =NCF n+1, the payback period should occur at half the step.
Substitute into the formula.
PBP= n + NCF na /(2 * NCF na) = n + 1/2
An example of calculating the payback period
Enlarged fragment of Chart 1.
The table and graph show that the integer number of steps for which the payback period is achieved n= 10. Let's calculate the share of the 11th step.
NCF 10a =150,000 (absolute value from -150,000)
NCF 11 =250,000
Substitute into the formula.
Payback period = 10 + 150000/(150000+250000) = 10.375 steps
or 2 years 7 months.
The payback period formula is one of the most important indicators when evaluating investments. The return period for investments is fundamental for investors.
The indicator makes it possible to determine how profitable and liquid an investment is. For proper calculation, it is important to understand what the indicator is.
One of the most important coefficients in determining the feasibility of an investment is the payback period of an investment project: its formula demonstrates over what time period the profit on the project will become greater than all the costs of it. The formula calculates the repayment period, then the investor compares the resulting figure with his acceptable and economically feasible period.
The formula for the payback period of investments (see) is appropriate and necessary to use if the investor chooses from several almost identical projects. Here it is better to choose a project that has the shortest return on investment period.
We must not forget that the payback period should be less than the time period during which the lender used the loan.
The payback period of an investment project is a formula showing the number of time periods after which the investor fully returns the invested money.
Important! In order for the formula: payback period of an investment project to be used adequately, expenses must be understood as the costs of improving production, reconstructing capacities, and the company’s main assets. Because of this, the return and effect of investments cannot be immediate.
Armed with a calculator
Let's take a closer look at the return on investment: the formula assumes that the following indicators are known:
- project costs. The total costs include all investments that have been made since the start of the project;
- net income for the year. It is understood as the profit received in the process of working on a project, minus all costs, including taxes;
- depreciation for the annual period. This is money spent on improving the project, methods of its implementation (modernization of production, improvement of equipment, etc.);
- time during which the costs are incurred. This means investment.
The formula for the payback period of investment projects taking into account discounting will be applicable if it is known:
- the amount of all revenue for the analyzed period of time;
- discount rate;
- project discounting period;
- the amount of the initial investment.
The formula for the payback period of investments takes into account the method of income from the project. If the cash flow is uniform throughout the analyzed period, the formula for the payback period of investments will be as follows: T=I/D
- T – investment payback period;
- I – investments;
- D – total amount of income.
Important! The formula “payback period of investment” implies that the profit on the project is obtained by adding net profit and the amount of accrued depreciation.
Whether the adoption of a project is profitable or not is calculated as follows:
- If the resulting value is less than the one specified by the investor, the project is approved and implemented.
- If the resulting period is higher, the project is rejected.
As in reality
Let's give an example of calculations that use the formula: payback period of an investment project. Let’s assume that 120,000 rubles are invested in the project.
Profit from the project:
We check the payback: 25,00 + 45,000 = 70,000 rubles.
The amount received is less than the invested funds, therefore, the project does not pay for itself in two months.
70,000 + 53,000 = 123,000 rub.
The profit for three months is higher than the amount of investment, that is, the project pays off in 3 months.
Advantages and disadvantages
What are the advantages of this method:
- ease of calculation;
- visibility;
- a chance to split the investment, taking into account the value specified by the investor.
Important! Formula: the payback period of an investment project provides a good opportunity to determine the risks associated with it, because an inverse relationship is visible: as the payback period decreases, the risks associated with the project also decrease. As the payback period of investments increases, the risk also increases, because investments may become non-repayable.
Minuses:
- inaccuracy of the results obtained, because in this case the time factor is not taken into account;
- in fact, the profit received after the “passing” of the payback period does not have any impact on its indicator.
Other calculation methods
When investing, the investor is aware that the profit from the project will not flow immediately, but only after a certain time. That is, it is important to understand what profit he will receive in the future, taking into account various economic factors. Therefore, dynamic calculation methods (described above) come to the aid of static calculation methods. They allow you to discount cash flow taking into account various factors that directly affect the implementation of the project.
The importance of using complex calculations is related to the discrepancy between the value of money at the beginning and end of the project.
The payback period of investments - the formula of which is written below, implies the adoption of a time factor when calculating such an indicator. That is, this is the NPV calculation: T=IC/FV
Where:
- T – payback;
- IC – investments in the project;
- FV – estimated profit for the project.
This takes into account the cost of the investment and expected future profits. Calculation of this value requires the use of a discount rate, which is determined based on various risks for the project:
- inflation indicators;
- country risks;
- lost profit, etc.
All indicators are determined as percentages and then added together.
Flow heterogeneity
Profit during the implementation of the project may vary from year to year.
In this case, the return on investment - the formula for which is discussed above - is determined as follows:
- We determine the number of time periods (one month, or one year, that is, equal), when the amount of income becomes approximately equal to the amount of invested funds. The amount is determined on a cumulative basis.
- We determine the balance: we reduce the amount of investment by the amount of profit accumulated on the project.
- We divide the amount of the uncovered balance by the amount of receipts for the next time period (month, year).
It is important in this case to use the already mentioned discount rate.
Important! The discount rate is calculated: the remaining risks of the project are added to the risk-free rate of return.
In custody
The payback period of investments - the formula of which is discussed in this article, shows how quickly the investor has the opportunity to return his investments and begin to make a profit. The choice is made on the option with the shortest term.
Each of these calculation methods has its own disadvantages and positive features. It is important to remember that payback period comparisons can only be made if the projects are the same.
Happy investing!
Let's consider such an investment indicator as the payback period of investments, its modifications, examples and calculation formulas.
Payback period of investment (EnglishPP,paybackperiod) is the minimum period of time for the return of funds invested in an investment project, business or any other investment. The payback period is a key indicator for assessing the investment attractiveness of a business plan, project and any other investment object. Let's consider various payback period indicators used in practice:
This indicator allows you to compare different projects with each other in terms of their efficiency in return on capital.
#1 Payback period (PP). Formula
IC( Invest Capital
CF i ( Cash Flow
To calculate cash flow, you must use the following formulas:
A ( Amortization) – depreciation, a type of cash flow that is not a cost;
NP( Net Profit) – net profit of the investment project.
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★ (calculation of Sharpe, Sortino, Treynor, Kalmar, Modiglanca beta, VaR) + forecasting course movements |
Payback period (PP). Example calculation in Excel
Let's calculate the payback period of investments in the project using Excel. To do this, it is necessary to determine the initial costs, which in our example amounted to 100,000 rubles, then it is necessary to predict future cash flows (CF) and determine from what period the amount of cash flow will exceed the initial investment costs. The figure below shows the calculation of the payback period of the project. The formula for calculating cash flow on an accrual basis is as follows:
Cumulative cash flow (CF)=C6+D5
An example of calculating the payback period of an investment in Excel
In the fifth month, the amount of cash receipts will cover the initial costs, so the payback period will be 5 months.
The main disadvantages of using this indicator in investment assessment are:
- Lack of discounting of business project cash flows.
- Cash receipts beyond the payback period are not considered.
#2 Discounted payback period (DPP). Calculation formula
Discounted payback period (EnglishDPPDiscountedPaybackPeriod) – the period for the return of funds, taking into account the time value of money (discount rate). The main difference from the simple payback period formula is the discounting of cash flows and the reduction of future cash receipts to the current time.
DPP ( Discounted Payback Period) – discounted payback period of investments;
IC( Invest Capital) – initial investment costs in the project;
CF ( CashFlow) – cash flow created by the investment;
r – discount rate;
n – project implementation period.
Calculation of discounted payback period of investments in Excel
Let's consider an example of estimating the discounted payback period for a business plan. The initial investment amounted to 100,000 rubles, the cash flow changed monthly and is reflected in column “C”. The discount rate was taken equal to 10%. To calculate discounted cash flow, we use the following formula:
Discounted Cash Flow=C7/(1+$C$3)^A7
Cash receipts on an accrual basis=E7+D8
An example of calculating the discounted payback period of an investment in Excel
The project will pay off for the 5th month, in which cash receipts will amount to 100,860 rubles.
Master class: “How to calculate the payback period for a business plan: instructions”
#3 Payback period of investments taking into account liquidation value
Payback period taking into account liquidation value (EnglishBail-OutPaybackPeriod) – represents the period for the return of funds, taking into account the residual value of the assets created in the investment project. When implementing an investment project, assets may be created that can be sold (liquidated), as a result of which the payback period of the project is significantly reduced.
Where:
IC( Invest Capital) – initial investment costs in the project;
RV ( Residual Value) – liquidation value of project assets;
CF i ( Cash Flow) – cash flow from the project in the i-th period of time, which is the sum of net profit and depreciation.
The liquidation value may either increase as a result of the creation of new assets, or decrease due to depreciation.
Calculation of the payback period of an investment taking into account the liquidation value in Excel
The figure below shows the calculation of the payback period of the project taking into account the liquidation value. The formula in Excel is quite simple and looks like:
Cash receipts with liquidation value=C6+E5+D6
An example of estimating the payback period taking into account the liquidation value in Excel
As a result, the payback period taking into account the liquidation value will be ~4 years. This assessment method is advisable to use when the liquidity of the assets being created is high. As you can see, in this version of calculating the payback period, a discount rate can also be used.
Summary
The payback period is the most important indicator of investment analysis of projects and businesses. It allows you to determine the feasibility of investing in a particular project. The use of discounted cash flows and the liquidation value of assets allows the investor to more accurately estimate the period of return of capital. In addition to this coefficient, analysis is required through other performance indicators: net present value (NPV), internal rate of return (IRR) and profitability index (PI). In addition to the point estimate, an analysis of the dynamics of cash flows and their uniformity is necessary.
