Discounted method for calculating project payback
Posted: Sun Dec 22, 2024 5:56 am
In market conditions, cash flows are unstable and inflation affects the value of capital. The simple payback period method ignores the time factor, which is critical for long-term investments. The discounted approach takes into account the time value of money, providing a more accurate assessment of projects.
The discounted payback period (DPP) formula is as follows:
DPP = ∑ni=1 CFi / (1+r)i > IC
The key indicators are:
DPP (Discounted Pay-Back Period) — the payback period in years or months, taking into account discounting;
CF (Cash Flow) — expected cash flows for a specific interval;
IC (Invest Capital) — the volume of initial investment;
r — discount rate;
n is the calculation period (measured in years or months).
The project payback formula using the discounted phone number identifier philippines method is based on the concept of the time value of money. It allows one to determine the current value of future financial receipts, taking into account, for example, the value of funds received in a year in a modern equivalent.
This approach minimizes the uncertainty factor, since the cost of capital may fluctuate significantly in the future. Therefore, to forecast income in subsequent periods, it is advisable to rely on current economic parameters.
It is important to note that the discounted payback period always exceeds the figure calculated by the simple method. This is explained by taking into account the time value of money in the calculations. Despite the longer period, the discounted method provides a more accurate and adequate assessment of the economic efficiency of the project in the long term.
Examples of calculating project payback
Let's look at the main ones:
Example of calculation using a simple method
Gennady plans to open a small household appliances store and invest 1,000,000 rubles in its launch.
The estimated monthly income is 400,000 rubles.
Calculation of the project's payback period using the following formula: 1,000,000 / 400,000 = 2.5 months. This means that in two and a half months the store will reach payback and start generating net profit.
Example of calculation using a simple method
Source: shutterstock.com
An alternative approach to calculating payback involves using average annual profits instead of monthly figures. This method is particularly relevant for projects with large capital investments and a long payback period.
For example, with an investment of 5,000,000 rubles and an average annual profit of 1,000,000, the project pays off in the period: 5,000,000 / 1,000,000 = 5 years.
For example, monthly profits often change. Therefore, determining and finding breakeven points can be done using tables, and they can take into account such fluctuations.
Period, month 0 1 2 3
Investments, rubles -1,000,000
Profit per month, rubles 300,000 250,000 450,000
Cash flow, rubles -1,000,000 -700,000 -450,000 0
Financial analysis shows that the store will reach the break-even point in the third month of operation, after which the store will begin to make a profit.
If you add the amount of expenses to the calculation, the payback formula will be as follows:
simple payback period = total initial investment / (expected average net profit for the period - costs)
Let's assume that the initial data remains the same, but the expenses are 100,000 rubles per month. Then the calculation will look like this: 1,000,000 / (400,000 - 100,000) = 3.3 months.
Let's calculate using the dynamic method
Let's consider the assessment of the payback of an investment project using the example of Gennady, who plans to invest 1 million rubles in the development of a store. To determine the exact payback period of the project, we will apply the calculation using the discounted method.
Let's set the discount rate at 12% per annum (1% per month). The monthly net profit varies from 250 to 450 thousand rubles. Let's make a calculation taking into account the discount:
Month 1: 300,000 / ((1 + 0.01) ^ 1) = 297,030 rubles.
Month 2: 250,000 / ((1 + 0.01) ^ 2) = 245,074 rubles.
Amount for 2 months 297,030 + 245,074 = 542,104 < 1,000,000 rubles. Let's continue the calculation.
Month 3: 450,000 / ((1 + 0.01) ^ 3) = 436,766 rubles.
Amount for 3 months 297,030 + 245,074 + 436,766 = 978,870 < 1,000,000 RUB. Calculation continues.
Month 4: 350,000 / ((1 + 0.01) ^ 4) = 336,343 rubles.
Total amount: RUB 1,315,213 > RUB 1,000,000
Thus, the payback period of the project is 4 months.
Period, month 0 1 2 3 4
Investments, rubles -1,000,000
Monthly profit, rubles 300,000 250,000 450,000 350,000
Monthly profit with a 1% discount, rubles 297 030 245 074 436 766 336 343
Amount of profit, rubles 0 297 030 542 104 978 870 1 315 213
For clarity and better understanding of the methodology for calculating the payback of an investment project, we have presented a detailed analysis. In real practice of financial modeling, it is more efficient to use Excel spreadsheets, where formulas and variables automate the calculation process.
A comparative analysis of the indicators obtained by the simple and dynamic methods reveals significant differences. With identical input data on profit (as in example 2 for the simple method), the calculation results demonstrate discrepancies. The dynamic method gives a higher term, taking into account the factor of the time value of money and its depreciation.
The discounted payback period (DPP) formula is as follows:
DPP = ∑ni=1 CFi / (1+r)i > IC
The key indicators are:
DPP (Discounted Pay-Back Period) — the payback period in years or months, taking into account discounting;
CF (Cash Flow) — expected cash flows for a specific interval;
IC (Invest Capital) — the volume of initial investment;
r — discount rate;
n is the calculation period (measured in years or months).
The project payback formula using the discounted phone number identifier philippines method is based on the concept of the time value of money. It allows one to determine the current value of future financial receipts, taking into account, for example, the value of funds received in a year in a modern equivalent.
This approach minimizes the uncertainty factor, since the cost of capital may fluctuate significantly in the future. Therefore, to forecast income in subsequent periods, it is advisable to rely on current economic parameters.
It is important to note that the discounted payback period always exceeds the figure calculated by the simple method. This is explained by taking into account the time value of money in the calculations. Despite the longer period, the discounted method provides a more accurate and adequate assessment of the economic efficiency of the project in the long term.
Examples of calculating project payback
Let's look at the main ones:
Example of calculation using a simple method
Gennady plans to open a small household appliances store and invest 1,000,000 rubles in its launch.
The estimated monthly income is 400,000 rubles.
Calculation of the project's payback period using the following formula: 1,000,000 / 400,000 = 2.5 months. This means that in two and a half months the store will reach payback and start generating net profit.
Example of calculation using a simple method
Source: shutterstock.com
An alternative approach to calculating payback involves using average annual profits instead of monthly figures. This method is particularly relevant for projects with large capital investments and a long payback period.
For example, with an investment of 5,000,000 rubles and an average annual profit of 1,000,000, the project pays off in the period: 5,000,000 / 1,000,000 = 5 years.
For example, monthly profits often change. Therefore, determining and finding breakeven points can be done using tables, and they can take into account such fluctuations.
Period, month 0 1 2 3
Investments, rubles -1,000,000
Profit per month, rubles 300,000 250,000 450,000
Cash flow, rubles -1,000,000 -700,000 -450,000 0
Financial analysis shows that the store will reach the break-even point in the third month of operation, after which the store will begin to make a profit.
If you add the amount of expenses to the calculation, the payback formula will be as follows:
simple payback period = total initial investment / (expected average net profit for the period - costs)
Let's assume that the initial data remains the same, but the expenses are 100,000 rubles per month. Then the calculation will look like this: 1,000,000 / (400,000 - 100,000) = 3.3 months.
Let's calculate using the dynamic method
Let's consider the assessment of the payback of an investment project using the example of Gennady, who plans to invest 1 million rubles in the development of a store. To determine the exact payback period of the project, we will apply the calculation using the discounted method.
Let's set the discount rate at 12% per annum (1% per month). The monthly net profit varies from 250 to 450 thousand rubles. Let's make a calculation taking into account the discount:
Month 1: 300,000 / ((1 + 0.01) ^ 1) = 297,030 rubles.
Month 2: 250,000 / ((1 + 0.01) ^ 2) = 245,074 rubles.
Amount for 2 months 297,030 + 245,074 = 542,104 < 1,000,000 rubles. Let's continue the calculation.
Month 3: 450,000 / ((1 + 0.01) ^ 3) = 436,766 rubles.
Amount for 3 months 297,030 + 245,074 + 436,766 = 978,870 < 1,000,000 RUB. Calculation continues.
Month 4: 350,000 / ((1 + 0.01) ^ 4) = 336,343 rubles.
Total amount: RUB 1,315,213 > RUB 1,000,000
Thus, the payback period of the project is 4 months.
Period, month 0 1 2 3 4
Investments, rubles -1,000,000
Monthly profit, rubles 300,000 250,000 450,000 350,000
Monthly profit with a 1% discount, rubles 297 030 245 074 436 766 336 343
Amount of profit, rubles 0 297 030 542 104 978 870 1 315 213
For clarity and better understanding of the methodology for calculating the payback of an investment project, we have presented a detailed analysis. In real practice of financial modeling, it is more efficient to use Excel spreadsheets, where formulas and variables automate the calculation process.
A comparative analysis of the indicators obtained by the simple and dynamic methods reveals significant differences. With identical input data on profit (as in example 2 for the simple method), the calculation results demonstrate discrepancies. The dynamic method gives a higher term, taking into account the factor of the time value of money and its depreciation.