CN115271909A - Improved calculation method for internal yield of financing lease - Google Patents

Abstract

The invention discloses an improved method for calculating the internal rate of return of financing lease. Setting an initial value IRR _ S and an end value IRR _ E of an internal yield IRR value range of the heliostat rent; calculating the internal yield rate IRR = (IRR _ E + IRR _ S)/2 of the daily rent, entering the step 4 to perform an iterative loop when the condition (IRR _ E-IRR _ S) > is met, otherwise, calculating the annual internal yield rate IRR = 360 of the daily rent, executing the iterative loop when the condition (IRR _ E-IRR _ S) > is met, and otherwise, directly calculating the annual internal yield rate. The method is convenient and simple, has strong applicability and high accuracy, and only eliminates the difference with the calculation according to the period of the pedestrian; the difference between actual comparison and plan comparison can be reflected; the method is suitable for most financing leasing companies under 360-day interest regulation by adopting a bank system.

Description

Improved method for calculating internal yield of financing lease

Technical Field

The invention relates to the technical field of improved financing lease internal rate of return calculation methods, in particular to an improved financing lease internal rate of return calculation method.

Background

Financing lease is the second largest financing mode of credit with banks internationally, and the financing lease industry in China is also in the rapid development stage. Compared with bank credit, financing lease has the characteristics of self-defining financing scheme according to the actual condition of a customer, flexible repayment mode and the like, and the repayment period can be unfixed. Currently, a financing lease company mainly performs feasibility assessment on a financing lease project by combining two dimensions of risk and income of the project. The internal profitability is the discount rate when the cash flow of a series of income and expenditure of the project in the whole calculation period reaches the beginning of the period according to a certain period rule and the net present value is equal to zero, reflects the profitability of the fund occupied by the project and is the most important index for evaluating the profitability level of the project. The IRR in the period rule is a certain value obtained by the period rule according to different period definitions (such as daily, monthly, or seasonal). In fact, internal rate of return is often referred to as annual internal rate of return without specific mention.

The internal yield calculation of the existing rental company project is realized mainly by depending on a related formula in Excel or an IRR calculation framework of a people bank.

(1) Deficiency of the IRR function method

The value returned by the IRR function in Excel is the yield of a set of cash flows (i.e., leases) in "fixed interval time units". These cash flows need not be balanced, but they must be generated at regular intervals, such as monthly or quarterly. The financing rental company will typically multiply the return value of the IRR function by the number of rentals in the year to obtain the internal rate of return. The calculation method mainly comes from the conversion rule between the annual rate and the monthly rate and the daily rate of the bank system, wherein the monthly rate = the annual rate/12, and the daily rate = the annual rate/360, so the financing leasing company industry basically follows the calculation rule.

However, because the interval periods of rent payment of the financing lease project are not completely the same, when the IRR function method is used, unequal intervals need to be converted into equal intervals for calculation, the number of vacant periods is sufficient with zero, and the calculation workload is large in Excel. And once the time interval is to be changed to days, the workload is doubled.

In addition, the IRR function method has different rest periods, and the conversion to the annual rate of return has an error. The actual arrival date of the rent is often not completely consistent with the planned collection date, which causes the calculation interval between the planned internal yield and the actual internal yield to be different, and the difference between the planned situation and the actual situation cannot be accurately compared.

(2) Deficiency of the XIRR function method

The XIRR function in Excel can solve the problems of the IRR function to a certain extent, and can directly return the annual internal yield of a group of cash flows, so that the conversion between interest rates is omitted, and the method is suitable for cash flows with any date interval. However, most of the early practitioners in the chinese financing lease industry have a background of banking, and the conversion mode of annual and monthly interest rates is used up to now, and the information is recorded for 360 days in a year. Although the XIRR can solve the problem of inconsistent lease duration, the XIRR is counted for 365 days a year, and the standard is inconsistent, so that communication obstacles are brought, and the index used by a lease company cannot adapt to cross-border competition with financial industries such as banking industry and the like.

(3) IRR computing framework for the people's bank

The financial leasing industry repayment rhythm is different from the standard repayment rhythm of a bank, so that irregular repayment conditions are frequently realized. In such a difference characteristic, it is not difficult to find the formula after analyzing the formula, and n in the formula of the pedestrian text is not fixed for the financing leasing company, so that the formula is difficult to carry out. Meanwhile, in reality, the actual date of rent arrival is often not completely consistent with the planned collection date and actually affects the internal yield, and the pedestrian method calculates the internal yield by time and cannot reflect the difference, so that the front and back IRRs are consistent.

Disclosure of Invention

The invention aims to provide an improved method for calculating the internal rate of return of financing lease aiming at the defects in the prior art.

To achieve the above object, the present invention provides an improved method for calculating the internal rate of return of financing lease, comprising:

step 1, determining principal P and repayment amount V in each period_iForming a corresponding cash flow table, and determining the number of days t between the repayment day and the release day in each period according to a mode of interest counting for 360 days per year;

step 2, setting an initial value IRR _ S and an end value IRR _ E of the value range of the internal yield IRR of the daily rent;

step 3, calculating an internal yield rate IRR = (IRR _ E + IRR _ S)/2 of the daily rent, entering step 4 to perform iterative loop when a condition (IRR _ E-IRR _ S) > is met and a first set threshold, and otherwise entering step 7;

step 4, calculating the current daily rent internal yield rate IRR and the current IRR _ E as daily IRR in the following formula to obtain a first net present value Cn' and a second net present value Cn _ E;

wherein n is the initial period of total repayment in the financing contract period, NPV_iI is more than or equal to 0 and less than or equal to n, which is the folding value of the ith stage;

step 5, judging whether the first net present value Cn' is larger than 0, if so, entering step 6, otherwise, adjusting the value of IRR _ E to the internal rate of return IRR of the daily rent, and returning to step 3;

step 6, judging whether Cn _ E is larger than 0, if Cn _ E is larger than 0, increasing a second set threshold value for IRR _ E and returning to the step 3, otherwise, adjusting the value of IRR _ S to the daily rent internal yield rate IRR and returning to the step 3;

and 7, calculating the annual internal yield = daily rent internal yield IRR 360.

Further, the first set threshold is 0.0000000000000001.

Further, the second set threshold is 0.000001.

Further, the initial value IRR _ S of the value range of the internal yield IRR of the daily rent is set to be 0, and the end value IRR _ E of the value range of the internal yield IRR of the daily rent is set to be 0.5/step length.

Further, the step length is determined according to the number of days between the last repayment date and the release date, and specifically is as follows:

maxKey≤32，flag＝1

maxKey≤64，flag＝2

maxKey≤128，flag＝4

maxKey≤256，flag＝8

maxKey≤512，flag＝16

maxKey≤1024，flag＝32

maxKey≤2048，flag＝64

maxKey≤4096，flag＝128

maxKey≤8192，flag＝256

maxKey≤16384，flag＝512

wherein maxKey is the number of days between the last repayment date and the release date, and flag is the step length.

Has the advantages that: the invention accords with the IRR calculation framework in No. 3 announcement published by the Chinese people's bank in 2021, calculates the interval date according to days360, calculates the internal yield rate by days by taking the days as the calculation units of the period, can solve the influence caused by unstable payment frequency, and realizes the IRR of all items to be unified for comparative analysis; distribution can be carried out according to daily rent IRR, and the deviation of the deletion only exists between the distribution and the distribution according to the period; the internal rate of return is the instant internal rate of return, can reflect the difference of actual IRR and plan IRR. The advantages of the invention can be summarized as the following points:

(1) The method is convenient and simple, and the conversion among the monthly rate, the seasonal rate and the annual rate is saved;

(2) The applicability is strong, and the method is used for cash flows of any date interval;

(3) The accuracy is high, and only the rounding difference with the calculation according to the period of the pedestrian is eliminated;

(4) The internal yield is the timely yield, and the contrast difference between the reality and the plan can be reflected;

(5) The method is suitable for most financing leasing companies adopting the 360-day interest rule under the bank system.

Drawings

FIG. 1 is a schematic structural diagram of an improved method for calculating the internal rate of return of financing lease according to an embodiment of the present invention.

Detailed Description

The present invention will be further illustrated with reference to the accompanying drawings and specific examples, which are carried out on the premise of the technical solution of the present invention, and it should be understood that these examples are only for illustrating the present invention and are not intended to limit the scope of the present invention.

As shown in fig. 1, an embodiment of the present invention provides an improved method for calculating an internal rate of return of a financing lease, including:

step 1, determining principal P and repayment amount V in each period_iAnd forming a corresponding cash flow table, and determining the number of days t between the repayment day and the release day in each period according to a mode of interest counting for 360 days per year.

And 2, setting a starting value IRR _ S and an ending value IRR _ E of the value range of the internal yield IRR of the daily rent. The IRR _ S and IRR _ E can be set empirically, preferably, the initial value IRR _ S of the range of the daily internal rate of return IRR is set to 0, and the final value IRR _ E of the range of the daily internal rate of return IRR is set to 0.5/step. The step length can be determined according to the number of days between the last repayment day and the release day, and is specifically as follows:

maxKey≤32，flag＝1

maxKey≤64，flag＝2

maxKey≤128，flag＝4

maxKey≤256，flag＝8

maxKey≤512，flag＝16

maxKey≤1024，flag＝32

maxKey≤2048，flag＝64

maxKey≤4096，flag＝128

maxKey≤8192，flag＝256

maxKey≤16384，flag＝512

wherein maxKey is the number of days between the last repayment date and the release date, and flag is the step length. By the arrangement of the mode, irrational numbers can be avoided in the calculation process.

And 3, calculating the internal yield rate IRR = (IRR _ E + IRR _ S)/2 of the daily rent, entering step 4 to perform iterative loop when the condition (IRR _ E-IRR _ S) > is larger than a first set threshold, and otherwise entering step 7. The first set threshold is preferably 0.0000000000000001, that is, when the step difference is close to 0, the current internal rate of return IRR for the daily rent is regarded as the true value, otherwise, an iteration loop is performed until the IRR _ E and the IRR _ S after iteration adjustment satisfy the above condition.

Step 4, respectively taking the daily rent internal yield IRR calculated in the current step 3 and the current IRR _ E as daily IRR in the following formula to calculate a first net present value Cn' and a second net present value Cn _ E;

wherein n is the initial period of total repayment in the financing contract period, NPV_iI is more than or equal to 0 and less than or equal to n.

Step 5, judging whether the first net present value Cn' is larger than 0, if so, entering a step 6, otherwise, adjusting the value of IRR _ E to the daily rent internal yield IRR calculated in the step 3, and then returning to the step 3;

and 6, judging whether the second net present value Cn _ E is larger than 0, if the second net present value Cn _ E is larger than 0, increasing the second set threshold value of IRR _ E and returning to the step 3, otherwise, adjusting the value of IRR _ S to the daily rent internal yield rate IRR calculated in the step 3 and returning to the step 3. The second set threshold is preferably 0.000001.

And 7, calculating the annual internal yield = daily rent internal yield IRR 360. Obviously, the daily rental internal rate of return IRR here is a value that satisfies the condition (IRR _ E-IRR _ S) > the first set threshold value, and is calculated from the daily rental internal rate of return IRR = (IRR _ E + IRR _ S)/2.

The following is detailed by specific cases:

a certain rental item of a certain financing rental company finances 100 ten thousand yuan, and is rented at 22 days 7 and 7 in 2021, all financing money is paid once, and the financing period is 3 years. In the financing period, the repayment intervals of the leasing project parties are inconsistent, the rent is paid for 6 times in total, and the repayment is carried out for 2 times every year. Wherein, the payment is 17 ten thousand yuan at 22 days of 10 months and 22 months in 2021, 10 ten thousand yuan at 22 days of 3 months and 22 months in 2022, 18 ten thousand yuan at 22 days of 10 months and 22 months in 2022, 9 ten thousand yuan at 22 days of 3 months and 22 months in 2023, 17 ten thousand yuan at 10 months and 22 days in 2023 and 4, and 16 ten thousand yuan at 22 months and 3 months in 2024 respectively.

And (3) calculating flow:

1. all cash inflows and cash outflows form a corresponding cash flow table, which is specifically shown in table 1:

TABLE 1

2. According to the mode of 360 days of a year, determining the number t of days between the repayment date and the release date in each period, which is specifically shown in the table 2:

TABLE 2

3. According to the financing lease internal rate of return algorithm of the embodiment of the invention, daily IRR is calculated, and then annual internal rate of return is obtained according to annual IRR = daily IRR 360. Calculating IRR as shown in table 3:

in summary, the invention takes the day as the calculation unit of the period, calculates the repayment interval date of each period according to 360 days in a year, calculates the daily income through a formula, and multiplies the daily income rate by 360 to finally obtain the annual internal income rate. The invention not only accords with the core thought of the pedestrian, but also can solve the influence caused by unstable payment frequency, realizes that IRRs of all items can be unified and compared for analysis, and is suitable for most financing leasing companies using the 360-day interest-counting rule; distribution can be carried out according to daily rent IRR, and the deviation of the deletion only exists between the distribution and the distribution according to the period; the internal rate of return is an instant internal rate of return, which can reflect the difference between the actual IRR and the planned IRR.

The foregoing is only a preferred embodiment of the present invention, and it should be noted that other parts not specifically described are within the prior art or common general knowledge to those of ordinary skill in the art. Without departing from the principle of the invention, several improvements and modifications can be made, and these improvements and modifications should also be construed as the scope of the invention.

Claims (5)

1. An improved financing lease internal rate of return calculation method, comprising:

step 1, determining principal P and repayment amount V in each period_iForming a corresponding cash flow table, and determining the number of days t between the repayment day and the release day in each period according to a mode of interest counting for 360 days per year;

step 2, setting an initial value IRR _ S and an end value IRR _ E of the value range of the internal yield IRR of the daily rent;

step 3, calculating an internal yield rate IRR = (IRR _ E + IRR _ S)/2 of the daily rent, entering step 4 to perform iterative loop when a condition (IRR _ E-IRR _ S) > is met and a first set threshold, and otherwise entering step 7;

step 4, respectively taking the current day rent internal yield IRR and the current IRR _ E as the day IRR in the following formula to calculate and obtain a first net present value Cn' and a second net present value Cn _ E;

wherein n is the initial period of total repayment in the financing contract period, NPV_iI is more than or equal to 0 and less than or equal to n;

step 5, judging whether the first net present value Cn' is larger than 0, if so, entering step 6, otherwise, adjusting the value of IRR _ E to the internal yield rate IRR of the daily rent, and returning to step 3;

step 6, judging whether Cn _ E is larger than 0, if Cn _ E is larger than 0, increasing a second set threshold value for IRR _ E and returning to the step 3, otherwise, adjusting the value of IRR _ S to the daily rent internal yield rate IRR and returning to the step 3;

and 7, calculating the annual internal yield = daily rent internal yield IRR 360.

2. The improved method of claim 1, wherein said first threshold is 0.0000000000000001.

3. The improved method of claim 1, wherein said second threshold is 0.000001.

4. The improved financing lease internal rate of return calculation method according to claim 1, characterized in that the initial value IRR _ S of the range of the daily lease internal rate of return IRR is set to 0, and the end value IRR _ E of the range of the daily lease internal rate of return IRR is set to 0.5/step.

5. The improved financing lease internal rate of return calculation method as claimed in claim 4, wherein the step size is determined according to the number of days between the last repayment date and the release date, specifically as follows:

maxKey≤32，flag＝1

maxKey≤64，flag＝2

maxKey≤128，flag＝4

maxKey≤256，flag＝8

maxKey≤512，flag＝16

maxKey≤1024，flag＝32

maxKey≤2048，flag＝64

maxKey≤4096，flag＝128

maxKey≤8192，flag＝256

maxKey≤16384，flag＝512

wherein maxKey is the number of days between the last repayment date and the release date, and flag is the step length.

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