Project investment value analysis
There are three main methods of investment value analysis:
- Net Present Value (NPV)
- Internal Rate of Return (IRR)
- Equal Annuity Act (EAA)
Net Present Value (NPV) Method
It is the difference between the discounted value of the future cash flow generated by an investment and the investment cost of the project.
Net present value investment rule: When making an investment decision, the option with the largest NPV value should be accepted. Accepting this option is equivalent to receiving cash equal to the NPV value today.
In an independent project decision, the choice that needs to be made is whether to accept or reject the project. The NPV law means that the NPV value of an item is compared to zero, and if the NPV is positive, the item is accepted.
The two basic considerations when selecting project investment are capital cost and opportunity cost, and other factors should also consider inflation cost and risk cost.
Internal Rate of Return (IRR) Method
overview
The internal rate of return method (English: Internal Rate of Return; IRR for short) is a method to use the internal rate of return to evaluate the financial benefits of project investment. The so-called internal rate of return is the interest rate that makes the total present value of the project's inflowing funds equal to the total present value of the outflowing funds, in other words, the discount rate that makes the net present value (NPV) equal to zero. If you do not use a computer, the internal rate of return is calculated using several discount rates until you find a discount rate that equals zero or is close to zero net present value.
In simple terms, the internal rate of return is the discount rate that makes the net present value of a business investment zero. It has some characteristics of the DCF method, and is most often used to replace the DCF method in practice. Its basic principle is to try to find a value that summarizes the characteristics of enterprise investment. The internal rate of return itself is not affected by the interest rate of the capital market, but depends entirely on the cash flow of the enterprise, reflecting the inherent characteristics of the enterprise.
[Note: The DCF method, also known as the free cash flow discount method, is generally used in the valuation of enterprises. Its connotation is to restore the expected cash flow of the enterprise in a specific period in the future to the present value. Obviously, the essence of enterprise value is its future value. Profitability, and profitability is reflected in the cash flow brought by operating activities, so the discounted cash flow method is usually used as a method to measure the value of enterprises in theoretical circles, and it has also been widely used in evaluation practice, and has been increasingly perfected and Mature. 】
However, the internal rate of return method can only tell investors whether the value of the evaluated company is worth investing in, but it does not know how much it is worth investing in. Moreover, the internal rate of return method is just the opposite when facing investment companies and financing companies: for investment companies, when the internal rate of return is greater than the discount rate, the company is suitable for investment; when the internal rate of return is lower than the discount rate, the company Not worth the investment; financing-oriented businesses are not.
Generally speaking, when it comes to corporate investment or mergers and acquisitions, investors not only want to know whether the target company is worth investing in, but also want to know the overall value of the target company. However, the internal rate of return method cannot satisfy the latter, so this method is more applied to individual project investment.
calculation steps
- On the basis of calculating the net present value, if the net present value is positive, it is necessary to use a higher discount rate in the calculation of the net present value until the calculated positive net present value is close to zero.
- Continue to increase the discount rate until a negative net present value is calculated. If the negative value is too large, reduce the discount rate and then measure to a negative value close to zero.
- According to the discount rate of two adjacent positive and negative net present values close to zero, the internal rate of return is obtained by linear interpolation.
Advantages and disadvantages
The advantage of the internal rate of return method is that it can link the income during the life of the project with its total investment, point out the rate of return of the project, and compare it with the industry benchmark investment rate of return to determine whether the project is worth building. When borrowing is used for construction, when the borrowing conditions (mainly the interest rate) are not clear, the internal rate of return method can avoid the borrowing conditions and first obtain the internal rate of return as the upper limit of the acceptable borrowing rate. However, the internal rate of return is a ratio, not an absolute value. A program with a lower internal rate of return may have a larger net present value due to its larger scale, so it is more worthy of consideration. Therefore, when selecting and comparing various schemes, the internal rate of return and net present value must be considered together.
Internal Rate of Return Analysis
The internal rate of return is the rate of return that an investment is expected to achieve, and it is the discount rate that can make the net present value of the investment project equal to zero. It is to make the present value of the cash flow generated by an investment in the future exactly equal to the rate of return when the investment cost is taken into account when the time value is taken into account, instead of the "net present value is zero no matter whether it is high or low, so high or low It doesn't matter," that's an upside-down thought. Because the premise of calculating the internal rate of return is to make the net present value equal to zero.
In layman's terms, the higher the internal rate of return, it means that the cost you invest is relatively small, but the benefits you get are relatively large. For example, the cost of two investments, A and B, are both 100,000 yuan, and the operating period is 5 years. A can get a net cash flow of 30,000 yuan a year, and B can get 40,000 yuan. Through calculation, it can be concluded that the internal rate of return of A is approximately equal to 15%, and B's is about 28%. These can actually be seen from the annuity present value coefficient table.
Points to note
The internal rate of return refers to the highest rate of return that a project can actually achieve. From a calculation point of view, any discount rate that can make the net present value of an investment project equal to zero is the internal rate of return. The following points should be noted in the calculation:
(1) Judging which method to use to calculate the internal rate of return according to the distribution of cash flow in the project calculation period: If the investment in a certain investment project is invested at the beginning of the investment, and the cash flow in each year of the operating period is equal (that is, it is a typical postpaid annuity), at this time, the annuity method can be used to determine the valuation range of the internal rate of return, and then the interpolation method can be used to determine the internal rate of return
If the distribution of the cash flow of an investment project cannot meet the above two conditions at the same time, the test method can be used to determine the valuation range of the internal rate of return, and then the interpolation method can be used to determine the internal rate of return.
(2) When using the annuity method and interpolation method to determine the internal rate of return, since the three elements of the investment amount (that is, the present value), the annuity (that is, the cash flow that is equal to each year), and the calculation period are known, therefore: first, the annuity cash flow can be used Calculate the present value coefficient of the annuity using the calculation formula of the annuity value, then check the table to determine the valuation range of the internal rate of return, and finally use the interpolation method to determine the internal rate of return.
(3) When using the test method and interpolation method to determine the internal rate of return, since the cash flow varies from year to year, the
① Firstly, a discount rate i1 should be set, and then the cash flow in the calculation period of the project should be discounted to the present value according to the discount rate, and the net present value NPV1 should be calculated;
②If NPV1>0, it means that the set discount rate i1 is lower than the internal rate of return of the project. At this time, the discount rate should be increased (set to i2), and the cash flow of the project calculation period should be re-discounted according to i2 value, calculate the net present value NPV2;
If NPV1<0, it means that the set discount rate i1 is greater than the internal rate of return of the project. At this time, the discount rate should be reduced (set to i2), and the cash flow of the project calculation period should be re-discounted to the present value according to i2 , calculate the net present value NPV2;
③If the calculation results of NPV2 and NPV1 are opposite at this time, that is, the net present value is one positive and one negative, the test is completed, because zero is between positive and negative (the discounted value when the net present value of the investment project is equal to zero) rate of return is the internal rate of return); but if the calculation results of NPV2 and NPV1 are the same at this time, that is, there is no situation where the net present value is positive and negative, the test will repeat the work of ② until the net present value is positive and negative. negative case;
case analysis
An enterprise plans to invest in a project with a one-time investment of 1 million yuan. The expected service life of the project is 5 years. The annual income is shown in the figure below. Assuming that the benchmark rate of return is 12%, try to evaluate the economic effect of the project.
Solution: According to the calculation formula of internal rate of return:
NPV(i + ) = − 100 + 20(1 + i + ) − 1 + 30(1 + i + ) − 2 + 20(1 + i + ) − 3 + 40(1 + i + ) − 4 + 40(1 + i + ) − 5 = 0
It is difficult to solve this high-order equation, and the internal rate of return i + .
Set i1 = 10%, i2 = 15%, respectively calculate their net present value as follows:
NPV(10%) = − 100 + 20(1 + 10%) − 1 + 30(1 + 10%) − 2 + 20(1 + 10%) − 3 + 40(1 + 10%) − 4 + 40 (1 + 10%) − 5 = 10.16 (10,000 yuan)
NPV(15%) = − 100 + 20(1 + 15%) − 1 + 30(1 + 15%) − 2 + 20(1 + 15%) − 3 + 40(1 + 15%) − 4 + 40 (1 + 15%) − 5 = − 4.02 (10,000 yuan)
Then by the formula
have to
Because i + > i0 = 12%, the project is economically acceptable .
Comparison of NPV and IRR methods
Both the net present value method and the internal rate of return method are methods for calculating the present value of the future cash flow of an investment plan.
When using the net present value method to make investment decisions, the decision-making criteria are: NPV is a positive number, (the actual rate of return on investment is higher than the cost of capital or the lowest rate of return on investment) the program is feasible; NPV is negative, (the actual rate of return on investment lower than the cost of capital or the lowest rate of return on investment) is not feasible; if it is a comparison of multiple programs with the same investment, the larger the NPV, the better the return on investment. The advantage of the net present value method is that it considers the minimum remuneration level of the investment plan and the analysis of the time value of funds; the disadvantage is that NPV is an absolute number and cannot consider the ability of the investment to make a profit. Therefore, the net present value method cannot be used to compare different schemes with different total investment.
When using the internal rate of return method to make investment decisions, the decision-making criteria are: IRR is greater than the minimum return on investment or capital cost required by the company, the plan is feasible; IRR is less than the minimum return on investment required by the company, the plan is not feasible; The higher the internal rate of return, the better the return on investment. The advantage of the internal rate of return method is that it takes into account the real rate of return level and the time value of money of the investment plan; the disadvantage is that the calculation process is relatively complicated and cumbersome.
In general, for the same investment program or investment programs independent of each other, the conclusions drawn by using the two methods are the same. But using these two approaches can lead to conflicting conclusions when used in different and mutually exclusive investment scenarios. The most basic reason for the inconsistency is the different assumptions about the rate of return on the reinvestment of the annual cash inflows of the investment scheme. The net present value method assumes that the annual cash inflow is reinvested at the cost of capital as the standard; the internal rate of return method assumes that the cash inflow is reinvested at the standard internal rate of return calculated by it.
The cost of capital is a more realistic reinvestment rate, so the NPV method is superior to the IRR method in the absence of a capital limit.
equal annuity method
The cash flow with a life cycle of N years is discounted to the beginning of the first year, and the present value is equivalent to an N-year annuity, and the annuity amount obtained is the equivalent annuity.
If the two projects have different life cycles, then the method of using equal annuities is more efficient.
Three methods of code implementation
import numpy as np
cf_projectl=np.array([-700,100,150,200,250,300,350,400])
cf_project2=np.array([-400,50,100,150,200,250,300])
irr_project1 = np.irr(cf_project1)
print("IRR of project 1:" + str(round(irr_projectl, 2))+"%")
irr _project2= np.irr(cf_project2)
print("IRR of project 2:"+ str(round(100*irr_project2, 2)) + "%")
npv_projectl= np.npv(rate=0.12, values=cf_projectl)
print("Net present value of project 1:" + str(round(npv_projectl, 2)))
npv_project2= np.npv(rate=0.12, values=cf_project2)
print("Net present value of project 2:" + str(round(npv_project2, 2)))
eaa_projectl= np.pmt(rate=0.12, nper=8,pv=-npv_projectl,fv=0)
print("EAA of project 1:" + str(round(eaa_projectl, 2)))
eaa_project2= np.pmt(rate=0.12, nper=7,pv=-npv_project2,fv=0)
print("EAA of project 2:" + str(round(eaa_project2, 2)))