(1) Calculation of Net Present Value and Profitability Index
Net present value refers to the difference between the inflow and outflow of funds in each year of the project life cycle, which is converted into the present value at the initial stage of project implementation according to the prescribed discount rate. Because money has time value; The calculation of present value is to compare the final value of investment with future income. You can calculate the present value (that is, the discount of the bank) by calculating the final value of the bank, and get the calculation formula: NPV = f/( 1+I) n (where f is the final value, NPV is the present value, I is the discount rate and n is the term). The key to calculate the net present value is to determine the discount rate. Generally speaking, the lowest return on investment is the bank interest rate, which is equivalent to the time value of money, and the opportunity cost of investment is the lowest. When initially testing the discount rate, it is appropriate to use the one-year deposit rate of the bank at that time.
For example, a property company invested 654.38+10,000 yuan in new service projects to meet the needs of owners in its jurisdiction. In the actual operation process, the net profit after deducting various expenses in the first year was 0.1million yuan, the net profit after deducting various expenses in the second year was 0.2 million yuan, and it was sold at 654.38+0.1million yuan two years later. What is the net present value of this project?
If the one-year bank deposit interest rate is 5% and the discount rate is set, the sum of the present value of the annual income is:
0. 1× 1/ 1+0.05+0.2× 1/( 1+0.05)2。 +1/kloc-0 /×1(1+005) 2 =102536 yuan.
Net present value is the total present value of income minus the present value of investment, and profitability index = total present value of income/present value of investment.
Net present value, namely:10.2536-10 = 0.2536 million yuan; Profitability index, namely:
10.2536/ 10= 1.025。
We can draw the conclusion that:
The net present value is greater than 0, and the profitability index is greater than 1, which shows that the investment of this project is feasible.
(2) Calculation of internal rate of return
According to the NPV and profitability indicators, the range of return on investment of this project can be roughly determined. In order to more accurately understand the realized rate of return of this investment, the expected rate of return of this investment is determined to be 65,438+00% by combining the bank interest rate, investment risk rate and inflation rate and comparing the profit rate of the same industry, and the internal rate of return of this investment is calculated and verified.
Through linear interpolation formula: IRR = I1+NPV1(I2-I1)/NPV1+npv2.
In the formula, IRR-internal rate of return: I 1- discount rate when the net present value is a positive value close to zero; I2-discount rate with negative net present value approaching zero; NPV 1 is the positive value of net present value when the low discount rate i 1 is adopted; NP v2—— Negative NPV of i2 at high discount rate.
When the low discount rate is set to 5% i6 5438+0, the high discount rate is set to 8% I2, and the discount rate is 8%, the sum of the present value of the annual income of the above investment projects is:
0. 1× 1/ 1+008+0.2× 1/( 1+0.08) 2+ 1 1× 1/(65438)
The net present value is: 9.691-10 =-0.309 million yuan.
Internal rate of return = 5%+(8%-5%) (10.2536-10)/(10.2536-9.691) = 6.35%.
If the expected rate of return (benchmark rate of return) of the project is 10%, and the realized rate of return is far lower than the expected rate of return, the investment is not feasible.
A more intuitive and clear way to understand IRR is to use the geometric figure method to calculate it: first draw two discount rates I 1 = 5% and I2 = 8% on the abscissa, then draw two straight lines perpendicular to the abscissa at these two points, which are respectively equal to the positive net present value (NPV 1) and negative net present value (NPV2) of the corresponding discount rate, and then connect the two ends of the net present value to draw it all the time. As shown in the figure:
From the two similar triangles in the figure, similar triangles's mathematical formula can be deduced:
NPV1/-NPV2 = IRR-I1/I2-Internal rate of return
Add the numerator and denominator on both sides of the equation to get:
npv 1/npv 1︱npv2︱=irr- i 1/I2-i 1
Second, the main points of internal rate of return calculation
1. To reasonably determine the low discount rate i 1 and the high discount rate i2, first set a discount rate. If the obtained net present value is not a positive number close to zero, try a higher or lower discount rate so that the obtained net present value is a positive number close to zero, thus determining the low discount rate i 1. On the basis of i 1, continue to increase the discount rate.
2. In order to ensure the accuracy of IRR calculation, the difference between the low discount rate i 1 and the high discount rate i2 should not be greater than 5%.
3. The data used, such as bank interest rate, inflation rate, industry profit rate, expected rate of return, etc., must be investigated and demonstrated by many parties, and try to use the latest and accurate data.
Definition of internal rate of return
Internal rate of return (IRR) is the discount rate that the total present value of capital inflow is equal to the total present value of capital flow and the net present value is equal to zero. If the computer is not used, the internal rate of return will be tried with several discount rates until the discount rate with net present value equal to or close to zero is found. Internal rate of return (IRR) is the expected rate of return on investment and the discount rate that makes the net present value of investment projects equal to zero.
It is the expected rate of return of an investment, and the bigger the index, the better. Generally speaking, the project is feasible when the internal rate of return is greater than or equal to the benchmark rate of return. The sum of discounted cash flows of investment projects in each year is the net present value of the project, and the discount rate when the net present value is zero is the internal rate of return of the project. In the project economic evaluation, according to the different levels of analysis, the internal rate of return can be divided into financial internal rate of return (FIRR) and economic internal rate of return (EIRR).
At present, investment methods such as stocks, funds, gold, real estate and futures have been familiar and used by many financial managers. However, many people's understanding of the effectiveness of investment is limited to the absolute amount of income, lacking scientific judgment basis. For them, the internal rate of return indicator is an indispensable tool.