(1) the net present value and the calculation of the present value index
The net present value is the difference between the inflow of funds and outflow of funds occurring in each year of the life of the project, in accordance with the specified discount rate discounted to the present value of the project at the beginning of the implementation. Because of the existence of the time value of money,; the calculation of the present value of the dispute is to discount the investment into the final value of the comparison with future income, you can use the bank to calculate the final value of the method of calculating the present value (that is, the bank's discount). Derived from its formula: NPV = F / (1 + i) n (which F for the final value, NPV for the present value, i for the discount rate, n for the period). The key to calculating the net present value is to determine the discount rate, in general, the lowest rate of return on investment is the bank interest rate, the bank interest rate is equivalent to the time value of money, but also the minimum opportunity cost of investment, the initial test of the discount rate, it is appropriate to use the then one-year bank deposit rate.
For example: a property company to adapt to the needs of the owners of the jurisdiction to 100,000 yuan to invest in a new service project. In the actual operation of the process, the first year after deducting all kinds of expenses net profit of 0.1 million yuan, the second year after deducting all kinds of expenses net profit of 0.2 million yuan, 2 years later to 110,000 yuan to sell, to find the net present value of the project?
If: the interest rate on a one-year bank deposit is 5%, set as the discount rate, the present value of the sum of the returns in each year is:
0.1 x 1/1 + 0.05 + 0.2 x 1/(1 + 0.05)2. + 11 x 1/(1 + 0.05)2 = $102,536,000.
The net present value is the total present value of earnings minus the present value of investment, and the present value index = total present value of earnings / present value of investment.
NPV, i.e.: 10.2536-10=O.2536 million yuan; present value index, i.e.
10.2536/10=1.025.
We can conclude that:
NPV is greater than 0 and present value index is greater than 1, which means that the project is feasible for investment.
(2) the calculation of the internal rate of return
By the net present value and present value index, you can roughly determine the range of the project's investment rate of return, in order to more accurately understand the rate of return on the realization of the investment, through the combination of the bank interest rate, the investment risk rate and the rate of inflation, profitability comparisons of the same industry and other factors, to determine that the expected rate of return of the investment is 10%, and the investment in the The internal rate of return on investment is calculated and verified.
By linear interpolation formula: IRR = i1 + NPV1 (i2 i1) / NPV1 + ︱ NPV2 ︱
Formula, IRR - internal rate of return: i1 - NPV is close to zero when the discount rate of the positive value; i2 - NPV is close to zero when the negative value of the discount rate; NPV1 a low discount rate i1 when the positive value of the net present value; NPV2 - using a high discount rate i2 negative value of the net present value.
Set 5% for the low discount rate i1, set 8% for the high discount rate i2, the discount rate of 8%, the sum of the present value of each year's earnings in the above investment project is:
0. 1×1/1 + 0 08 + 0.2×1/(1+0.08)2 + 11×1/(1+0.08) 2 = 96,910,000 yuan.
The net present value is: 96.91 - 10 = -0.309 million dollars.
Internal rate of return = 5% + (8% - 5%)(10.2536 - 10)/(10.2536 - 9.691) = 6.35%
If the project's expected rate of return (the base rate of return) is 10%, the realized rate of return is much lower than the expected rate of return, and the investment is not feasible.
More intuitive, clear understanding of the internal rate of return method, is the use of geometric illustration method of calculation: first in the horizontal coordinates of the two discount rate i1 = 5%, i2 = 8%, and then in the two points drawn perpendicular to the horizontal coordinates of the two straight lines, respectively, equal to the corresponding discount rate of the net present value of the net present value of the positive (NPV1), the negative net present value of the net present value of the net present value of the net present value of the net present value of the (NPV2), and then connect the ends of the net present value of the net present value of the net present value of the drawing of a Straight line, this straight line and the horizontal axis of the intersection of the point that the net present value of zero discount rate, that is, the internal rate of return (IRR). As shown:
By the two similar triangles in the figure, can be derived from the mathematical formula for similar triangles:
NPV1 / ︱ NPV2 ︱ = IRR - i1 / i2 - IRR
The denominator on both sides of the equation are added to the numerator of the:
NPV1 / NPV1 ︱ NPV2 ︱ = IRR - i1 / i2 i1
II Internal Rate of Return (IRR), the internal rate of return (IRR). p>
Second, the key points in the calculation of internal rate of return
1. To determine the reasonable low discount rate i1 and high discount rate i2, first set a discount rate, if the net present value is not close to zero positive, we must try a higher or lower discount rate, so that the net present value of the net present value is close to zero positive, so as to determine the low discount rate i1, on the basis of the i1, and continue to increase the discount rate, until we find a close to zero positive. Until we find a negative net present value close to zero, determine the same discount rate i2.
2. In order to ensure the accuracy of the internal rate of return calculation, the difference between the low discount rate i1 and the high discount rate i2 should not be greater than 5%.
3. The use of data such as: bank interest rates, inflation rates, industry profitability, expected rate of return, etc. to be demonstrated through multiple investigations, try to use the latest, accurate data.