[Soft test] detailed explanation and Application of net present value NPV, instance explanation and collection (Information System Project Manager-Project Management)

Opening remarks:The formula for net present value must be kept in mind. Do not calculate the number of errors during calculation, or note when rounding. Do not make the decimal point incorrect. The formula is very simple and is not easy to calculate, therefore, you must be careful when doing this kind of questions.

The article is simplified, simplified, and profound, coupled with your own understanding. It is inevitable that there are some mistakes. If your colleagues who pass through this article find errors or have better ideas for solving problems, please do not hesitate to give us a further explanation.

Net present value (NPV)): The economic meaning is to reflect the profitability of the project during the calculation period. It indicates the net cash flow that occurs at different time points in the case of the Specified discount rate I0, the net income that can be obtained throughout the life cycle. If the net present value of the scheme is equal to zero, it indicates that the scheme has reached the specified benchmark rate of return. If the net present value of the scheme is greater than zero, it indicates that the scheme can not meet the specified benchmark rate of return, it can also obtain excess profits. If the net present value is smaller than zero, it means that the scheme cannot reach the specified benchmark rate of return.

Therefore, the criterion for evaluating a single scheme using net present value indicators is: If NVP is greater than or equal to 0, the scheme is economical and reasonable; If NVP is less than 0, the scheme should be rejected.

 

The NPV expression is:

(1) Financial Net Present Value: NPV indicates that the y of a certain year in the future is equivalent to the x RMB of this year.

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In the formula: Ci -- cash inflow, Co -- cash outflow, (CI-CO) -- net cash flow for the T year, I -- baseline discount rate, T = 0 at the time of initial investment calculation, cash flow for the first year after investment, T = 1

Fund transfer at different time points

• The final value is calculated based on the present value: fn = P (1 + r) n where F is the end value at the end of N, P is the present value at the beginning of N, r is the annual interest rate, (1 + r) n is the compound interest factor.

• Calculate the present value based on the final value: P = FN/(1 + r) N

• NPV> 0 indicates that after the implementation of the project, in addition to ensuring a predetermined rate of return, higher profits can be obtained.

• NPV <0 indicates that after the project is implemented, the expected rate of return cannot be reached, and the loss of the project cannot be determined.

• NPV = 0 indicates that the ROI after the project is implemented is exactly as expected, rather than the profit/loss balance of the investment project.

For example, if the discount rate is 10%, the discount rate in the first year is (1 + 10%), and the discount coefficient in the second year is (1 + 10%) * (1 + 10%), which is the square of 1.1, and so on. Multiply the annual discount coefficient by the annual return value, and the principal value is the net present value.

 

(2) ROI

After completion and production, the ratio of the net income obtained in the normal year of operation to the total investment of the project.

 

(3) payback period (payback period)

The time for the project to fully recover the initial investment from the production year with the annual net income.

Calculation Formula for static investment payback period (PT:

PT = [cumulative net cash flow beginning to show positive annual views]-1 + [absolute value of cumulative net cash flow in the previous year/net cash flow in the current year]

Formula for Calculating the dynamic payback period (t:

Dynamic payback period (year) = [the current value of cumulative net cash flow begins to show positive values for years]-1 + [the absolute value of the current value of cumulative net cash flow in the previous year/the current value of net cash flow in the current year]

 

Instance 1The profit analysis of project a of a software company is shown in the following table. The discount rate is 10%, and the net profit value in the second year is () yuan.

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A, 231000 B, 200000 C, 220000 D, 210000

Answer and analysis: economic feasibility is a measure of the cost-effectiveness of a project or solution. There are three common technologies available for evaluating economic feasibility, also known as cost-effectiveness: Investment Recovery analysis, ROI and net present value. The formula for calculating the present value is fn = P (1 + r) n, that is, 139000/(1 + 10%) 2.

 

Instance 2Assume that the investment for the first year is 10,000, and the income for each year in the next three years is 3,000, 4,200, and 6,800 respectively. Assume that the annual discount rate is 10%, the net present value of the investment is ().

Answer and analysis:

(3000/1. 1 + 4200/1 .12 + 6800/1 .13)-10000.

Investment1	Revenue2	Revenue3	Revenue4	Net Present Value
-10000	3000	4200	6800	1307.29

 

Instance 3The cash flow of each period of a project is shown in the table:

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If the discount rate is set to 10%, the project's net present value is about ____.

A. 140 B .70 c.34 D.6

Answer and analysis:

C. A year's net cash flow refers to the year's cash flow multiplied by the current year's discount coefficient. Based on the data in the preceding table, the cost-benefit analysis table of the project is as follows.

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Therefore, NPV = (330/1. 1 + 440/1 .21)-630 = 33.63636.

Therefore, the project's net present value is about 0.33619 million yuan. In addition, the dynamic investment payback period of the project = the cumulative net present value of profit starts to show positive values of the Year-1 + the absolute value of the cumulative net present value of the previous year/the net present value of a positive year = 2-1 + |-329.997 |/363.616 = 1.908; the project's investment return rate = 1/1. 908 * 100% = 52.41%.

 

Instance 4In the calculation of the payback period, a software company plans to invest 2004 yuan in developing a set of middleware Products in early 10 million. It is estimated that the annual sales revenue will reach 2005 yuan starting from 15 million, and the annual sales cost will be 10 million yuan. According to the discount rate provided by the chief financial officer, Zhang Gong, a system analyst of the product, produced the following cash flow statement for product sales. Based on the data in the table, the dynamic payback period of the product is (1) year, and the return on investment is (2 ).

(1) A, 1 B, 2 C, 2.27 D, 2.73

(2) A, 42% B, 44% C, 50% D, 100%

Answer and analysis:

Dynamic payback period Pt = (the current value of cumulative net cash flow shows positive years-1) + the absolute value of the current value of cumulative net cash flow in the previous year/the present value of net cash flow in a positive year.

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Simple Calculation shows that the cumulative present value of the third year is greater than 0, and the dynamic investment payback period is = (3-1) + (1-(428.67 + 396.92 + 367.51-925.93)/367.51) = 2.27.

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The return on investment reflects the profitability of an enterprise's investment, which is equal to the reciprocal of the dynamic payback period. Therefore, answer (7) C (8) B.

 

Instance 5The following table shows the planned income of the project to be put into operation. The investment payback period of the project is ____.

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A. 4.30 B .5.73 c.4.73 d.5.30

Answer and analysis: B. The payback period refers to the period of time for the project to return the original investment from the date of project construction. It can also be divided into static and dynamic payback periods. The static investment payback period PT refers to the time required to recover all the investment without considering the Capital Occupation cost (time value. Generally, the static investment payback period is measured by the annual cash flow after the project is built.

If the annual net income (I .e., net cash flow) after the project is completed and put into operation is the same, Pt = K/.

If the net income for each year after the project is completed and put into operation is different, Pt can be obtained based on the accumulated net cash flow, that is, in the cash flow statement, the cumulative net cash flow changes from a negative value to the year between positive values, the following formula is used to solve the problem.

PT = the cumulative net cash flow begins to show positive annual views-1 + the absolute value of the cumulative net cash flow for the previous year/the net cash flow for the current year.

Based on the data in the table above, the PT of the project to be put into production is 6-1 + |-26 |/35.5 = 5.7324. The PT value can be compared with the determined baseline investment payback period (PC). If PT <= pc, it indicates that the project investment can be withdrawn within the specified time, you can consider accepting this investment scheme: If Pt> PC, it indicates that the investment scheme is not feasible.

 

Instance 6A software company plans to invest 2006 RMB in developing a product in Early 20 million. It is expected to make a profit starting from 2007, as shown in the table. Based on the data in the table, the static investment payback period of the product is (1) years, and the dynamic investment payback period is (2) years. (Tip: Set the discount rate to 0.1)

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(1) a.1.8 B .1.9 C.2 d.2.2

(2) A.2 B .2.1 c.2.4 D.3

Answer and analysis: Add "cumulative annual profit" and "cumulative annual profit current value" on the basis of the question stem table. The following table is displayed:

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Assume that 2007 is the current time, the static investment payback period is 1 + 1010/1210 = 1.83, and the dynamic investment payback period is 2 + 100/900 = 2.1. Therefore, the correct option for (69) is, (70) the correct option is B.

 

Instance 7The investment amount of a project is 1.9 million yuan. The profit analysis after implementation is shown in the following table:

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If the discount rate is 0. 1, the ROI of the Project is ____.
A. 0. 34 B .0.41 c.0.58 d.0.67

Answer and analysis:. The discount rate refers to the annual percentage of a certain amount of funds converted into the present value. For example, if the discount rate is 0.1 and the discount rate is 1 for 0th years, the discount rate for 1st years is 1/(1 + 0.1) 1 = 0.9.91, that is, the RMB 100 after one year is only equivalent to the current RMB 90.91. If PV represents the present value, FV represents the next value, I represents the discount rate, and N represents the number of years to pass, there is a formula:

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The net present value of a year refers to the annual profit value multiplied by the current year's discount coefficient. Based on the data of the next unit, the cost-benefit analysis table of the project is as follows.

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Dynamic payback period of the project = cumulative net cash flow beginning to show positive annual copies-1 + absolute value of cumulative net cash flow in the previous year/net cash flow in the same year = 3-1 + |- 38.0425 |, 44.4995 = 2.8549.

The return on investment of a project refers to the percentage of profit equal to the cost after the project is invested for a period of time. It is an indicator that reflects the profitability of the project investment. Its value is the reciprocal of the payback period of the project. For this project, the investment return rate is 1/2. 8549 * 100% = 35.03%.

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[Soft test] detailed explanation and Application of net present value NPV, instance explanation and collection (Information System Project Manager-Project Management)