Net present value method (also known as discounted cash flow method) is a popular capital budgeting technique that takes into account the time value of money. It uses net present value of the investment project as the base to accept or reject a proposed investment in projects like purchase of new equipment, purchase of inventory, expansion or addition of existing plant assets and the installation of new plants etc.
First, I would explain what is net present value and then how it is used to analyze investment projects.
Net present value (NPV):
Net present value is the difference between the present value of cash inflows and the present value of cash outflows that occur as a result of undertaking an investment project. It may be positive, zero or negative. These three possibilities of net present value are briefly explained below:
Positive NPV:
If present value of cash inflows is greater than the present value of the cash outflows, the net present value is said to be positive and the investment proposal is considered to be acceptable.
Zero NPV:
If present value of cash inflow is equal to present value of cash outflow, the net present value is said to be zero and the investment proposal is considered to be acceptable.
Negative NPV:
If present value of cash inflow is less than present value of cash outflow, the net present value is said to be negative and the investment proposal is rejected.
The summary of the concept explained so far is given below:
The following example illustrates the use of net present value method in analyzing an investment proposal.
Example 1 – cash inflow project:
The management of Fine Electronics Company is considering to purchase an equipment to be attached with the main manufacturing machine. The equipment will cost $6,000 and will increase annual cash inflow by $2,200. The useful life of the equipment is 6 years. After 6 years it will have no salvage value. The management wants a 20% return on all investments.
Required:
- Compute net present value (NPV) of this investment project.
- Should the equipment be purchased according to NPV analysis?
Solution:
(1) Computation of net present value:
*Value from present value of an annuity of $1 in arrears table.
(2) Purchase decision:
Yes, the equipment should be purchased because the net present value is positive ($1,317). Having a positive net present value means the project promises a rate of return that is higher than the minimum rate of return required by management (20% in the above example).
In the above example, the minimum required rate of return is 20%. It means if the equipment is not purchased and the money is invested elsewhere, the company would be able to earn 20% return on its investment. The minimum required rate of return (20% in our example) is used to discount the cash inflow to its present value and is, therefore, also known as discount rate.
Investments in assets are usually made with the intention to generate revenue or reduce costs in future. The reduction in cost is considered equivalent to increase in revenues and should, therefore, be treated as cash inflow in capital budgeting computations.
The net present value method is used not only to evaluate investment projects that generate cash inflow but also to evaluate investment projects that reduce costs. The following example illustrates how this capital budgeting method is used to analyze a cost reduction project:
Example 2 – cost reduction project:
Smart Manufacturing Company is planning to reduce its labor costs by automating a critical task that is currently performed manually. The automation requires the installation of a new machine. The cost to purchase and install a new machine is $15,000. The installation of machine can reduce annual labor cost by $4,200. The life of the machine is 15 years. The salvage value of the machine after fifteen years will be zero. The required rate of return of Smart Manufacturing Company is 25%.
Should Smart Manufacturing Company purchase the machine?
Solution:
According to net present value method, Smart Manufacturing Company should purchase the machine because the present value of the cost savings is greater than the present value of the initial cost to purchase and install the machine. The computations are given below:
*Value from present value of an annuity of $1 in arrears table.
Net present value method – uneven cash flow:
Notice that the projects in the above examples generate equal cash inflow in all the periods (the cost saving in example 2 has been treated as cash inflow). Such a flow of cash is known as even cash flow. But sometimes projects do not generate equal cash inflows in all the periods. When projects generate different cash inflows in different periods, the flow of cash is known as uneven cash flow. To analyze such projects the present value of the inflow of cash is computed for each period separately. It has been illustrated in the following example:
Example 3:
A project requires an initial investment of $225,000 and is expected to generate the following net cash inflows:
Year | 1 | 2 | 3 | 4 |
Cash inflow | $95,000 | $80,000 | $60,000 | $55,000 |
Compute net present value of the project if the minimum desired rate of return is 12%.
Solution:
The cash inflow generated by the project is uneven. Therefore, the present value would be computed for each year separately:
Year | Present value of $1 at 12% | Net cash flow | Present value of cash flow | ||
1 | 0.893* | $ | 95,000 | $ | 84,835 |
2 | 0.797 | 80,000 | 63,760 | ||
3 | 0.712 | 60,000 | 42,720 | ||
4 | 0.636 | 55,000 | 34,980 | ||
——– | |||||
Total | $ | 226,295 | |||
Initial investment required | 225,000 | ||||
——– | |||||
Net present value | $ | 1,295 | |||
——– |
*Value from present value of $1 table.
The project seems attractive because its net present value is positive.
Choosing among several alternative investment proposals:
Sometime a company may have limited funds but several alternative proposals. In such circumstances, if each alternative requires the same amount of investment, the one with the highest net present value is preferred. But if each proposal requires a different amount of investment, then proposals are ranked using an index called present value index (or profitability index). The proposal with the highest present value index is considered the best. Present value index is computed using the following formula:
Formula of present value or profitability index:
Example 4:
Choose the most desirable investment proposal from the following alternatives using profitability index method:
Proposal X | Proposal Y | Proposal Z | |
Present value of net cash flow | $212,000 | $171,800 | $185,200 |
Amount required to invest | 200,000 | 160,000 | 180,000 |
———– | ———– | ———– | |
Net present value | 12,000 | 11,800 | 5,200 |
———– | ———– | ———– |
Solution:
Because each investment proposal requires a different amount of investment, the most desirable investment can be found using present value index. Present value index of all three proposals is computed below:
Present Value Index | ||
——————————————————— | ||
Proposal X | 1.06 | (212,000/200,000) |
Proposal Y | 1.07 | (171,800/160,000) |
Proposal Z | 1.03 | (185,200/180,000) |
Proposal X has the highest net present value but is not the most desirable investment. The present value indexes show proposal Y as the most desirable investment because it promises to generate 1.07 present value for each dollar invested, which is the highest among three alternatives.
Assumptions:
The net present value method is based on two assumptions. These are:
- The cash generated by a project is immediately reinvested to generate a return at a rate that is equal to the discount rate used in present value analysis.
- The inflow and outflow of cash other than initial investment occur at the end of each period.
Advantages and Disadvantages:
The basic advantage of net present value method is that it considers the time value of money. The disadvantage is that it is more complex than other methods that do not consider present value of cash flows. Furthermore, it assumes immediate reinvestment of the cash generated by investment projects. This assumption may not always be reasonable due to changing economic conditions.
August 7th, 2013 at 4:50 am
where did you get the $1000 from on this problem under the 25% factor column?
August 7th, 2013 at 4:59 am
Christina! It is 1.000 not $1000. 25% dicount factor is 3.859 for 1 – 15 years and 1.000 for Zero years i.e., now.
August 23rd, 2013 at 10:57 am
Example 3. $1 at 12%. where did get 0.797?
November 14th, 2013 at 7:38 am
IN EXAMPLE 3 ….THE RATE OF RETURN IS 12%……..
THEN HOW DID WE GET THE VALUS……LIKE..
0.893
0797
0.712
0.636
November 25th, 2013 at 5:38 am
AJAY, See present value of $1 table for these values.
http://www.accountingformanagement.org/present-value-of-1-table/
For 0.893; use 1 period row and 12% interest rate column;
For 0.797; use 2 period row and 12% interest rate column;
For 0.712; use 3 period row and 12% interest rate column;
For 0.636; use 4 period row and 12% interest rate column;
Hope this helps.
January 14th, 2014 at 12:09 pm
Very Helpful, thanks!
–Visitor
January 29th, 2014 at 8:37 am
The content is very useful.
The way you give the difference scenarios( examples) of how to use the NPV.
Many thanks.
April 22nd, 2014 at 6:45 am
How to calculate Net Present Value index if cost of capital is given instead of discount rate?
August 4th, 2014 at 8:19 pm
If expected profit is given and the note stated that profit is calculated after deducting depreciation, how should I treat this in the question please?
October 8th, 2014 at 9:01 pm
what will happen with example 1 if there was a salvage value
October 17th, 2014 at 5:03 pm
How do you determine how many years to calculate to get the NPV? Is it the first year to become a positive number?
December 18th, 2014 at 3:14 pm
Given pretax cash inflows for a given duration of time and corporate tax in percentage. How do you get net cash inflow?
January 28th, 2015 at 7:21 pm
who is the author of this site? need an author to reference in my paper
February 12th, 2015 at 8:40 pm
I am with “student” on here where is the author as I would love to cite this in a research essay. Thanks!
February 15th, 2015 at 12:55 pm
I HAVE INTERESTED WITH YOUR ECONOMICS MATERIAL, BRING MORE TO MY EMAIL
February 24th, 2015 at 7:32 pm
Rhonda and Student, google how to reference an article or webpage/link. There isn’t always an author to this type of site.
Good Luck
March 16th, 2015 at 10:16 am
Really, all topics presented here are very useful for accountants and the concerned people, thank you.
March 25th, 2015 at 12:39 pm
Can you further explain the disadvantage
it assumes immediate reinvestment of the cash generated by investment projects. this assumption may not always be reasonable due to changing economic conditions.????
April 2nd, 2015 at 4:25 pm
Very helpful thnku .. If capital is given
only how we calculate tha discount rate
August 12th, 2015 at 8:03 pm
At the beginning of, and during a development project I periodically update the Net Present Value (NPV). I use the NPV to compare returns among other projects. The NPV is for a full project. What is the advantage/disadvantage of also calculating the NPV going forward from a particular period, and ignoring the past costs. So rather than comparing full project to full project, this comparison compares the return to finish the project from the period of calculation. Assuming the returns stay the same and the ‘costs to finish’ are less-and-less, the NPV will get better-and-better. Is this a good/rational/acceptable way to assess an investment among all other investments?
I really appreciate your view on this question. Thanks!
September 7th, 2015 at 8:51 am
Question is (calculate the net present value for 2)
Initial investment is 100000, discout rate is 10% and net cash flow is 20000.
October 24th, 2015 at 11:49 pm
Please I have given this question but I did not know how to solve it. I have the initial investment 1000 and the cost of capital 9 percentage and then year one was this figure .917 and year two is .842
And then year three .772 And year four .708 and year five .650 and year sixes .596
What should I do I need your help on this please because they suppose give the cash follow for all the but they gave me the discounted factors for all the years it seems for me like that
October 30th, 2015 at 7:27 am
This has really helped me so much thanks
May u be Blessed .
Best regards
Ruth Mirembe
November 8th, 2015 at 5:27 pm
Cheers for this useful article although, what is the purpose of the % factor that you have included in every table and how was it calculated?
November 30th, 2015 at 7:52 pm
What do I do if there is a salvage value for the first example?
March 12th, 2016 at 2:56 pm
Thanks your examples are helpful. But what do I do if I have initial investment costs as well as fixed cost and operating cost (excluding depreciation)?
April 10th, 2016 at 2:00 pm
how did you get the $3.326 under 20% factor in example no 1 and the $7317
Thank you
April 21st, 2016 at 7:24 pm
So if I had an investment of $3,000,000 for a useful life of 5 years with a company discount rate of 15% and a minimum ROI of 20% and a net income of 300,000 per year, what would the NPV be?
May 31st, 2016 at 3:12 pm
hii there plz help me …if in the question it’s written cost to remove equipment is $2000 n cost of equipment is 60000 n inflows are 80000. Then how much would be the net present value ???
Is it 20000 (80000-60000) (inflows -outflows) or
22000 (80000-58000) (inflows- (outflows- cost to remove equipment))
June 8th, 2016 at 3:21 pm
how was the net present value for proposal z gotten please?
June 15th, 2016 at 12:26 pm
1. A large manufacturing firm wants to know if building a new plant in order to manufacture more goods will be feasible for both the company and the firm. The construction of the new plant is estimated to cost around $600,000. If the plant is built it is expected that the company will generate $170,000 each year over 5 years by which time they plan to sell the plant for around $200,000. Shareholders required rate of return is 12%. Determine;
a. NPV of the project (3 marks)
b. Profitability index of the project
c. Should the project be undertaken?
July 20th, 2016 at 10:08 pm
Hi ,
Can you break it down how to get the 1.000 I don’t understand it.
August 24th, 2016 at 9:21 am
Hi there. I require some assistance.
Machine X is expected to cost $30000 and has a useful life of 6 years. Annual net cash inflows from this machine is forecasted to be $8800 per year. The machine is expected to have a salvage value of $3000 (excluded in above amount)at the end of its useful life. The cost of capital is 12%.
Do you add the scrap value before or after the Total PV.
Annual Cash flow 8800
Discount Factor x 4.1114
Total PV 36180.32
Scrap Value 3000x.5066 1519.80
Investment -30000
NPV 7700.12
October 15th, 2016 at 7:23 pm
Expected net cash flows (including residual values)
Initial investment Year 1 Year 2 Year 3
Project £ £ £ £
A -310,000 96,000 113,000 210,000
B -115,000 45,000 42,000 47,000
C -36,000 -41,000 -23,000 127,000
October 30th, 2016 at 4:29 pm
writing exam tomorrow need urgent assistance:
you have the opportunity to invest in an income generating asset (machine) for an initial investment of $70000. It is expected that the annual return will be $15000 for the first five years and due to normal wear and tear, only $10000 for the next five years. Machine can then be sold for $5000 to a scrap dear. the cost of capital s 15%
Please help
January 22nd, 2017 at 11:07 pm
Can any one help me how to calculate the following question
A paper mill produces large volumes of waste water contaminated with suspended solid material, organic pollutants and metals, including arsenic. Before the water can be discharged to a river it is treated to reduce the pollution load. The treatment process produces a solid waste that is sent to landfill. The discharged effluent must be sampled and tested daily to ensure that it complies with the conditions of the discharge consent issued by the water company. The mill’s environmental manager is concerned that possible future water shortages could lead to restrictions on the amount of water that the mill can use. She is also aware that regulatory pressures may result in a need to reduce arsenic discharges from the mill. She has proposed spending £380 000 on the installation of an additional effluent treatment system that will reduce the overall operating cost of treatment and discharge. In addition, a number of process modifications will be introduced to reduce water consumption. It is estimated that the following changes in costs will result:
Saving (£/year)
Effluent treatment chemicals
18 500
Solid waste collection and disposal
3 000
Treatment plant maintenance
5 000
Discharge permit costs
10 300
Water consumption
20 000
Sampling and analytical costs
30 000
Determine the net present value of the project over a five-year timescale. State and justify any assumptions you make including your choice of discount rate. Provide a clear recommendation for whether the project should proceed
February 4th, 2017 at 4:13 pm
Can any one help me how to illustrate the following question and which appropriate equations used
Blackwell Ltd., a steel manufacturer is considering the selection of one from two mutually exclusive investment projects, each with an estimated five-year life. Project A costs$1,616,000 and is predicted to generate annual cash flow of $500,000. Its estimated residual value after five years is $301,000. Project B, costing $556,000 and with a scrap value of $56,000, should generate annual cash flow of $200,000. The company operates a straight-line depreciation policy and discounts cash flows at 15 per cent per annum
February 4th, 2017 at 4:14 pm
how i can use scrap value in project B
March 4th, 2017 at 1:42 pm
thnx, very helpfull
March 13th, 2017 at 4:50 pm
how to solve with no other info:
Expected Cash Flow
Now ($100,000)
End of Year – 1 50,000
End of Year – 2 50,000
End of Year – 3 50,000