# Net present value method

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:

1. Compute net present value (NPV) of this investment project.
2. 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:

A D V E R T I S E M E N T

## 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“.

A D V E R T I S E M E N T

## 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: \$95,000

Year 2: \$80,000

Year 3: \$60,000

Year 4: \$55,000

Required: 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:

*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:

### 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:

Proposal X: 212,000/200,000 = 1.06

Proposal Y: 171,800/160,000 = 1.07

Proposal Z: 185,200/180,000 = 1.03

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:

1. 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.
2. The inflow and outflow of cash other than initial investment occur at the end of each period.

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.

Show your love for us by sharing our contents.
A D V E R T I S E M E N T

### 75 Comments on Net present value method

1. Christina

where did you get the \$1000 from on this problem under the 25% factor column?

1. Tewolde

Thanks to u!!!!

1. Abduljelil

Any body to help pls…..A project has a net cash flow of N10,000,000 per annum for the next four years. If the applicable cost of capital for the project is 15%, then the NPV of the project is

2. Dileep

Its not \$1000 but it is 1.000 its point value and multiply with 15000 you will get correct

1. Vanessa

How do we get the 3.859 in example 2

3. NOOR

A state is planning to rehabilitate an asphalt concrete pavement using a 5-cm asphalt concrete
overlay, which is projected to last 12 years. Given that the overlay costs \$20,000 per lane-
km, calculate its annualized costs assuming a discount rate of 4%.
I want solution plz

2. Accounting for Management

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.

1. aanchal

how do we got the values like 3.859 and 1.000?

1. Accounting For Management
2. Michael onunga

It good i understand it but in a case where the initial cash flow is given ( 8000) and cash inflows are given for three yrs 2000, 4000 6000 respectively discounting factor10% and capital budget 20m reffrence atd 2 may 23 2017 kasneb

3. Neema

Example 3. \$1 at 12%. where did get 0.797?

4. AJAY

IN EXAMPLE 3 ….THE RATE OF RETURN IS 12%……..
THEN HOW DID WE GET THE VALUS……LIKE..

0.893
0797
0.712
0.636

You are supposed to use this formula
1/(1+r)^yr number
For eg ;1/(1+0,12)^0 in year 0 to get 1
Then following years u will only change ^1,^2 ….

2. melekot mengistu

Use the following formula
Discount factor =1/((1.12) to the power n), n=1,2,3 ……

3. laprincia

table of annuity ( for example at year 1) look at the present value at year 1 and 12%

4. Moya

1/(1.12)
1/(1.12)^2
1/(1.12)^3
1/(1.12)^4

5. Ms. Esha

You can find these numbers in the Present Value of Annuity Table.
I found mine in my Appendix of my Managerial Accounting course book. Hope this helps you and anyone else with the same question!

5. Accounting For Management

AJAY, See present value of \$1 table for these values.
https://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.

6. Visitor

–Visitor

7. Miguel

The content is very useful.
The way you give the difference scenarios( examples) of how to use the NPV.
Many thanks.

8. basanth babu

How to calculate Net Present Value index if cost of capital is given instead of discount rate?

1. Sneha

The percentage given for the cost of capital is the discount rate

9. Shola

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?

10. gilbert

what will happen with example 1 if there was a salvage value

1. Elena

do you have the answer finally?

2. Accounting For Management
11. CAYLA

How do you determine how many years to calculate to get the NPV? Is it the first year to become a positive number?

12. samson

Given pretax cash inflows for a given duration of time and corporate tax in percentage. How do you get net cash inflow?

13. student

who is the author of this site? need an author to reference in my paper

14. Rhonda

I am with “student” on here where is the author as I would love to cite this in a research essay. Thanks!

15. MKALAVA Benjamin

I HAVE INTERESTED WITH YOUR ECONOMICS MATERIAL, BRING MORE TO MY EMAIL

1. Saheed Benson

Please send Economics Investment Appraisal to my mail.
400Level Economics Students University of Ibadan, Nigeria

16. Tracey

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

17. khalaf amer

Really, all topics presented here are very useful for accountants and the concerned people, thank you.

18. JR 9

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.????

19. Deepika pal

Very helpful thnku .. If capital is given

only how we calculate tha discount rate

20. Mike

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!

1. opeyemi

A firm uses a cost of capital of 12% and plan to invest 7million in a new machine with a life of 4 years. The units to be produced by the new machine will sell at 9.20k and will cost 6 naira each to make it expected that 8000 units will be produced and sold each year. At what level of sales revenue per units will be project NPV be zero ?

21. eugene

Question is (calculate the net present value for 2)
Initial investment is 100000, discout rate is 10% and net cash flow is 20000.

22. ousman

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

23. Ruth mirembe

This has really helped me so much thanks
May u be Blessed .

Best regards
Ruth Mirembe

24. Jim

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?

25. nicole

What do I do if there is a salvage value for the first example?

26. Portia

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)?

27. Nd

how did you get the \$3.326 under 20% factor in example no 1 and the \$7317
Thank you

You use the formula for unuity present value
That is 1-(1+r)^-n all over r
Where r is discount rate
n is number of years
So in this case you will say
1-(1+0,2)^-6 all over 0,2
=3,325510117 and then round it off

28. Tommy

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?

29. Deepti

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))

30. angie

how was the net present value for proposal z gotten please?

1. prabhakar jha

how to calculate the net present value with salvage value?

31. karan

Hey how to rank different projects on the basis of IRR?

32. manikanta

sir i need clarification with problem that will shown the reinvestment of cash flows genereted in the project

33. Angel

Diamond Company is considering purchasing a machine that would cost \$756,000 and have a useful life of 8 years. The machine would reduce cash operating costs by \$132,632 per year. The machine would have a salvage value of \$151,200 at the end of the project
Compute:
a. Net present value
b. Internal rate of return
c. Profitability index
d. Payback period
e. Simple rate of return
f. Should the company purchase the machine? Why or why not?
can anyone help?

34. zama

Can somebody help me with following question:
Project A : Net cash inflows is 120000 (1st yr); 150000 (2nd yr); 160000 (3rd yr);180000 (4th yr);170000 (5th yr), initial cost is 600000, depreciation per year is 110000, machinery scrap value of 50000
Project B: Net cash inflows is 170000 (1st yr); 170000 (2nd yr); 170000 (3rd yr);170000 (4th yr);170000 (5th yr), initial cost is 600000, depreciation per year is 120000. no scrap value
Calculate the:
1. Accounting Rate of Return (on average investment) of Project A
2 Net Present Value of each project
Note: discount rate to be used is 12%

35. PERSEUS

Well explained. BRAVO !!!!!!!!

How to calculate net prasent value of a project if initial investment is not given

37. witness

Thanks alooot.
M done with my assignment with the help of this site.

You use the formula for unuity present value
That is 1-(1+r)^-n all over r
Where r is discount rate
n is number of years
So in this case you will say
1-(1+0,2)^-6 all over 0,2
=3,325510117 and then round it off

39. Floki

How about a situation where you have a one time investment of net working capital of additional amount? How do you calculate npv?

40. Ravinesh

Can someone please solve this as follows;

A company is planning to make an investment of \$100,000 in a Machine. The
company’s analyst had estimated that the useful life of the Machine is 5 years and
that each year (from Year 1 to Year 5), the company will receive a net income of
\$35,000 from this investment. The acceptable cost of capital is assumed to be 10%
p.a. Calculate:
(a) The payback period of this project/investment plan.
(b) The net present value (NPV) of this project/investment plan.
(c) The internal rate of return (IRR) of this project/investment plan.

(d) Analyze the different results from (a)-(c) and make a proposal whether
the company should proceed with this project.
(e) Determine the IRR that will reverse the decision you proposed in (d)

41. melisewfan

What is the internal IRR of an investment which involves a current outlay of \$300,000 and results in an annual cash inflow of \$60,000 for 7 years?

42. kapeua gerha musambani

The following 2 mutually exclusive projects (Project A and Project B) are available to Okahandja Farm Enterprise. They are into poultry farming. The initial cash outlay and cash flows are shown below. Okahandja farm will use straight line depreciation over each of the assets 4 year life and there will be no residual value on either investment.
Year/s Cash flow (A) N\$ Cash flow (B) N\$
0 -240 000 -90 000
1 -280 000 40 000
2 38 000 40 000
3 100 000 30 000
4 200 000 7 000
NB:
a. The company requires a minimum accounting rate of return of 25% on all its investments
b. It regularly applies a payback period of no more than 3.5 years
c. The costs of capital is 12%
2.1. Which project is more lucrative if the discounted payback rule is required (5)
2.2. Apply the Accounting rate of Return (ARR) test. Which project is more viable? (8)
2.3. Determine which project is more lucrative if the NPV rule is applied. (8)
2.4. Which of the above projects would you recommend to Okahandja Farm. Explain in details your choice of answer (by critically assessing each of the above calculations that you have made).

43. Kainat

how can we calculate without given rate?

44. Rhol

A company puts \$25,000 down and will pay \$5,000 every year for the life of a machine, 10years. If the salvage value is zero and the interest rate is 10% compounded annually. What is the present value of the machine?
Help me pls..

45. opeyemi

A company puts \$25,000 down and will pay \$10,000 every year for the life of a machine, 10years. If the salvage value is zero and the interest rate is 15% compounded annually. What is the present value of the machine?
Help me pls

46. Agazi Benard

47. Deborah

I have a land I inherited from my father 5 years ago which encountered leaching, poor moisture retention and poor yields due to poor soil conservation measures, presence of weeds and use of incorrect fertilizers. I wish to adopt new techniques to restore land fertility which includes building terraces, planting bananas and grass and purchasing planting plant materials, which give me an initial cost of Ksh. 3830.
However, I will also incur, cost of production (which is the same to both planting maize with conservation measures or without) and cost maintance of terraces which add up to Ksh 7000 and Ksh 500 respectively. The price of maize is Ksh 14 per kg. Help me find out weather soil conservation is profitable at 12% and 6%

48. Vanessa

How do you calculate npv with scrap value

49. Sai Kumar

Explain NPV reinvestment assumption in detail with example?

50. Shafi3ina WaQudwatina

Thanks so much it’s very usefull explanation Thank a lot

51. Nteh Peace Nkechi

using a numerical example illustrate how to calculate NPV and benefit/cost of project

52. Vuyisa Mahlangu

Hi

On example 1 and 2 , how do you incorporate your salvage value to calculate your final NPV if your provided with the salvage value

53. Festus

I have a question on this same topic but still could not figure it out. I am to calculate NOV, IRR, BCR and Payback period. In the data available, the initial capital was not given. However costs and benefits were given from year 1 to 30. opportunity cost was given in form of a value and not in percentage. Also discount rate was not given. How can this be solved? Thanks for your response.

54. Bentra

Please assist, determine npv of the project given revenues, costs as follows;
Year revenues `000′ costs `000′
1 1900 450
2 1800 400
3 1700 350
4 1600 300
5 1500 250