How to calculate net present value (NPV) – an introduction

Corporate finance

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I’ve been meaning to write a bit about NPV after having discussed and using NPV to calculate the valuation of this site. Since I haven’t written about corpoate finance in a while, I thought this might be a good change of pace.

When we calculate DCFs, what we’re essentially trying to do is calculate the value of all the future cash flows at a given point in time, most often at the present moment. As discussed earlier, to do this, you need to know or forecast future cash flows in each period as well as have a in mind that reflects the riskiness of the project or events leading to the cash flows.

One way to determine whether a project is worth accepting or not is to look at its net present value (NPV). At a high level, NPVs are very much like DCFs. NPVs involve comparing the present value of cash inflows with cash outflows, and calculating each one can get complicated depending on how a company is set up (leveraged or unleveraged) because deciding what to include or exclude and their interactions with tax can get hairy. So, to simplify this discussion on IRR, I’ll use Experiments in Finance’s NPV calculations to demonstrate.

As you can see from the upper left-hand graph, I’ve been plotting the “cash flows” from this site each quarter in order to determine whether running this site is a worthwhile “project” from an NPV standpoint. (You can read through each month’s valuation updates if you’re curious.) The only trick here is that whereas you normally project future cash flows and discount them back to the present to determine a project’s value, I’m running a what-if experiment by putting in each month’s cash flows and discounting them back to the date I started this site (in the past).

I also decided to define the cash flows in my NPV calculation as simply the revenues from this site (in the form of payments from ads) less my monthly expense for hosting costs. Note that I conveniently ignored labor costs, because, as you should be able to guess without doing an NPV, this site is really not worth doing once I calculate the time I’m putting into writing here! (This isn’t always the case, as some people run a perfectly good business doing this…take a look at Darren for example.)

As a general rule, and assuming that the assumptions in your calculations are reasonable, you want to accept projects whose NPVs are positive and reject those that are negative.

Here’s how I calculate the NPV of this site each month using Excel:

1) Calculate free cash flows (FCFs):

I started this site in January, with paltry earnings from ads and $15.01 to purchase my domain name ($15) and hosting costs for that month. (Hostgator had a special for $0.01). Hence, as is normal in any project or business, you can see that I had negative cash flows for the first few months. My normal expenses each month just comprise my hosting costs, but in April I made a donation to pfblogs.org, so I decided to include that in as an expense.

To me, in corporate finance the biggest challenge in setting up a good NPV is getting the cash flows correct, especially when ensuring that all possible project expenses and revenues are taken into account and timed correctly. The calculation itself is easy; it’s the accurate information-gathering that’s always the hardest part!

2) Determine your discount rate or cost of capital

I chose 5% as my discount rate in this valuation. I decided on this figure because I consider the amounts involved in running this site small and not very risky and more akin to putting the money in a savings account rather than anything else. After all, if the project fails, I quit running the site, and that’s that. The ads I run are done through pretty established companies that will pay when they’re supposed to. And I can’t very well invest the small amount I’m putting in each month nor the amounts I’m getting back in other places (like the stock market), so my opportunity cost is also minimal. Note that 5% is the annual rate, and I in order to calculate the NPV correctly. Using my , the monthly equivalent of 5% is around 0.407% or so.

3) Use Excel’s NPV function to calculate your net present value.

The NPV function is pretty simple to use. Just type:

=NPV(rate, free cash flow1, free cash flow 2, … free cash flow n)

to run the calculation. In my case, I’ve got my correctly adjusted rate in cell B3 and cash flows from cells C10 to I10, so the equation looks like:
=NPV(B3, C10:I10)

Through the month of July, my NPV is $89.93, so it’s an acceptable project to undertake, as long as we don’t consider labor costs. (Taking labor costs into account at even $10 per hour * 10 hours a week * 4 weeks a month, which is an underestimation, I think, NPV stands at a whopping -$2,766.85 for this site!)

NPV’s limitations

Just like DCFs and any sort of valuation method, NPVs have their limitations. For one, they’re pretty inflexible. If you have decisions and options midway through the project, their values aren’t considered in NPV calculations, and in these cases, real options might be a better valuation method.

Also, whether a project’s NPV is positive or negative is irrelevant if the inputs into the calculation are out of whack. If you’re a project’s supporter, try to avoid the tendency to overestimate the amounts and timing of revenues or cash inflows or underestimate their counterpart outflows. Finally, both DCFs and NPVs are highly sensitive to terminal values. For example, if you have an project with an infinite life (or are running a valuation on a company), the last cash flow in your calculation essentially represents not only the cash flow for that period but also all the future cash flows past that point. If you overestimate this amount (or the implied growth rate that that amount represents), then you can easily come up with a very positive NPV.

In fact, this is probably one of the biggest criticisms of the NPV and DCF analyses done by sell-side analysts in investment banking. If you ever get a chance to look at such estimations, you might notice that oftentimes the implied steady-state growth rate is even greater than GDP. If that were the case, then the company would eventually take over the entire world!

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132 Feedbacks on "How to calculate net present value (NPV) – an introduction"

Marialukas

Internal rate of return is the rate of return used to measure the profitability of investments in the projects. Thanks for providing the cost details for the feasibility study of the project. As said by other this information will be very useful for the students who do projects on financial concepts.



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A project to build a new sports complex involves a capital outlay of £24 000.000 profits before depreciation each year would be £50.000 for six years. The cost of the capital is 12%. Is the project worthwhile? use an discounted cash flow technique



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Andy Novian Ragiltya

Help!! Can you solve this problem?

A new machine requires an investment of A500,000 and will generate profits of A100,000 for 10 years.
Will the investment have a positive net present value assuming that a realistic interest is 6 per cent?

A local government housing office is considering investing in a new computer system for managing the
maintenance of its properties. The system is forecast to generate savings of around £100,000 per year and
will cost £400,000. It is expected to have a life of 7 years. The local authority expects its departments to use a
discount rate of 0.3 to calculate the financial return on its investments. Is this investment financially worthwhile?

In the example above, the local government’s finance officers have realized that their discount rate has been
historically too low. They now believe that the discount rate should be doubled. Is the investment in the new
computer system still worthwhile?

A new optical reader for scanning documents is being considered by a retail bank. The new system has a fixed
cost of A30,000 per year and a variable cost of A2.5 per batch. The cost of the new scanner is A100,000. The
bank charges A10 per batch for scanning documents and it believes that the demand for its scanning services
will be 2,000 batches in year 1, 5,000 batches in year 2, 10,000 batches in year 3, and then 12,000 batches per
year from year 4 onwards. If the realistic discount rate for the bank is 6 per cent, calculate the net present value
of the investment over a 5-year period.



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hi please help me by solving my problems

year CF
0 -2600
1 4000
2 5000
3 6000
4 1000
calculate internal rate of return?
please tell how to decide what rate should be used to discount cash flow in these type of questions?



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rose

please help solve this
You are a risk-averse investor considering an investment that requires an initial outlay of �50,000. You have calculated the present values of the future distribution of gains and losses, their associated probabilities, as well as their equivalent utilities based upon a personal utility function that conforms to Figure 2.5. The summarised data is as follows:

Cost Discounted gains and losses
�000s (50) 200 100 50 (10) (15)
Probability 1.0 0.1 0.3 0.4 0.1 0.1
Utility 0.65 1.67 1.00 0.65 (0.75) (1.52)

Using the concept of expected monetary value (EMV), would you accept the investment based upon its E(NPV)?

How does your answer compare with a decision using the present value of the cash flows of your expected utilities drawn from Figure?

and finally
Do you think mean variance analysis would alter your final choice? You need not calculate the standard deviation. Just write down a brief explanation of what it has to offer.

Thanks
Confused Financial advisor trainee



peter

Technotronic Ltd currently requires payment from customers by the month end after the month of delivery (45 days). On average, it takes them 87 days to pay. Sales amount to �2 million per year and bad debts to �40,000 per year. It is planned to offer customers a cash discount of 2% for payment within 30 days. Technotronic estimate that 50% of customers will accept this facility but the remainder will not pay until 80 days after the sale. At present, the company has an overdraft facility costing 10% per annum. If the plan goes ahead bad debts will fall to �20,000 per annum and there will be savings in credit administration of �10,000 per annum.

Should Technotronic offer the new terms to customers?



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Hi, Can you help me with this question?

A five-year financial project is expected to have cash inflow of 10,000, 25,000, 45,000, 20,000, and 50,000 in the next five years. It will cost $15,000 at the beginning of year one, $10,000 at the end of year one, and $5000 at the end of year two to buy the necessary equipment for the project. We found that the project cleared the barrier of a 5 percent hurdle rate for acceptance while the expected annual inflation rate is 2 percent. What is the NPVof the project? (Assume all the cash inflow occurs at the end of each year.)



Dayasarki

Plea can u help me out
A company wants to install a plant costing RS 1000000 in jan2015.A plant is expected additional sales of its product .The forecasted sales and the operating cost of the machine is 6yrs .After which it can be sold as scrap for rs 40000!depreciation is on straight line basis .The cost of capital is 10% and the tax rate are expected to remain at 30% .The company has deffered tax liability worth RS 1000000 for which 6% interest is to be payable annually ?Working capital to be introduced in the beginning of the project RS 80000 .The machine will require a replacement of part at the end of the 3rd year and an amount RS 50000 has to be invested .The statement of expected sales and cost are given for different years

Year. Sales(in lakhs). Operating cost

2015. . 9. 450000
2016. 10. 450000
2017. 12. 500000
2018 14. 500000
2019. 15. 600000
2020 15.6. 600000
Find the N.P.V of the project and make your recommit ion regarding its exceptances.
What is the I.R.R of the project.



manisha lakum

Hi, Can you help me to solve this question?

A five-year financial project is expected to have cash inflow of 10,000, 25,000, 45,000, 20,000, and 50,000 in the next five years. It will cost $15,000 at the beginning of year one, $10,000 at the end of year one, and $5000 at the end of year two to buy the necessary equipment for the project. We found that the project cleared the barrier of a 5 percent hurdle rate for acceptance while the expected annual inflation rate is 2 percent. What is the NPVof the project? (Assume all the cash inflow occurs at the end of each year.)



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Please help me with this ques!!! please

The Kretovich Company is trying to evaluate a capital budgeting project based in Thailand. It has recently completed a $200,000, two-year study on its latest project. It estimated that 20,000 of its new geothermal heat pump could be sold annually over the next ten years at a price of $8,521 each. Subcontractors would install the pump at a cost of $6,200 per installation. Fixed costs of $10 million per annum will be incurred.
The initial outlay includes $50 million to build production facilities and $2.4 million in land. The facility will be depreciated using the prime cost method over the project’s life (fully depreciated at the end of the project). At the conclusion of the project the facilities (including the land) will be sold for an estimated value of $10 million. The land value is expected to increase by 1 per cent annually over the project period.
The firm is an ongoing profitable business and pays taxes at a 30% rate in the year of income. It uses a 12% discount rate on the new project. Using the NPV approach, advise the firm whether the project should be undertaken.



Zayn browne

Hi, could I please get help answering this?:
Technotronic Ltd currently requires payment from customers by the month end after the month of delivery (45 days). On average, it takes them 87 days to pay. Sales amount to �2 million per year and bad debts to �40,000 per year. It is planned to offer customers a cash discount of 2% for payment within 30 days. Technotronic estimate that 50% of customers will accept this facility but the remainder will not pay until 80 days after the sale. At present, the company has an overdraft facility costing 10% per annum. If the plan goes ahead bad debts will fall to �20,000 per annum and there will be savings in credit administration of �10,000 per annum.
Should Technotronic offer the new terms to customers?



Jac

Hello,

I’m just entering into the University for the business, anyone can help to give some clues on this question?

A firm has undertaken a feasibility study to evaluate a project that has the following estimated cashflows:

o Increased sales to business of $140,000 for the next 5 years (starting in one year’s time)

o Increased costs of $20,000 for the next two years (starting in one year’s time)

o The initial capital expenditure required is $100,000.

o The study cost $10,000 to conduct.

-Amount borrowed to fund project is $200,000 with interest of 8% pa paid yearly.

If the firm is facing a discount rate of 10%, what is the NPV of this project?

Many thanks for your kind assistance.



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