# Net Present Value Definition

**Net Present Value (NPV)** is defined as the present value of the future net cash flows from an investment project. NPV is one of the main ways to evaluate an investment. The net present value method is one of the most used techniques; therefore, it is a common term in the mind of any experienced business person.

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## Net Present Value Method Explanation

Net present value can be explained quite simply, though the process of applying NPV may be considerably more difficult. Net present value analysis eliminates the time element in comparing alternative investments. Furthermore, the NPV method usually provides better decisions than other methods when making capital investments. Consequently, it is the more popular evaluation method of capital budgeting projects.

When choosing between competing investments using the net present value calculation you should select the one with the highest present value.

If:

NPV > 0, accept the investment.

NPV < 0, reject the investment.

NPV = 0, the investment is marginal

### Net Present Value Discount Rate

The most critical decision variable in applying the net present value method is the selection of an appropriate discount rate. Typically you should use either the weighted average cost of capital for the company or the rate of return on alternative investments. As a rule the higher the discount rate the lower the net present value with everything else being equal. In addition, you should apply a risk element in establishing the discount rate. Riskier investments should have a higher discount rate than a safe investment. Longer investments should use a higher discount rate than short time projects. Similar to the rates on the yield curve for treasury bills.

Other **net present value discount rate** factors include: Should you use before tax or after tax discount rates? AS a general rule if you are using before tax net cash flows then use before tax discount rates. After tax net cash flow should use after tax discount rate.

### Net Present Value Formula

The **Net Present Value Formula** for a single investment is: NPV = PV less I

Where:

PV = Present Value

I = Investment

NPV = Net Present Value

The Net Present Value Formula for multiple investments is:

The sum of all terms of:

CF (Cash flow)/ (1 + r)^{t}

Where:

CF = A one-time cash flow

r = the Discount Rate

t = the time of the cash flow

### Net Present Value Calculation

For a **single investment**:

$120,000 – $5,000 = $115,000

Where:

PV = $120,000

I = $5,000

NPV = $115,000

For **multiple investments**:

$120,000 / (1 + 10%)^{1} = $109,091

Where:

CF = $120,000

r = 10%

t = Year 1

NPV = $109,091

### Net Present Value Advantages

**Net present value benefits** include the following:

- Uses cash flow not earnings
- Eliminates time component
- Results in investment decisions that add value

### Net Present Value Limitations

**Net present value disadvantages** include the following:

- Difficult to predict cash flows
- Assumes a constant discount rate over life of investment

### Net Present Value Example

For example, Jody is the owner of a debt collections firm called Collectco. Jody has been working on his company for several years. As the years have piled up on Jody, so has the urge to retire and live a simpler life. Finally reaching the end of his rope, Jody is ready to move on and spend more time with his children. In order to do this, Jody must sell his company. Adding to this, Jody must first make sure his company is up to date with industry standards. If Jody’s company is not performing to the same efficiency as the industry standard, then he will loose some of it’s value in negotiations with a buyer.

Jody begins by hiring an expert consultant in the industry to conduct an audit on the company. The audit turned out to be much better than Jody expected. But despite this, Jody must update his collections software as it is no longer supported by technical assistance from the creator. Jody performs the net present value calculation to evaluate this investment.

$120,000 – $5,000 = $115,000

Where:

PV = The yearly income of Collectco = $120,000

I = The cost of the new collections software = $5,000

NPV = $115,000

Now, Jody can begin the process of finding a buyer for his company. His consultant, an expert in the business dealings of collections firms, tells him that it is in his best interest to know the Net Present Value of his company before he begins negotiations. So, Jody starts this process by attempting to find the easiest way to perform this calculation. After finding few relevant online results for the search “net present value calculator”, Jody happens to find the NPV formula. Jody then performs the following calculation:

$120,000 / (1 + 10%)^{1} = $109,091

Where:

CF = Collectco yearly cash flow = $120,000

r = 10%

t = Year 1

NPV = $109,091

With this investment and information, Jody can begin to achieve what he has always dreamed of: a comfortable retirement which allows him to spend time with the people he cares about most. Jody is pleased because all of his efforts are resulting in the life he has worked to gain.

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#### Net Present Value Template

An excellent net present value template can be found at the Microsoft Office site here: http://office.microsoft.com/en-us/templates/TC100152681033.aspx

See also:

Valuation Methods

Adjusted Present Value Method

Internal Rate of Return Method

Time Value of Money

Capital Budgeting Methods

Rule of 72

how do you calculate npv and payback period given depreciation amount eg 80000 each year for 5 years

Project A Project B

initial investment 40000

expected useful life 5 years

salvage value 0

depreciation 80000

year 1 40000

year2 10000

year3 20000

year 4 120000

year 5 140000

12%

Depreciation of 80 000 for each of 5 years = 80 000/5 = Annual depreciation of 16,000 (straight line deprec.)

Need to minus 16 000 depreciation from each cash flow

NPV @ 12% = 24 000/(1.12) + (-6 000/(1.12)^2 + 4 000/(1.12)^3 + 104 000/(1.12)^4 + 124 000/(1.12)^5 – 40 000

= 21 428.57 -4 783.16 + 2 847.12 + 66 093.88+ 70 360.93 – 40 000

= 155 947.34 – 40 000

NPV = 115 947.34

Payback period

Year

0 1 2 3 4 5

Cash flow (40 000) 40 000 10 000 20 000 120 000 140 000

Cumulated cash flows (40 000) 0 10 000 30 000 150 000 290 000

Payback period = 1 year

Depreciation of 80 000 for each of 5 years = 80 000/5 = Annual depreciation of 16,000 (straight line deprec.)

Need to minus 16 000 depreciation from each cash flow

NPV @ 12% = 24 000/(1.12) + (-6 000/(1.12)^2 + 4 000/(1.12)^3 + 104 000/(1.12)^4 + 124 000/(1.12)^5 – 40 000

= 21 428.57 -4 783.16 + 2 847.12 + 66 093.88+ 70 360.93 – 40 000

= 155 947.34 – 40 000

NPV = 115 947.34

Payback period

Year

0 1 2 3 4 5

Cash flow (40 000) 40 000 10 000 20 000 120 000 140 000

Cumulated cash flows (40 000) 0 10 000 30 000 150 000 290 000

Payback period = 1 year