**What is Net Present Value definition and the NPV ( Net Present Value ) Formula** –

*Net Present Value*or often abbreviated as NPV is the deviation between the present value of incoming cash flows and the present value of cash flows out of a certain period of time.

This NPV or *Net Present Value* estimates the present value of a project, asset, or investment based on expected future cash inflows and cash outflows adjusted to interest rates and the initial purchase price.

Net Present Value uses the initial purchase price and the time value of money to calculate the value of an asset. Thus, it can be said that the NPV is the Present Value of the Assets less than the initial purchase price.

Please to also read What is Time Value of Money Definition and How to Calculate It.

NPV or *Net Present Value* is widely used in capital budgeting to analyze the profitability of a project or investment projections. The owners of capital or company management can use this NPV calculation to evaluate whether or not to invest in a new project or investment in the purchase of new assets.

## Definition of Net Present Value (NPV) according to Experts

The following are some definitions of NPV according to experts:

Understanding NPV (Net Present Value) according to **Dian Wijayanto** in the book Introduction to Management (2012: 246), *Net Present Value (NPV) is a combination of the present value of income and the present value of expenditure.*

Understanding NPV (Net Present Value) according to **Dr. Sobarsa Kosasih** in the book Operations Management (2009: 99), *NPV is the Excess Present Value (PV) of cash inflow generated by a project for a number of initial investments.*

Understanding NPV (Net Present Value) according to **R. Agus Sartono (2010: 195)**, *Net Present Value is the difference between the present value of net cash flow or often referred to as proceeding with the present value of the investment.*

The definition of NPV (Net Present Value) according to **Syafaruddin Alwi (2001,163)**, *Net Present Value is a model that takes into account the overall cash flow pattern of an investment, in relation to time, based on a certain discount rate.*

## How to Calculate Net Present Value (NPV)

Net Present Value is a formula used to determine the present value of an investment with the discounted amount of all cash flows received from the project. The following is the NPV formula and also a case example of NPV.

### NPV (Net Present Value) formula

The NPV formula is quite complicated because it adds up all future cash flows from an investment, discounts those cash flows at the discount rate, and subtracts them from the initial investment. The net present value (NPV) equation and formula can be seen below:

**NPV = (C1/1+r) + (C2/(1+r) ^{2}) + (C3/(1+r)^{3}) + … + (Ct/(1+r)^{t}) – C0**

*or*

**Where :**

- NPV = Net Present Value (in Dollar)
- Ct = Cash Flow per Year in Period t
- C0 = Initial Investment Value in year 0 (in Dollar)
- r = Interest Rate or Discount Rate (in%)

In addition to the NPV formula above, we can also use the PVIFA (Present Value Interest Factor for an Annuity) table then enter the results into the NPV equation or formula below:

NPV = (Ct x PVIFA_{(r) (t)}) – C_{0}

The FVIFA table can be seen in the image below:

### Example of NPV Calculation Case (Net Present Value)

Management BBBB Company wants to buy production machines to increase the amount of its product. The price of the new production machine is $. 150 Million with a loan interest rate of 12% per year. The estimated cash flow is around $. 50 Million per year for 5 years. Can the investment plan for purchasing this production machine be continued?

**The solution:**

**Known :**

- Ct = $. 50 Million.
- C0 = $. 150 Million.
- r = 12% (0.12)

**Answer:**

- NPV = (C1 / 1 + r) + (C2 / (1 + r)
^{2}) + (C3 / (1 + r)^{3}) + (C3 / (1 + r) 4 ) + (Ct / (1 + r )^{t}) – C0 - NPV = ((50/1 + 0.12) + (50/1 + 0.12) 2 + (50/1 + 0.12) 3 + (50/1 + 0.12) 4 + (50/1 + 0,12) 5) – 150
- NPV = (44,64 + 39,86 + 35,59 + 31,78 + 28,37) – 150
- NPV = 180,24 – 150
- NPV = 30, 24

So the NPV value is **Rp. 30.24 Million.**

### Using the PVIFA Table

As said before, the NPV can also be calculated using the PVIFA table. If we have this PVIFA table, NPV calculations will be easier and faster.

Based on the PVIFA table, the figure obtained from an interest rate of 12% (r) and a period of 5 years (t) is 3.6048. This figure is entered into the NPV formula below:

- NPV = (Ct x PVIFA
_{(r)(t)}) – C_{0} - NPV = (50 x PVIFA
_{(12%)(5)}) – C_{0} - NPV = (50 x 3,6048) – 150
- NPV = 180,24 – 150
- NPV = 30,24

The result is also the same as the NPV value obtained from the first NPV formula, namely se30.24 or **Rp. 30.24 million**.

## Net Present Value (NPV) Analysis and Assessment

From the results of the calculation of our sample problem above, the net present value or the Net Present Value (NPV) is positive with a value of $. 30.24 million. This means that the Production Machine concerned can produce around $. 30.24 million after paying off the machine purchase costs and interest costs.

In accordance with these calculations, it can be decided that the investment plan to purchase new production machines can be continued.

A positive NPV value (NPV> 0) indicates that the income is greater than the value invested while a negative NPV value (NPV <0) indicates that the income is smaller than the expenditure or will experience a loss on the investment after considering the Time Value of Money).

However, if the NPV calculation result is Zero (NPV = 0), it means that the investment or purchase is only a return on investment (no gain and no loss).

And of course, the bigger the positive number, the greater the acceptance it can get. Therefore, this NPV calculation is not only used to evaluate whether or not it is feasible to invest, but it is also used to compare which investment is better if there are two or more investment options.

It should also be noted that although this NPV calculation is an excellent tool for making investment decisions, but it is not always accurate.

This is because the equations rely on many estimates and assumptions which are very difficult to be completely accurate.

As in the example above, the BBBB company management does not know for sure whether the machine will produce $. 50 million per year (because it is only an estimation or assumption) and it is also possible that the interest rate will change along with market developments unless there is a definite agreement with the creditor.

The only thing that the management of the company knows about is the current cost of buying the production machine.