Tuesday 8 January 2019

Net Present Value (NPV) Formula

A Net Present Value or NPV is often abbreviated with the difference between the present value of cash flows that go with the present value of cash flows that come out during the period a certain time. NPV or Net Present Value estimates of this present value on a project, assets or investments based on the expected incoming cash flows in the future and cash flow out tailored to interest rates and the price of the original purchase.

NET Present Value using the original purchase price and the time value of money (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 Asset is reduced by the purchase price of the original.

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 management companies can use this NPV calculation to evaluate whether to invest or not to invest in a new project or investments in new assets purchase. In the language of Indonesia, Net Present Value or NPV is also called with the "Net Present Value" or "Clean now".

The sense of the NPV (Net Present Value) according to experts

The following are some definitions and notions of NPV according to experts:

The NPV is Excess Present Value (PV) of the cash inflow generated by a project over a number of initial investment.

The Net Present Value (NPV) is a combination of the acceptance of the present value and present value expenses.

The Net Present Value is the difference between the present value of net cash flow or often referred to also by proceed with the present value of the investment.

Net Present Value is a model that takes into account the overall pattern of cash flows from an investment, in relation to time, based on the Discount Rate certain.

How to Calculate The NPV (Net Present Value)?

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

The Formula of The NPV (Net Present Value)

This NPV formula is quite complex because adding all future cash flows from the investments, discount the cash flow discount rate and decrease it with the initial investment. Formula equations and Net Present Value (NPV) this can be seen below:

NPV = (C1/1 + r) + (C2/ (1 + r)2) + (C3/ (1 + r)3) + ... + (Ct/ (1 + r) t) – C0



NPV = Net Present Value (in Rupiah)
Ct = cash flow per year in the period t
C0 = initial investment in Value to 0 (in Rupiah)
r = interest rate or discount Rate (in%)

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

NPV = (Ct x PVIFA(r) (t)) – C0

Table FVIFA can be seen in the picture below:

Example Case Calculation of NPV (Net Present Value)

Managing Company AAZZ wanted to buy machine production to increase the number of production of the product. New production Machine price is $ 150 million loan with interest rates of 12% per year. Incoming cash flow estimated around $. 50 million per year for 5 years. Whether the investment plan the purchase of machine production can be resumed?

The solution:


CT = $. 50 million
C0 = USD 150 million
r = 12% (0.12)


(1) NPV = (C1/1 + r) + (C2/(1 + r)2) + (C3/(1 + r)3) + (C3/(1 + r)4) + (Ct/(1 + r)t) – C0
(2) 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
(3) NPV = (44.64 + 39.86 + 35.59 + 31.78 + 28.37) – 150
(4) NPV = 180.24 – 150
NPV = 30.24

So the value of NPV is amounting to $. 30.24 million.

Use Table PVIFA

As it was said earlier, that the NPV can also be calculated by using a table PVIFA. If we have a table of this calculation, PVIFA NPV became easier and faster.

Upon tabular PVIFA, figures obtained from the 12% interest rate (r) and the 5-year period (t) is of 3.6048. The figure entered into the NPV formula below:

(1) NPV = (Ct x PVIFA(r) (t)) – C0(2) NPV = (50 x PVIFA(12%) (5)) – C0(3) NPV = (50 x 3.6048) – 150
(4) NPV = 180.24 – 150
(5) NPV = 30.24

The result is also equal to the value of NPV formula is obtained from the first se30 .24 or $.  30.24 million.

Analysis and assessment of the NPV (Net Present Value)

From the results of a calculation example above, we question the value of current net value or Net Present Value (NPV) is positive with a value of $.  30.24 million. This means the corresponding Production Machine can produce approximately $.  30.24 million after paying off the cost of purchasing the machine and also the cost of interest. In accordance with the calculation, then it can be decided that the investment plan the purchase of new production machines can proceed.

A positive NPV values (NPV > 0) showed that acceptance is greater compared to the value invested while the value of NPV is negative (NPV < 0) signifies acceptance of smaller compared to expenses or will suffer losses on his investment after considering time value of money (Time Value of Money). But when the results of the calculation of NPV is zero (NPV = 0), then this means that investments or the purchase of capital behind only (no profit and no loss).

And of course, the larger the number, the greater the positive reception that can also he obtain. Therefore, the calculation of NPV is not only use for evaluating the worth or whether to invest, but also use to compare investment which is better if there are two or more investment options.

Also note, although it is the NPV calculation tool that is great for making decisions in investing, but not always accurate. This is because of the equation depend on many estimates and assumptions that are very difficult to be completely accurate. As in the case above, the management of the company not AAZZ know for certain whether the machine will generate $. 50 million annually (since only estimates or assumptions) and perhaps also the interest rate will change along with the development market, except there is a definite agreement with the borrower. The only known by management companies is the cost to purchase the production machine at this time.

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