Net present value

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The net present value, also known as net present value or net present value (in English net present value), whose acronym is VAN (in English, NPV), corresponds to the present value of the net cash flows (income - expenses) originated by an investment.

The formula to calculate the Net Present Value is:

${displaystyle {mbox{VAN}}=sum _{t=0}^{n}{frac {V_{t}}{(1+k)^{t}}}-I_{0}}$

Where:

{displaystyle V_{t}}

represents the cash flows in each t period.

{displaystyle I_{0}}

is the value of the initial disbursement of the investment.

n

is the number of periods considered.

k

is the discount rate.

The value of k which makes the VA take a value equal to 0, is called the internal return rate (IRR) and is a measure of the profitability of an investment.

Interpretation

Value	Meaning	Decision to take
VAN ▪	Investment would produce profits above the required profitability (r)	The project can be accepted
VAN ≤ 0	Investment would result in losses below the required profitability (r)	The project should be rejected
VAN = 0	Investment would not produce profits or losses	Since the project does not add monetary value above the required profitability (r), the decision should be based on other criteria, such as obtaining better market positioning or other factors

The current net value is very important for the assessment of investments in fixed assets, despite their limitations in considering unforeseen or exceptional market circumstances. If its value is greater than zero, the project is profitable, considering the minimum yield value for investment. In this regard, Johnson (1998) expresses itself: "In summary, a capital investment project should be accepted if it has a positive net present value, when expected cash flows are discounted to the opportunity cost." (p. 45)

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A company usually compares different alternatives to see if a project suits them or not. Normally the alternative with the highest NPV is usually the best for the entity; but it doesn't always have to be that way. There are occasions in which a company chooses a project with a lower NPV due to various reasons such as the image that it will bring to the company, strategic reasons or other reasons that are of interest to said entity at that time.

The interpretation of the VAN can also be considered, depending on the creation of value for the company:

- If the NPV of a project is positive, the project creates value.

- If the VAN of a project is negative, the project destroys value.

- If the VAN of a project is zero, the project does not create or destroy value.

Fixed Income

When the cash flows are of a fixed amount (fixed income), for example bonds, the following formula can be used:

${displaystyle {mbox{VAN}}=-I+{frac {R[1-(1+i)^{-n}]}{i}}}$

R

represents the constant cash flow.

{displaystyle i}

represents the minimum cost of opportunity or profitability that is required to the project.

n

It's the number of periods.

I

is the initial investment necessary to carry out a project.

Rising income

In some cases, instead of being fixed, rents can increase with a growth rate "g", always being g<i. The formula used then to find the VAN is the following:

${displaystyle {mbox{VAN}}=-I+{frac {R[(1-(1+g)^{n}*(1+i)^{-n})]}{(i-g)}}}$

R

represents the cash flow of the first period.

{displaystyle i}

represents the minimum cost of opportunity or profitability that is required to the project.

{displaystyle g}

represents the rate of increase in the value of the income of each period.

n

It's the number of periods.

I

is the initial investment necessary to carry out the project.

If the number of periods to be projected (in perpetuity) were not known, the formula would vary as follows:

${displaystyle {mbox{VAN}}=-I+{frac {R}{(i-g)}}}$ «»

Net current value procedures

As author Coss Bu mentions, there are two types of net present value:

Present value of total investment. Since the objective in selecting these alternatives is to choose the one that maximizes present value, the rules of use in this criterion are very simple. All that is required to do is to determine the present value of the cash flows generated by each alternative and then select the one with the maximum present value. The present value of the selected alternative should be greater than zero since in this way the performance obtained is greater than the minimum attractive interest. However, it is possible that in certain cases when considering mutually exclusive alternatives, all have negative present values. In such cases, the decision to take is to “do nothing”, i.e., all available alternatives should be rejected. On the other hand, if only your costs are known from the alternatives you have, then the decision rule will be to minimize the present value of the costs.

Present value of the increase in investment. When discussing mutually exclusive alternatives, they are the differences between them that would be most relevant to decision-making. The present value of the increase in investment precisely determines whether these investment increases that demand the most investment alternatives are justified.

When two mutually exclusive alternatives are compared using this approach, the net cash flows are determined from the difference in the cash flows of the two analyzed alternatives. Then it is determined if the increase in investment is justified. Such an increase is considered acceptable if its performance exceeds the minimum recovery rate.

Advantages

Your calculation only requires simple operations.
It counts the variation of the "value of money" in time (inflation).
Their use and understanding is extended.

Disadvantages

Difficulty establishing the value of K. Sometimes the following criteria are used:
- Cost of long-term money (inflation estimate)
- Long-term profitability rate of the company
- Coste of capital of the company.
- As an appreciative value
- As a cost of opportunity.

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