# Value Additivity Principle in the NPV method

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The Value Additivity Principle in NPV states that the value of the total NPV of a bigger project is equal to the summation of all smaller NPVs of projects. In other words, the summation of all smaller NPVs provides the bigger NPV of an investment project. The NPV of a group of the independent projects will be equivalent to the NPV of all the independent projects.

If A and B are two smaller projects, then the total NPV of the bigger project (A+B) would be −

NPV (A+B) = NPV (A) + NPV (B)

Value Additivity is an important principle because using it, we can find out the total NPV of an investment project by adding the smaller NPVs that are known to us. Alternately, if the total NPV and one project’s NPVs are known, we can find the unknown project’s NPV too.

## Uses of Value Additivity Principle

The Value Additivity Principle can be useful in the following situations −

• While calculating the valuation of a firm
• Finding out the valuation of projects in terms of cash flows
• Selection of projects
• While diversifying

## Valuation of a firm

The value additivity principle can be used to find the value of a firm. The value of a firm is the total value of individual assets deployed in the company. The assets help in generating cash which can be paid to equity and debt holders. The value of a firm is therefore equal to the total of the owner’s capital plus debt.

Let’s suppose,

• The Value of a Firm = V
• Equity in the business = E
• Total Debt liabilities = D

V = E + D

Thus, the justification of the right-hand side (RHS) of the equation can be found with the help of the Value Additivity Principle, where the firm’s value is equal to its Equity and Debt.

## Valuation of Projects in Terms of Cash Flows

The Value Additivity Principle helps to calculate the total cash flows by considering all the individual cash flows occurring in the future. Therefore, the value of a project is equal to the addition of all individual cash flows. Taking all the cash flows on the right-hand side (RHS) of the equation and adding them, we can find the value of the project on the left-hand side (LHS).

## Selection of the Best Project

The Value Additivity Principle helps in finding out the best project for a firm. According to value additivity, the bigger NPV is better than a smaller one. By choosing the right NPV project, managers can benefit from higher profitability and increased growth in the future of the project.

## Diversification

When a company diversifies, the total value of the subsidiaries is equal to the total value of the company. If the diversified company value is A and B, then according to the Value Additivity Principle,

NPV (A+B) = NPV (A) + NPV (B)

Where NPV (A+B) is the net present value of the firm after diversification into A and B.