net present value (NPV)

Example:

The Alpha Corporation is considering investing in a riskless project costing $100. The project receives $107 in one year and has no other cash flows. The discount rate is 6 percent.

The NPV of the project:

$ 0.94 = -$100 +( $107 / 1.06)

The project should be accepted because its NPV is positive.

The basic investment rule can be generalized to:

• Accept a project if the NPV is greater than zero
• Reject a project if NPV is less than zero.

Why does the NPV rule lead to good decision? Considering the following two strategies available to the managers of Alpha Corporation:

• Use $ 100 of corporate cash to invest in the project. The $107 will be paid as a dividend in one year.
• Forgo the project and pay the $100 of corporate cash as dividend today.

If strategy 2 is employed, the stakeholder might deposit the dividend in a bank for one year. With an interest rate of 6 percent, strategy 2 would produce cash of $106 = ($100 x1.06) at the end of the year. The stockholder would prefer strategy 1 because strategy 2 produces less than $107 at the end of the year.

Accepting positive NPV projects benefit the stockholders.

How do we interpret the exact NPV of $0.94? this is the increase in the value of the firm from the project. For example, imagine that the firm today has productive assets worth $V and has $ 100 of cash. If  the firm forgoes the project, the value of the firm  today would simply be:

$V + $100

If the firm accept the project, the firm will receive $107 in one year but will have no cash today. Thus, the firm’s value today would be:

$V + ($107 / 1.06)

The difference between these equations is just $0.94, the Net Present Value of Equation:

The value of the firm rises by the NPV of the project.

Note that the value of the firm is merely the sum of the values of the different projects, divicion, or other entities within the firm. This property, called value additivity, is quite important. It implies that the contributor is quite important. It implies that the contribution of any project to a firm’s value is simply the NPV of the project.

The key to NPV is its three attributes:

• NPV uses cash flows
• NPV uses all the cash flows of the project.
• NPV discounts the cash flows properly.

Source: Source: Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.