# Net Present Value Interpretation and Explanation

## Definition

NPV is defined as

“Present value of all expected future cash flows (both inflows & outflows) stemming from investment less the initial cost of the investment.”

Net present value is one of the techniques used in capital budgeting process to evaluate investment decisions (i.e. whether to make investment in long term assets or not).

The basic rule or logic of Net present value method is to provide the investment’s value in terms of today’s dollar value. Thus comparison of investment with its cost becomes easier.

## Formula

From definition, we can extract the formula of net present value.

 NPV = Present value of future cash inflows & outflows associated with investment _ Initial cost of the investment

Or, in mathematical terms

 NPV  =    ∑ n t=1 FCFt - IC (1 + r)t

Where
FCF = Future cash flows
r = the discount rate. Normally this is required rate of return for particular investment.
t = are periods (usually year wise) in which cash flows are generated.
n = is the total life of the project / investment; and
IC = Initial cost of starting the project or making the investment.
Formula can best be understood by knowing the method of calculating the npv and example.

## How to calculate Net Present Value (NPV)

#### Step 1: Determine the future cash flows of the investment / Project

Predict / forecast all the relevant future cash flows of the investment. For this purpose future cash flows can be divided into following four broader categories.

• Inflows: Identify year wise cash inflows over the life of the project. These inflows are revenues generated from the investment e.g. by installing a new plant, the sales of the company increased. The revenue from these extra sales is inflows.
• Outflows: Identify year wise cash outflows over the life of the project. These outflow could include operating costs but do not include non-cash costs. For example the outflows associated with a new plant will be salaries of staff, repair & maintenance expenses of plant etc. But this will not include depreciation of the plant as it is non-cash cost.
• Taxes: Year wise government claims i.e. taxes etc. will also be predicted and taken as cash outflow for the purpose of determining future cash flows.
• Salvage value at the end of project: At the completion of the project’s life it has some salvage value. This value will be taken as an inflow. For example the plant has 10 years of useful life, after which it will be sold at some salvage value.

#### Step 2: Determine the required rate of return for the investment / project

Ideally required rate of return for each project should be determined separately. However for the sake of simplicity companies use their overall required rate of return for the purpose.
Required rate of return takes into account the riskiness of project and cost of capital. How to calculate the required rate of return is explained separately.

#### Step 3: Discount the future cash flows with required rate of return

Step 3 involves concept of time value of money.
Discount the future cash flows of investment (determined in step 1) with the discount rate (determined in step 2). Apply

• Simple interest discount formula in case of uneven cash flows or
• Annuity interest discount formula in case of even cash flows.

The resulting figure will be “discounted cash flows.”

#### Step 4: Subtract initial cost of investment from “discounted cash flows”

As per formula given above, subtract initial cost of investment form “discounted cash flows” as determined in step 3. The result is net present value of the project. For example purchase price of plant was \$100 and “discounted cash flows” of the plant are \$115. NPV is \$115 - \$100 = \$15 for the plant.

#### Step 5: Interpret the net present value

It is simple and explained below after the example.

## Interpretation of net present value

The result of npv will be either positive, negative or zero. This result will determine whether to take the project or not.

#### When npv is positive i.e. npv > 0

Accept the project.
Positive npv means the projects value exceeds its cost. As a financial manger our goal is to maximize the shareholder’s wealth (value). Projects with positive npv fulfill this goal of financial manger and should therefore be accepted.

#### When npv is zero i.e. npv = 0

Accept the project.
Zero npv means, financial manager is indifferent to decision of accepting or rejecting the project. Although project is not increase the value, it is at least recovering the required rate of return (remember cash flows were discounted using the required rate of return). Therefore project should be accepted.

#### When npv is negative i.e. npv < 0

Reject the project.
Negative npv means, project has failed to recover event the cost of the project. Accepting such project will harm the goal of maximizing the shareholder’s wealth and it should therefore be rejected.

Among the techniques of Capital Budgeting Decisions, npv is the most accurate in theory. Advantages include

• Time of value of money: npv recognizes the important phenomenon “a dollar today, worth more than a dollar after one year.” Therefore npv uses discounting techniques.
• Risks of projects: npv realized the fact that “some investments are more risky than others and proper weightage should be given to investment according to risk involve.” Npv do this by either adjusting the cash flows or the discount rate for appropriate risks.
• Cash not profits: npv is based on cash flows rather than on accounting profits. Thus it accounts for the “true timing of the costs & benefits” as opposed to accounting where accrual concept of costs & benefits is used.

• Time consuming requiring professionals: Npv is normally calculated by the professionals only. Also it is lengthy process. Cost of employees and cost of time both are valuable resources of business.
• Prediction of future cash flows: predicting the future inflows and outflows associated with an investment is a difficult task.