Net Present Value Calculations

The net present value (NPV) is the most important concept in corporate finance. It is on the basis of this concept that investment decisions are made or not made. It is on the basis of this concept that stocks and bonds are valued. Thus, it is an absolute imperative for any student of corporate finance to be thoroughly well versed with this concept. One needs to have a fair understanding of future and present value calculations to understand the net present value concept. The NPV is best understood with the help of a cash flow timeline. This article will use the same to explain it:

The Cash Flow Timeline:

The cash flow timeline is a representation of the periods when cash is expected to be paid or received during the project. Point Zero, represents today. Hence all the amounts listed in point Zero are present values. We do not have to adjust them by compounding or discounting for the net present value calculations.
The values listed under point 1 are the amounts that will be received or paid at the end of period one. The values listed under period 2 are the amounts that will be received or paid at the end of period 2, so on and so forth.

Future Values Occur In Different Periods

When we compare two numbers, we must ensure that that are of similar nature. Hence, when comparing cash flows we must ensure that all of them are either present values or future values belonging to the same future period. Comparing a present value to a future value or comparing a future value in period 1 to a future value in period 2 is like comparing apples to oranges.
Since future values all occur in different periods, we cannot compare them with each other. The only way to add or subtract these values is if we bring them all back to day zero i.e. convert every future value to their equivalent present values.

Present Values Occur at the Same Time i.e. Day Zero

Since present values depict the value of money on day zero i.e. in the same period, it would be correct for us to add, subtract or perform any other mathematical operation on this number. The key point to understand is that all values involved in the calculation must be present values.

NPV Calculation Example

Let’s consider the following schedule of cash outflows and inflows:

Period 0: $10,000 Cash Outflow
Period 1: $5,000 Inflow
Period 2: $4,000 Inflow
Period 3: $3,500 Inflow
Period 4: $3,000 Inflow

Cost of Capital is 10%.
The question is whether it is financially wise to invest $10,000 today and receive 4 installments of $5000, $4000, $3500 and $3000 if our cost of capital is 10%.
Solution:
Outflow: $10,000
Present Value of Inflows: PV (Inflow in Year 1) + PV (Inflow in Year 2) + PV (Inflow in Year 3) + PV (Inflow in Year 4)
= ($5,000/1.1)¹ + ($4,000/1.1)² + ($3,500/1.1)³ + ($3,000/1.1)⁴
= $4,545.46 + $3,305.79 + $2,629.60 + $2,049.04
= $12,529.89
Net Present Value = Present Value of Inflows – Present Value of Outflows
= $12,529 - $10,000
= $2,529

Net Present Value Rule

The net present value rule states that if the NPV of the proposal is greater than 0, it must be accepted. For less than and equal to zero the proposals must be rejected. In this case, the NPV is $2529. Hence, this proposal is financially sound given the cost of capital of the firm. It would be in their best interest to accept this proposal.