Net present value (NPV) is a financial calculation that measures the profitability of an investment or project. It is the present value of the investment’s expected cash flows, minus the initial investment outlay.

NPV is typically used to evaluate the potential profitability of an investment or project, by comparing the investment’s expected cash flows to the initial investment outlay. If the NPV is positive, then the investment is expected to be profitable. If the NPV is negative, then the investment is expected to be unprofitable.

NPV is a useful tool for making investment decisions, because it accounts for the time value of money. This means that it takes into account the fact that a dollar today is worth more than a dollar in the future, due to the potential for that dollar to earn interest. By discounting future cash flows at an appropriate rate, NPV provides a way to compare investments or projects that have different cash flow profiles over time.

## Differences of sunk cost between finance and accounting perspective

Before learning what’s NPV is, let’s review what’s SUNK COST is about

Sunk cost is a term used in both finance and accounting to refer to costs that have already been incurred and cannot be recovered. In other words, sunk costs are past costs that have no bearing on future decisions and cannot be recovered, regardless of the outcome of those decisions.

From a finance perspective, sunk costs are considered to be irrelevant to decision-making because they do not affect the future cash flows of a project or investment. For example, if a company has already spent a large amount of money on a project, but the project is not expected to be profitable, the sunk costs of the project should not be considered when deciding whether to continue with the project or not. Instead, the decision should be based on the expected future cash flows of the project and the potential returns on investment.

From an accounting perspective, sunk costs are recorded as expenses in the current period, regardless of whether they can be recovered or not. This is because accounting rules dictate that expenses should be recognized in the period in which they are incurred, rather than in the period in which the related cash flows are received or paid. Therefore, sunk costs are recorded as expenses in the current period, even if they cannot be recovered, and are not carried forward to future periods.

In summary, the main difference between the finance and accounting perspectives on sunk costs is that finance considers sunk costs to be irrelevant to decision-making, while accounting records sunk costs as expenses in the current period.

## Differences between the formula of present value and net present value

The present value formula is used to calculate the current value of a future cash flow or series of cash flows, based on a given interest rate. It takes into account the time value of money, which states that a dollar received in the future is worth less than a dollar received today. The present value formula is typically expressed as follows:

PV = CF / (1 + r)^t

Where PV is the present value, CF is the future cash flow, r is the interest rate, and t is the number of periods in the future that the cash flow will be received.

The net present value (NPV) formula is similar to the present value formula, but it takes into account multiple cash flows that may occur at different times in the future. It is used to determine the overall value of a project or investment, by calculating the present value of all expected future cash flows and then subtracting the initial investment. The NPV formula is typically expressed as follows:

NPV = CF1 / (1 + r)^t1 + CF2 / (1 + r)^t2 + … – I

Where NPV is the net present value, CF1, CF2, etc. are the expected future cash flows, r is the interest rate, t1, t2, etc. are the periods in the future when the cash flows will be received, and I is the initial investment.

In summary, the main difference between the present value and net present value formulas is that the present value formula is used to calculate the current value of a single future cash flow, while the net present value formula is used to calculate the overall value of a project or investment by taking into account multiple future cash flows and the initial investment.

## How to calculate the net present value NPV

To calculate the net present value (NPV) of an investment, you need to do the following steps:

- Determine the cash flows expected from the investment. This will typically include the initial investment outlay, as well as any future cash inflows and outflows.
- Determine the appropriate discount rate to use for the investment. This is the rate of return that could be earned on a similar investment with similar risks.
- Discount each cash flow using the discount rate, with the initial investment being discounted at time zero. This means that you will calculate the present value of each cash flow by dividing it by the discount rate raised to the power of the number of periods since the initial investment.
- Sum all of the discounted cash flows to get the NPV of the investment. This will be the present value of all the expected cash flows, minus the initial investment outlay.

If the NPV is positive, then the investment is expected to be profitable. If the NPV is negative, then the investment is expected to be unprofitable.

## Here are a few examples of how net present value (NPV) is used in the real world:

- A clothing company is considering investing in a new manufacturing plant. It estimates that the initial investment outlay will be $10 million, and that the plant will generate $1.5 million in annual cash flows for the next 10 years. Using a discount rate of 10%, the NPV of this investment would be calculated as follows:

- Initial investment: -$10,000,000
- Cash flow 1: $1,500,000 / (1 + 0.10)^1 = $1,363,636
- Cash flow 2: $1,500,000 / (1 + 0.10)^2 = $1,230,769
- Cash flow 3: $1,500,000 / (1 + 0.10)^3 = $1,105,128
- Cash flow 4: $1,500,000 / (1 + 0.10)^4 = $989,010
- Cash flow 5: $1,500,000 / (1 + 0.10)^5 = $881,901
- Cash flow 6: $1,500,000 / (1 + 0.10)^6 = $783,291
- Cash flow 7: $1,500,000 / (1 + 0.10)^7 = $692,621
- Cash flow 8: $1,500,000 / (1 + 0.10)^8 = $609,287
- Cash flow 9: $1,500,000 / (1 + 0.10)^9 = $533,826
- Cash flow 10: $1,500,000 / (1 + 0.10)^10 = $465,849
- NPV: -$10,000,000 + $1,363,636 + $1,230,769 + $1,105,128 + $989,010 + $881,901 + $783,291 + $692,621 + $609,287 + $533,826 + $465,849 = $2,085,049

In this example, the NPV of the investment is positive, so it is expected to be profitable.

- A consumer is considering taking out a loan to buy a new car. The loan has a principal amount of $25,000, and a monthly interest rate of 0.5%. The consumer expects to make monthly payments of $500 for the next 5 years. Using a discount rate of 5%, the NPV of this loan would be calculated as follows:

- Initial investment: -$25,000
- Cash flow 1: $500 / (1 + 0.05)^1 = $482.61
- Cash flow 2: $500 / (1 + 0.05)^2 = $465.51
- Cash flow 3: $500 / (1 + 0.05)^3 = $448.86
- Cash flow 4: $500 / (1 + 0.05)^4 = $432.64
- Cash flow 5: $500 / (1 + 0.05)^5 = $416.84
- Cash flow 6: $500 / (1 + 0.05)^6 = $401.44
- Cash flow 7: $500 / (1 + 0.05)^7 = $386.42
- Cash flow 8: $500 / (1 + 0.05)^8 = $371.78

….. You can calculate the NPV by yourself now