Net Present Value and risk assessment for investments projects

What is the Net Present Value?

The net present value (NPV) is the value of a project. This is simply the present value of the project’s free cash flows discounted at the cost of capital over the life of a project.

The NPV tells us how much a project contributes to shareholder wealth; the larger the NPV, the more value the project adds—and added value means a higher stock price. This is why the NPV is the best selection criterion, primarily because it addresses directly the central goal of financial management—maximizing shareholder wealth.

That is, a project with a NPV of $1 million is expected to increase shareholder wealth by $1 million. Thus, projects with positive NPV (NPV > 0) are expected to add to shareholder wealth while projects with negative NPV (NPV < 0) should be shunned.

The NPV is used in capital budgeting to analyze the profitability of a projected investment.

How to calculate the NPV?

A project’s NPV is calculated as the present value of all cash flows over the life of the project less the initial investment. You can also find here a broader introduction on NPV calculation.

So, to apply the NPV as a valuation method, we need to know the project’s estimated cash flows and the required rate of return (the cost of capital) in order to discount the cash flows. The required rate of return should reflect the cost of long-term debt and equity capital funds for projects with the same risk as the one under consideration.

What is Monte Carlo Analysis in Project Management?

Generally, Monte Carlo simulation can be understood as the process of repeating the same experiment for "n" times, using randomly generated numbers that follow the same distribution of our data to simulate a variable of the problem. For investment projects, NPV, IRR, payback period, etc. can be simulated.

The computer randomly picks a value for each variable—units sold, sales price, variable costs per unit, and so forth. Those values are then used to calculate an NPV (or, other indicator), and that NPV is stored. Next, a second set of input values is selected at random, and a second NPV is calculated. This process is repeated a number of times (1,000 or more), generating NPVs for each one of them. The mean of the NPVs as a measure of profitability and the probability for NPV > 0 as a meassure of risk are then determined.

Business analysts choose a probability distribution that fits the actual behavior of the process underlying the input parameter: uniform probability distribution, normal probability distribution or exponential probability distribution. Most distributions have their own input parameters you can use to closely fit the values in the distribution to the values of the process.

Assumptions used in this application

• For simplicity, we consider that the investment consists of fixed assets and their salvage value is zero, but the adaptation of our application to the various requirements can beeasily done upon request.
• After the initial investments are made, the project will hopefully produce positive cash flows over its operating life. These are calculated as EBIT(1 - tax rate) + Depreciation.
• In some cases, the firm may also need to make continued investments throughout the life of the project, particularly for a growing project where the company needs to steadily add fixed assets and inventory over time. This changes in my code can be insertd upon request.
• I use here the uniform probability distribution relevant for the annual revenues and annual operational expenditures. The probability that NPV > 0 as a measure of risk is calculated by using the Monte Carlo risk analysis method.
• The user must insert the investment expenditures (in dollars, euros etc.), so that the table in the form can generate other inputs for inserting the annual revenues and expenditures (also in dollars, euros etc.). Likewise, the cost of capital and the income tax rate as percentages (for example 5 for 5% etc.) are necessary for calculating the NPV, the mean and the probability of a NPV > 0.