NPV: Profitability Assessment, Done Right

Integrating Time, Risk, and Alternative Costs

Business Models for Smart Products - Chapter 3

Is My Project Profitable?

There are several methods used to answer this question, and as any finance professor will tell you, the preferred method is the Net Present Value (NPV) calculation.

But first, let address the lexical meaning of this quite complex term:

• “Net” means after all inflows and expenses
• “Present” means bringing future (positive and negative) cashflows to current date, accounting for the time value of money and the risk premium assigned to the project.

(Truth to be told, you rarely know all the parameters needed to answer, uncertainties are baked in, and there are many shortcut methods about - each to their benefit and use.)

NPV addresses the question:

What is the present value of a series of future cash flows?

Positive NPV indicates that the project is profitable .

Negative NPV suggests the project is expected to lose money.

The calculation takes a series of future cash flows, in their nominal future values, and discounts them -meaning it reduces each cash flow based on the cost of capital relative to the present.

An expense of $500,000 today is worth exactly $500,000.

But an expected income of $500,000 a year from now is worth less today – depending on the cost of capital, and we need to *discount *it by the discount factor based on the time frame and associated risk.

This is why it is also called DCF - Discounted Cash Flow.

NPV Calculation:

The present value (PV) of a future sum (FV) is calculated by dividing the future amount by a discount factor:

Discount factor = (1 + R)ⁿ

Where:

• R is the interest rate per period
• n is the number of periods

Critically, this discount factor is exactly the “Cost of Capital” mentioned in chapter 2 when we discussed risk premium. While I will not further detail here the making of the cost of capital, you can find further discussion here.

The present value for a cash flow at a future period n is:

PV = FVₙ / (1 + Rₙ)ⁿ

Where:

• PV is the present value
• FVₙ is the future value at period n
• Rₙ is the interest rate applicable to that period

The value of a series of future cash flows is:

NPV₀ = FV₀ / (1 + R₀)⁰ + FV₁ / (1 + R₁)¹ + FV₂ / (1 + R₂)² … + FVₙ / (1 + Rₙ)ⁿ

(Do note that some of these cashflows can - and will - be negative)

Let’s consider a hypothetical project:

An initial expense of $500,000 today, and an expected income of $500,000 in one year, accruing interest at period rate of** 5%**.

The present value of the future income is:

➔ PV = FV / (1 + R)ⁿ = 500,000 / (1 + 0.05)¹ = 500,000 / 1.05 = 476,190

The Net Present Value (NPV), however, is negative, accounting for the initial expense at period 0:

➔ NPV = -500,000 + 476,190 = -23,810

In other words, there’s no reason to invest in this project. Try it yourself:

It’s important to note that the the formula provided took a single interest value R, but in real life, variable interest rates (lower one, hopefully) can apply to later stages, when the business stabilizes and the risk decreases.

Indeed, the risk of a project that has already demonstrated, for instance, profitable sales is very different from the risk of a project that is still just a concept.

Additional factors should be incorporated into the NPV model, such as:

• Inflation
• Long-term continuity
• Revenue growth
• Planned project termination

The core principle, however, remains the same.

Note that there are advanced tools to calculate more complex scenarios - but in the above example I chose clarity over sophistication.

Read about Capital Budgeting in Part 4: Extending Customer Lifetime Value

Back to the directory: Smart Business Models for Smart Tangibles

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