How can contractors deploy limited resources in a way that maximizes return? An introduction to capital budgeting, Part 2.

Conceptual Framework for Net Present Value, or NPV

In the previous article, we built the case for considering the time value of money when choosing which projects to undertake. This article builds directly on the previous one and it’s worth looking over the first article before diving into this one.

NPV gives us, in a single number, a value of a project expressed in today’s dollars that accounts for the opportunity cost and the riskiness of the project. It allows us to directly compare projects with distinct characteristics and pick the one(s) that maximize return on our limited resources.

In the previous article, we introduced two concepts. First, we defined the value of a project as:

Value = Benefits – Costs, where

Benefits = cash coming in, and

Costs = cash going out.

Second, we said that the future value of a cash flow is calculated with:

FV = PV x (1 + r)^n, where

FV = Future Value

PV = Present Value, or the nominal value of the initial cash flow

r = Periodic effective interest rate*

n = Number of compounding periods where interest is earned

Future Value a dollar amount in “future” dollars. As we saw with the example in the previous article, we can only compare cash flows that ae expressed in the same time period’s dollars. Ignoring the time value of money can lead to value-destroying investment decisions.

We can use this same FV relationship to express future cash flows in today’s dollars by calculating the “Present Value”, or PV. This is an algebraic manipulation of the FV relationship:

If

FV = PV x (1 + r)^n,

then

PV = FV / (1 + r)^n
.

Combining our definition of “Value” (Value = benefits – costs) and the concept of “present value”, we can now introduce a simple and powerful metric for comparing the value of different projects:Future Value a dollar amount in “future” dollars. As we saw with the example in the previous article, we can only compare cash flows that ae expressed in the same time period’s dollars. Ignoring the time value of money can lead to value-destroying investment decisions.

Combining our definition of “Value” (Value = benefits – costs) and the concept of “present value”, we can now introduce a simple and powerful metric for comparing the value of different projects:

Net Present Value (NPV) = PV(benefits) – PV(costs), where

PV(benefits) represent the value of all cash inflows expressed in today’s dollars, and

PV(costs) represents the value of all cash outflows expressed in today’s dollars.

NPV then represents the value of the project expressed in today’s dollars. It is a direct measure of how much value is created by the project. We’ll take it one step further: Accepting a project is equivalent to receiving its NPV in cash today.

If you’re like me, that statement seems like quite a leap. Let’s look a simplified example to see how it works.

Example:

Suppose that in exchange for $500 today, your firm can receive $550 in one year with certainty. If the firm can borrow and lend at an 8% interest rate, should it make the investment?*

Here’s our timeline for the cash flows of the potential investment:

     0                                                    1

     |--------------------|

-$500                                           $550

Let’s start by attaching values to our terms in the NPV equation:
  • Benefit = $550
  • Cost = $500

We want to calculate:

NPV = PV(benefits) - PV (costs).

The cost is already in PV terms since the cash flow occurs today. We need to put the benefit in PV terms because it happens one year from today. Using the PV equation from above we find that:

PV(benefits) = $550 / 1.08 = $509.26

Now we can plug into the NPV equation to find:

NPV = 509.26 - 500 = $9.26

Let’s put these numbers on a timeline to get a picture of what we’ve done:

      0                                                    1

      |--------------------|

-$500.00                                    $550

$509.26 <---------------|

$ 9.26

A moment ago we said that the NPV of a project is equivalent to receiving its NPV in cash today. This means that taking the investment is equivalent to pocketing $9.26 today. So how can the firm pocket $9.26 today? By following these steps:

  1. Borrow PV(benefit) of $509.26,
  2. Make the investment of $500,
  3. Use the cash flow from the investment to repay the loan one year from today, and
  4. Pocket $9.26 today.

Let’s put these cash flows on a timeline to get a picture of what’s happening:

                    0                                                         1

                     |----------------------|

Borrow -> +$509.26                  -$550 <- Repay the loan

Invest -> - $500.00                   +$550 <- Receive from investment

                        $ 9.26                         $ 0

To be clear, we are not recommending that you to earn this week’s coffee money by taking out a loan against a promised future cash flow. We are just building the case that NPV is a conceptually rigorous method of estimating the ex-ante value of a project, i.e. the NPV of the project. We can then use projects’ NPV for comparison to other opportunities.

Of course, there are two glaring assumptions here. First, your firm cannot borrow and invest at the same interest rate. Your bank charges you a higher interest rate on a line of credit than it is willing to pay on your money market checking account. The assumption of borrowing and investing at the same interest rate is for computational ease while we explore the underlying concept. In practice we would use a rate equal to our next best investment alternative. That is, what could your firm do with the cash on hand? Take on as many projects as possible for additional income? Pay down existing debt? The “next best investment alternative” is unique to each firm, but cash is a limited resource for all firms. Choosing to take on one project means choosing to forgo another. The project we forgo is the opportunity cost of the accepted project.

We consider opportunity costs all the time. For example, suppose your firm has enough resources to accept only one of the following projects:

Project 1 offers a 15% margin Project 2 offers a 25% margin

Both projects are equally risky and require the same labor, material, and time to complete. They only differ in expected margin. Which would you choose? Most firms would take Project 2 with a 25% margin. Taking Project 2 means forgoing Project 1, and so we forgo the 15% margin we could have earned to make the 25% margin. Most firms would happily “pay” the opportunity cost of forgoing Project 1 to earn 25% on Project 2.

When we calculate the NPV of each project, we need to use an interest rate that reflects this opportunity cost. When we use an interest rate the represents the next best alternative investment (or the firm’s required rate of return), we call it a “discount rate”.* Firms that do not do strict capital budgeting still use this concept. Many firms have something like a “hurdle rate”, likely expressed as a certain margin below which they will not accept projects. This is very similar in concept to the discount rate we want to use for NPV calculations.

Now let’s consider the second glaring assumption in our simplified NPV example: Cash flows are known with certainty. In reality, few cash flows are known with certainty at the beginning of a project. Actual cash flows will differ in size and timing from budget projections. Firms know this and often adjust the required margin using a subjective assessment of a project’s risk. A firm may say something like, “We like to see at least a 15% margin on jobs like this, but this customer has surprised us on previous jobs in ways that caused us to bust our budget. Let’s build in a 20% margin for this one.”

Similarly, we want to include an adjustment for risk in the discount rate we use for NPV calculations. If a project is riskier than average, then we can add a subjective amount to the discount rate to account for this risk. If the project is less risky than average, you can subtract a subjective amount from the discount rate account for this (perceived) lower amount of risk.

NPV gives us, in a single number, a value of a project expressed in today’s dollars that accounts for the opportunity cost and the riskiness of the project. It allows us to directly compare projects with distinct characteristics and pick the one(s) that maximize return on our limited resources.

In short, the NPV Investment Decision Rule is:
When making an investment decision, take the alternative(s) with the highest NPV, which is equivalent to receiving the NPV in cash today. Take all positive NPV projects that the firm’s constraints allow. The higher the NPV, the better.

The next article in this series:

Using agile project management to increase a construction project’s financial utility

-Steven Stelk, PhD, FP&A; Financial Strategist, Cycle Rate Performance

*There is considerable debate among finance academics about how to choose an appropriate discount rate for capital budgeting. The interested reader can see an summary of the issues related to choosing a discount rate at: https://hbr.org/2012/07/do-you-know-your-cost-of-capital

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