Economic analysis in individual project selection

Using net present value analysis instead of the rate of return will treat investment scale as one of the key value drivers, and will help engineers select money-making projects.

06/18/2012


Consulting engineers are always under pressure to deliver the most cost-effective project possible for their client, whether it is for a simple replacement pump selection or a full HVAC system selection on a large building. This is no small feat, as cost effectiveness depends not only on the upfront cost of a project, but also on its impact on future operational and other costs. Most engineers will use some type of lifecycle cost estimate to make these types of decisions, to balance upfront and future costs for a client. This analysis might include consideration of any of the following measures:

  • The project’s payback ratio (simple payback)
  • Its internal rate of return
  • The net present value of its cash flows.

Making sound project decisions requires in-depth knowledge of economic tools. Courtesy: istockphoto.comThe payback ratio is an ad hoc measure that, while easy to apply, can provide misleading signals. The finance literature supports the internal rate of return and net present value metrics as the more proper tools for general economic analysis. Nevertheless, when a specific problem involves mutually exclusive investments, analysts should employ only the net present value measure, and not the rate of return. When projects compete directly against each other for capital, it is important that differences in investment scale factor into the analysis. The internal rate of return measures only return per dollar of capital invested, thereby eliminating the impact of scale in specific project analysis.

Finance principles make it clear that firms should maximize wealth, which can be measured only in dollars. Unlike rates of return, which are percentages, the net present value result is dollar based, aligning more properly with finance principles in that regard.

We demonstrate these points using theoretical finance examples, then end with a real-world example showing that a large-scale geothermal heating and cooling system is economically superior to a smaller-scale conventional HVAC design, even though the conventional system has a quicker payback and a higher rate of return.

Problems with the payback ratio

While the payback ratio can provide some useful information about a project, it is at best an incomplete measure of economic attractiveness. Applying a strict payback criterion (e.g., all projects must have a payback of 2 years or less) can in many cases steer us away from economically attractive capital investments.

The payback ratio tells us how long it takes for the cumulative cash flows generated by an investment to cover the upfront capital cost of the project. That is all that it tells us. For example, if an energy recovery unit costs $50,000 to install, and it produces annual energy savings of $20,000, the payback is:

Note that if our criterion required a 2-year payback, we would reject this project. It is difficult to know whether that is a proper economic decision because the payback ratio ignores critical information, such as the expected life of the project, the cost of capital, and other ancillary effects such as changes in cash flow due to inflation.

One big problem with the payback ratio is that it ignores cash flows that occur past the point of capital recovery. Returning to our example, note that the payback ratio for the energy recovery unit is 2.5 years whether the equipment lasts 3, 10, or 30 years. Assuming a 10% discount rate, the net present value (to be discussed in a moment) of the 3-year version of the equipment is negative (meaning the project destroys economic value rather than creating it), the 10-year version is worth about $70,000, and the 30-year version is worth about $140,000. The payback ratio provides no hint that the economic value varies to this extent depending on the useful life of the measure.

Financially sound metrics: Is one as good as the other?

Both the internal rate of return and net present value metrics rest on the same simple, but powerful, notion: If the project earns more than it costs to finance it, it creates economic value. The internal rate of return measures the result in percentage terms (i.e., in the form of an interest rate); the net present value calculation provides the result in terms of wealth (i.e., dollars).

When analyzing a project in isolation, the internal rate of return and the net present value approaches provide the same signal as to whether to invest. That is, if a project produces a rate of return in excess of the cost of capital, it will also produce a positive net present value result. This suggests to many that one can use either the internal rate of return or the net present value measure to select projects, regardless of the circumstances.

That conclusion is incorrect. We encounter problems with the internal rate of return metric when selecting among competing, mutually exclusive projects (projects in which multiple options exist, but only one can be chosen). In that realm, the net present value measure is superior to the internal rate of return. That is to say that firms will be better off financially if they consistently select from among mutually exclusive projects using the net present value criterion rather than the internal rate of return.

Project evaluation using financial metrics

We demonstrate all these financial metrics using data for two hypothetical, mutually exclusive projects, as presented in a standard financial management text (Robert C. Higgins, Analysis for Financial Management, Irwin, 1989). In this case let’s assume two different renewable energy installations, one being about twice the size of the other. Project engineers can recreate our calculations for their own projects quite easily in a spreadsheet.

Project Small requires an upfront investment of $522,000 and produces annual cash flows of $100,000 for each of the next 10 years. Project Large requires an upfront investment of $1.1 million and produces annual cash flows of $195,000 over the same period. The property owner can raise capital to finance either project at an annual cost rate of 10%.

The payback ratios for the projects in question are:

 

 

 

We see that we recover our upfront capital slightly faster under Project Small than we do under Project Large. If speed of capital recovery is our guide, then Project Small wins this contest, albeit only by a slight margin. But speed of capital recovery is not linked directly to wealth creation, which should be the ultimate objective of any for-profit firm.

One calculates the internal rate of return by setting the discounted present value of the project cash flows equal to the upfront cost. The internal rate of return is the discount rate (r) that solves the equation.

 

 

 

As noted above, a project creates value if its return exceeds the cost of capital (10% in this example). The internal rates of return for both projects meet that criterion, suggesting that both create value. If these were independent projects, the owner should invest in both.

This might be possible if the owner had two separate pieces of property upon which to place a renewable installation, but here we assume he has only one. As such, the projects truly are mutually exclusive. If we build the smaller version of the installation, we then forego the opportunity to simultaneously build the larger one at that same site.

Under those conditions, if maximizing the rate of return is our guide, then Project Small is clearly the winner, this time by a more noticeable margin. But maximizing rates of return is not the proper objective of a financially oriented business—maximizing wealth is the proper objective. We can measure wealth in one and only one form—dollars. The amount of wealth a project creates depends on the simultaneous interaction of three key variables:

  1. The rate of return
  2. The cost of capital
  3. The investment scale.

Note that none of these measures, when viewed in isolation, provides particularly useful information. Projects with high rates of return might not create much wealth if the investment scale is small or if the cost of capital for the project is high. On the other hand, projects with low rates of return can create large amounts of wealth even if the return exceeds the cost of capital only by a small margin, as long as the investment scale is large enough.

Of course, one should not reject all high-return, small-scale projects. Nor should one invest in all low-return, large-scale projects. It is the specific interaction of the three key variables shown above that determines which project creates the most wealth.

This leads us to the net present value measure, which simultaneously considers all three key value drivers. For this metric, instead of solving for r as we did when calculating the rate of return, we rearrange the terms and substitute the cost of capital (10% or 0.10) for the return.

 

 

 

The interaction between the key value drivers over the 10-year investment horizon reveals that investing in the larger project creates more economic wealth than does investing in the smaller one, even though the larger project produces a lower internal rate of return, as we saw earlier. As a standard corporate finance text suggests, if you want to feel good about making great percentage returns, select projects based on the internal rate of return. If you want to get rich, use net present value.

Net present value and excess returns

Letting scale influence the result as it does in this case may seem counterintuitive to many—don’t we want to use the rate of return to select projects because it eliminates the differences in scale, allowing for a more-balanced comparison? The answer is an unequivocal “no.” If we are interested in measuring wealth creation, which can be expressed only in absolute dollars, not percentages, we need to let scale shine through in the analysis, not be eliminated as it is in the rate of return calculation.

The internal rate of return fails to provide the proper signal here because it is insensitive to the scale of the investment, and scale is one of the primary wealth drivers. The net present value represents the excess dollar amount, that over and above the funds that flow to the capital providers. If the owner builds the smaller installation, it will produce a 14% return, the funds from which he uses to pay 10% to the capital providers, leaving him with the equivalent of $92,500 in excess funds; if he builds the larger installation, it will produce a 12% return, the funds from which he uses to pay 10% to the capital providers, leaving him with the equivalent of $98,250 in excess funds.

The choice here is clear. We purchase goods and services with dollars, not percentages. In the end, the owner can earn more dollars on the 2 percentage point spread (12% to 10%) for the larger installation than he can on the 4 percentage point spread (14% to 10%) on the smaller installation. How can he make more money on the smaller spread? It’s all about differences in investment scale.

Application: a geothermal heat pump system

Installing efficient conventional HVAC systems may produce high rates of return, but large-scale geothermal projects often yield greater net present value cost savings. Courtesy: Energy Center of Wisconsin

The discussion above would be well represented by a more concrete example. Let’s take a common building engineering challenge: an aging HVAC system. An engineer is brought in to a 350,000-sq-ft hospital in the mid-Atlantic to determine the best course of action in dealing with an aging boiler/chiller central plant that seemed to the owner to be a potential spot for an energy-efficiency upgrade. The engineer initially considers replacing the old boilers and chillers, and installing new high-efficiency units, pumps, and controls. This will certainly save the hospital energy and maintenance cost over time. But recently he has also attained some experience with geothermal systems, and decides to consider a much bigger change to a central plant geothermal system. He must use financial analysis to determine which of these two options will be more effective.

Replacing the boilers, chillers, pumps, and ancillary equipment is estimated to cost $4.30/sq ft, or $1.5 million. It will save approximately $85,000 per year in electricity, $63,000 per year in natural gas, and $15,000 per year in maintenance. The capital expenditure for the geothermal system is, of course, much more expensive. Though the inside equipment is actually somewhat similar (heat recovery chillers are installed in place of chillers, and only a small backup boiler is necessary), the geothermal system is much more expensive because a ground heat exchanger must be drilled in the field outside the hospital; the retrofit cost is estimated at $9.00/sq ft. But energy analysis indicates that the loads of the hospital are well suited to geothermal, and this technology will actually break even on electricity usage, while completely eliminating the hospital’s $265,000 natural gas bill; maintenance savings is estimated to be a little larger at $31,000 per year. The geothermal option also does not require replacement of cooling towers and boilers over time, saving the hospital $300,000 every 20 years.

The engineer takes all of those project details and calculates the financial metrics in the manner described above (see Table 1). We ask you to consider this information to make the call as to the better investment option. (Note: The hospital’s cost of capital is 7%.)

Table 1: Financial metrics for hospital HVAC projects

Project

 

Simple payback

 

Internal rate of return

 

Net present value of cash flows

 

Boiler/chiller

 

9 years

 

9.5%

 

$439,900

 

Geothermal system

 

11 years

 

8.6%

 

$523,100

 

 

Before you answer this question, consider another question: If you could receive a gift today of either $439,900 or $523,100, with no strings attached, which would you prefer? That is essentially the same question we ask here. The net present value calculation tells us how much wealth we create in today’s dollars after adjusting for risk and the timing of the cash flows, and after paying back both the principal and the required returns to those who provide the capital necessary to install the equipment. After considering all costs, including the capital costs, the hospital will increase its net worth in today’s dollars by $439,900 if it chooses the boiler/chiller; it will increase it by $523,100 if it chooses the geothermal system.

It is true that the geothermal system has a slower payback and a lower rate of return. But those metrics are nothing more than distractions for mutually exclusive projects. The only metric that matters when we choose from between investments of this nature in the net present value result and the geothermal system wins hands down by that measure.

Key takeaways

As a matter of practical advice to engineers, this analysis suggests that payback is a poor tool under most circumstances. It further suggests that we take a harder look at the scale of project options in our consulting assignments. Perhaps some of those larger projects are more valuable than we might have initially thought, especially if we were screening based on rates of return. Using net present value analysis instead of the rate of return will treat investment scale as one of the key value drivers, and will help us select wealth-maximizing projects.

 


Why maximizing NPV works for privately held firms

Some claim that while maximizing net present value may make sense for publicly traded firms that raise capital in the financial markets, privately held firms operate under different financial circumstances that make the net present value rule less applicable. As we shall see, such is not the case.

Assume a single-owner firm that has $25,000 of cash available for investment. The firm has two mutually exclusive, 1-year projects. Project A requires a $10,000 upfront investment and produces a $20,000 cash flow at the end of the year (a 100% internal rate of return); Project B requires a $20,000 upfront investment and produces a $35,000 cash flow at the end of the year (an 80% internal rate of return).

If the firm wanted to raise capital to fund these projects, it would need to pay capital providers a 10% return. When we conduct proper financial analysis, whether the firm actually uses external funds is not important—the cost of capital measures the opportunity cost of raising those funds. If you are skeptical, stay with us.

The net present value metric is only a tool to guide us to wealth maximization. We will demonstrate that following that rule leads to greater wealth for the private firm, even if the firm uses internal funds to finance its projects. Using the opportunity cost concept, we have enough information to calculate the net present values for the projects:

So if we use internal rate of return, we would select Project A (100% rate of return); if we use net present value, we would select Project B (net present value of $11,818).

But how does this mathematical analysis translate into firm performance? We can see the effect by examining the impact of each project on the firm’s wealth. Neither project uses the entire $25,000 cash balance. We assume for the sake of simplicity that the unused cash amount sits idle in the firm’s checking account. We show below the firm’s cash flow trail over the year for each project:

Project A: $25,000 beginning cash balance - $10,000 investment + $20,000 cash inflow = $35,000 ending cash balance

 

Project B: $25,000 beginning cash balance - $20,000 investment + $35,000 cash inflow = $40,000 ending cash balance

 

If you think $40,000 is better than $35,000, then you want to use net present value, and not internal rate of return, to select projects. That notion holds for all for-profit firms, regardless of ownership structure.

Portions of this example come from Brealey, Myers and Allen, Principles of Corporate Finance, McGraw-Hill Irwin, 2006.


Kihm is research director and Hackel is senior energy engineer at Energy Center of Wisconsin. Kihm evaluates energy-efficiency programs and develops, analyzes, and critiques energy policy. He was a 2011 Career Smart Engineers Conference presenter. Hackel consults with architects and engineers on energy-efficient building designs and systems. He conducts applied research on energy efficiency technologies and assists utilities in developing efficiency programs. He was a 2011 40 Under 40 award winner.



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