A wee bit more on payback

While not very well written, and at the risk of becoming ridiculously self referential, here are a few more thoughts about energy projects and their value to the organization that I wrote several years back:

http://tinyurl.com/cymdq2b

Surprisingly, I have found variations of this approach to have gained currency in the energy conservation community recently.  Note that while this was presented as an IT article, the approach is quite widely applicable.

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Payback!

I’ve worked in the energy conservation field for a long time, and it has frequently surprised me how inadequate the economic evaluation of energy projects tends to be.

Even very large organizations with significant investment in efficiency and “sustainability” often resort to “simple payback” as a way of assessing and selecting investments in energy savings.

It’s pretty easy to demonstrate why simple payback (SPB) is a lousy tool.  Let’s take a look, and then propose some better solutions.

Simple payback is simply (no pun intended, but there it is) the cost of the energy project divided by the anticipated annual energy cost savings (as an aside, I could argue that any annual maintenance savings should also be factored in, but they seldom are.)

Thus, a simple payback of three years means that the energy savings accruing over three years will cover the original cost of the project.

On the face of it, this has a certain appeal.  But simple payback is too blunt an instrument to make shrewd investment decisions.  Sort of like cutting cake with an axe.

As usual, a thought experiment is our tool of choice in probing for the soft spots of a metric like SPB.

Imagine two competing investment projects.  Both cost $100 and both save $35 per year, but one will last five years before needing replacement, while the other is expected to last 10 years.

Now, it is obvious that the longer lived project is a better deal, since it will deliver almost 7 years worth of savings after the initial investment is recouped, whereas the shorter lived project only delivers savings for two years after the investment cost is recovered.

And yet, the simple paybacks are identical.

At the risk of being overly pedantic, let me spell this out explicitly.  Simple payback is completely and utterly incapable of distinguishing the life cycle value of an energy investment.

Which is why it’s a pretty inadequate tool for sorting out energy investment opportunities.  And yet, I’ve seen simple payback used as the sole criteria in accepting or weeding out projects with six figure price tags in otherwise sophisticated organizations.

Crazy, right?

In fact, the reason this topic came to mind was that I was reading some posts on an energy oriented site where someone was talking about how a four year simple payback was the upper limit for a project to be deemed acceptable.

But what if it is an extremely long lived asset like a chiller (a big machine that makes cold water for air conditioning) that might last 35 years?   Would you not evaluate the benefit of 28 years of savings in light of a seven year payback?  Apparently not.

So you can see, SPB is not only a blunt instrument, it can also inadvertently exclude from considerations investment opportunities that might deliver excellent overall benefits to the organization.

Fortunately, simple but much more informative evaluations of energy investments can be made readily.  Let’s do a little background to see what issues we need to address, and then carry out a simple example or two.  As is typical on this blog, I don’t delve into great detail, but I try to get the fundamental ideas across (and more or less correct), but details need to be pursued elsewhere.

Well, as we mentioned above, one thing we need to account for is the useful life of the energy project.  Now, we may not know this precisely, but we know that a motor is going to last 10+ years typically, while a conventional fluorescent lamp might last 20,000 hours.  And generally speaking, you can make an educated guess for most energy projects.

Also, because energy project require an investment of capital, it is useful to understand the organization’s cost of capital.  Now, cost of capital might be the cost to borrow money to carry out a project, or it might be lost opportunity value of the investment spend, or it might be something else, but most organizations have (or should have) a sense of this.

The important thing to remember when considering cost of capital (or discount rate) is that it allows you to understand what value the organization puts on future savings in today’s dollars.

For instance, if I offered to give you $100 in two years, or $80 right now, which would you take?  You might well take the $80, figuring that you could invest it in something that would deliver equal or better results two years out.  So that $100 promised two years out might have an equivalent present value of $80.  And you will observe that if I offered you that $100 in five years, you might be happy with something like $50 today.  Meaning that the present value of money diminishes the further away it is in time.

You will notice immediately that if an organization has a non-zero cost of capital, the paybacks reported via SPB are actually overly generous (i.e. too short) because future savings dollars are treated just the same as present dollars.  And even if the organization itself does not recognize it, this is not true.  Those future savings are worth less – a bird in the hand and all that.

***

Anyway, our general approach will be to look at the energy investment it today’s dollars, but we should discount the future savings, taking into account the organization’s cost of capital. We then develop a “net present value” for the project, which equals the initial energy investment minus the discounted savings flow over the life of the project.

Often, you compare the NPV of a “base case” versus a “high efficiency” case to assess competing projects.

Let’s see how we do that on a simple project.  To make it easy, we’ll assume the base case costs nothing.  Thus, we only need to evaluate an incremental cost and the associated savings.  Here’s what we’re working with:

  • Project Cost                             $100,000
  • Annual Energy Savings         $   15,000
  • Project Useful Life                              15 years minimum
  • Cost of Capital                                       5%

Now, you will note that the simple payback is almost seven years, so this project will get shot down in plenty of shops.  But imagine we have a real savvy  CFO who evaluates all investment opportunities in terms of the value placed on capital – in this case 5%

At this point, a little simple math is in order.  Note that while we are doing the math, tables are widely available (or can be easily be created in a spreadsheet) to make this evaluation methodology almost trivially simple.

We recall that the future worth (F) of a current investment (P) at interest rate “r” at year “y” is expressed simply as:

F = P * (1 + r)^y

So, for instance, $100 invested today at 5% interest will in five years have a value of

$100 * 1.05^5 = $128.

To get present value of money in the future, we just massage our equation to get:

P = F / (1 + r)^y

or

P = F * (1 + r)^-y

So, if my cost of capital is five percent, $100 in savings five years from now has a present value of:

$100 * 1.05^-5 = $78

Okay, that’s all we need.  Let’s look at our project.

5% Cost of Capital
$15,000 Annual Savings in Today’s Dollars
$100,000 Capital Cost
Year PV Factor Present Value
0 1.00 ($100,000)
1 .095 $14,286
2 .091 $13,605
3 0.86 $12,958
4 0.82 $12,341
5 0.78 $11,753
6 0.75 $11,193
7 0.71 $10,660
8 0.68 $10,153
9 0.64 $9,669
10 0.61 $9,209
11 0.58 $8,770
12 0.56 $8,353
13 0.53 $7,955
14 0.51 $7,576
15 0.48 $7,215
Total  10.38 $55,695

As you can see, this project delivers a positive net present value.  And from our savvy CFO’s perspective, carrying out this project is equivalent to putting $55,695 in the bank.  Thus, the project would be approved despite the nearly seven year simple payback.  In this case, the simple payback is a little too simple to identify the investment opportunity.

You should note that, in theory, even a net present value of just $1 can justify a project, since that is still a benefit over doing nothing.  As such, the magnitude of the NPV allows you to sort through a batch of attractive investment alternatives, but if they all have positive NPVs, they are all good investments.  You are simply picking out the best of the best.

One final note.

You don’t have to make a table for an investment that delivers uniform returns year after year.  Instead, you can calculate the present value of an annuity over y years at discount rate r as:

P = 1/r * (1 – [1 / (1 + r)^y])

This formula would calculate a value of 10.38 for 15 years at 5% for our example (again, you set this up in a spreadsheet once and you are done) which leads to:

NPV = ($100,000) + 10.38 * 15,000 = $55,695

Which is quite a bit simpler than bothering with tables all the time.

Hopefully this makes a plausible argument for net present value as a preferred metric when evaluating energy investments.