YOUR PIPE RENEWAL CIP, PART 2: THE SANDS OF TIME Ken Harlow, Director of Management Services, Brown and Caldwell In Part 1 we considered a problem pipe with observed defects. We decided that it would be in the community s interest to renew this pipe through spot repairs, but if more costly measures were required the case might be otherwise. But we also identified some deficiencies in the methodology we used. The most serious (at least the one I went on the longest about) was that we didn t consider the time value of money. In this part we ll explore the time value of money and then take another look at our problem pipe to see if our plans should be changed. We're going to get a bit technical here, so be patient. If you take the time to plow through the next section, you'll find that applying time value of money principles to our pipe example is quick and easy. In this part we ll explore the time value of money and then take another look at our problem pipe to see if our plans should be changed. The Time Value of Money Investment is what utility managers do every day, as surely as if they were fund managers, oil drillers, or aircraft makers. They spend community money to gain future benefits for the community. The observation seems basic and obvious, but it is surprising how few utility managers ever see their work in this light. Every time we spend money, whether building a new treatment plant or greasing a machine, we expect (and if we re smart we require) that the benefits gained will outweigh the costs just as in any other business. Otherwise, we re hardly bringing value to our community. We need to remember, of course, that both costs and benefits are very broadly construed to include not just direct financial impacts but other community impacts as well. This means we need a benefit/cost analysis to ensure value. But we typically invest now for future benefits. But how do we compare today's outlay with tomorrow's benefits when we know very well that future events are less important than things happening right now? The question is appropriate and, fortunately, has an answer. Conceptually, we (or our community) has a required rate of return. An investment yielding less has no attraction. An investment yielding more will be very interesting. Most public utilities consider their required rate of return to be their cost of long-term borrowing (say, 20-year bonds). The idea, of course, is that if they can use somebody else s money at 5% and earn 6% by investing it in their assets, the community comes out ahead essentially for free. - 1 - Investment is what utility managers do every day, as surely as if they were fund managers, oil drillers, or aircraft makers.
Example 1: The grasshopper and the ant. We have deposited $1,000 in a savings account earning 4 percent annually. How much will we have in the account after ten years? Let s do the numbers. The formula for the future value (FV) of an amount earning compound interest is: Future value = Present value x (1 + Interest rate) Number of years Substituting the actual numbers for the elements of the equation: Future value = $1,000 x (1 +.04) 10 After ten years we will have $1,480.24 in our savings account. Example 2: A bad investment. If we invest $1,000 dollars today, we will receive $1,480 ten years from now. Is this a good investment at our required rate of return of 5.5 percent? Let s do the numbers. The formula for the present value (PV) of a single future cash flow is: Present value = Future value (1+k) Number of years where k is the required rate of return. Substituting the actual numbers for the elements of the equation: Present value = $1,480.24 (1 + 0.055) 10 From this formula, the PV of the future cash flow is $867. In other words, we are being asked to invest $1,000 in return for an amount that, today, is worth less to us than $1,000. The investment is not a good one for us. Single payments So let s get started. Example 1 at the left shows something we all know the effect of compound interest. We put money in the bank and it earns interest, and the interest earns interest. Rather slowly these days to be sure, but it does happen. If our required rate of return is 4% as shown, and somebody says, You can have $1,000 today or $1,480 ten years from now, we will be indifferent. One will be as good as the other to us (assuming that we have no immediate need for the money, total faith in the other party, and so forth). We will immediately pay $1,000 for a higher future payment and just as readily reject a lower payment. But what if somebody makes us exactly the same offer, but our required rate of return is 5.5%? In the first case we asked, What is the future value of $1,000 10 years from now at 4%? In this case, we simply turn the question around and ask, What is the present value of $1,408 10 years from now at 5.5%? The term present value, or PV, is simply the value today of some cost or benefit in the future. Similarly, we turn the equation around and instead of compounding the interest we decompound it as shown in Example 2. And we find that the most we are willing pay today for the $1,408 that we will receive 10 years out, at our required rate of return of 5.5%, is $867. So paying $1,000 is not for us. And that s really all there is present value, at least in principle. In finance-speak, to bring a future value back to the present as in Example 2 is to discount it. Thus the terms discounted cash flow (or DCF) analysis and "discount rate" for the rate at which the discounting is done. Not very complex or mysterious. Annuities There is one more thing that s useful to know a kind of shortcut, actually. We are often faced with investments that yield similar costs or benefits over a number of years. Examples might be reduced maintenance costs, lower energy consumption, a long-term continuing reduction in spills, and so forth. If we ignore inflation, those benefits can often be seen as level cash flows or, again in finance-speak, an "annuity." We can see that calculating the present value of each of (for instance) 20 years of savings would be more than a nuisance if we proceeded as above. But if we consider the savings as an annuity, things get a lot simpler. - 2 -
So our shortcut is to calculate the present value of a level series of future costs or benefits in short the present value of an annuity all at once. This can be done by a rather complicated formula or, much more easily and quickly, with Excel's annuity functions. Example 3: Investing to avoid costs. A new pump is expected to save $1,000 a year in energy and maintenance costs over its 20-year life. What is the value of those savings today if our required rate of return is 5.5 percent? Let s do the numbers. We know that the payment (Pmt) is $1,000, the number of periods (Nper) is 20, and the required rate of return (Rate) is 5.5%. We need to solve for the present value (PV), which uses, by more than mere chance, Excel s PV function. Using Excel s help screens, we find that the proper format is PV(rate,nper,pmt,fv,type). The last two entries are not in bold so they aren t required (and we can just ignore them here). So we click on a blank cell and type in =PV(.055,20,1000). We hit the return key and see: -11950.38 The amount looks reasonable, but it s negative. What s up? Excel is simply analyzing the annuity as an investment. It s saying, A 20-year annuity consisting of inflows of $1,000 a year at a required rate of return of 5.5% is worth the investment (i.e., an outflow) of $11,950.38 today. To Excel, inflows are positive (they add to our checkbook balance) and outflows are negative. They always balance one another in annuity analysis. When we think about it, this makes sense. In the case at hand, we now know that we are justified in spending up to $11,950 more for the new pump to achieve the savings anticipated. In the example at the left, we look at the PV (present value) of 20 years of anticipated cost savings over the life of a pump. The pump certainly seems attractive, but we need to know if its benefits are worth its higher price. The simplest way to approach this is to calculate the PV of the savings to us, given our required rate of return, and then to compare the result with the added cost of the pump. We obviously want the PV of the savings to exceed the added cost. In this example, it is exactly as if somebody has offered us an iron-clad promise of $1,000 a year for 20 years. If our required rate of return is 5.5% and the price demanded is $11,950, we will be "indifferent" and say, "I really don't care either way." If the price is lower, we will accept the offer. If higher, we will reject it. Note that there are always four values associated with an annuity: the present value or value today (PV), the discount rate (rate), the number of periods (nper), and the periodic payment (pmt). Excel will solve for any of the four if the other three are known. For example, if we were offered a choice $10,000 today or $1,000 a year for 10 years, we d readily take the $10,000 now because we could then invest it in something that might earn a return. But if our required rate of return were 5% and we were offered $1,400 a year, we could use Excel s PMT function and quickly calculate that we are indifferent between getting $10,000 now and $1,295 a year for 10 years, so $1,400 a year sounds pretty good. In fact, we could use Excel s RATE function and find that our actual return would be 6.6%, enough to put a smile on our face. This last example will be of some importance later. We will use the PMT function to convert a one-time capital investment yielding benefits over a certain number of years to an equivalent annual capital cost of ownership that can be compared with annual benefits to help in our analysis. Two other things and then we can move on. 1. In annuity calculations, we usually need to exclude any component for expected inflation. An inflationary component is always part of our actual borrowing rate because lenders need to be sure that the payments they receive will give them some profit over and above the loss of buying power of money over time. In annuities, though, we often intentionally - 3 -
exclude inflation to keep things simple and the cash flows level. If so, we need to exclude it from our required rate of return as well and base our discount rate instead on the socalled "real cost of money" without inflation, which has historically been between 3% and 3.5%. 2. We often overestimate benefits for a number of reasons that all of us know or can imagine. This is true in all businesses, so most establish an investment "hurdle rate" well above their cost of money. This discounts future benefits more severely. Hunter Water in Australia, for example, normally uses a discount rate of 7%. Since the uncertainties are quite pronounced when we deal with pipes, we'd better keep this in mind. We often overestimate benefits for a number of reasons that all of us know or can imagine. Let's Revisit our Pipe Now let's take another look at our problem pipe from Part 1. This time we'll take the time value of money into account and see if it changes anything. Here's a repeat of what we know about this pipe: Cost of failure This is an 8-inch residential area pipe without too much consequence. We estimate the cost of failure at $20,000 including community costs. Probability of failure Our pipe people's consensus is that the pipe has a 10 percent chance of failure over the next 10 years and is almost certain to fail within 40 years. Cost of renewal We can renew this pipe in either of two ways: First, spot repairs at $5,000 with a useful life of 20 years; second, relining the pipe at $25,000 with a useful life of 40 years. Both these costs include, of course, community costs. A simple approach We know we want to perform a benefit/cost analysis of renewing this pipe. So let's start with the benefit, which is the avoidance of the community's costs arising from the potential failure of the pipe. Since we re about to calculate a present value, we first need a discount rate. We know that our pipe experts are a conservative lot and may well be painting a grimmer picture than actually exists. That means that the risk costs, and thus our renewal benefits, may be overstated. Even without this, we know that there is a lot of uncertainty in their estimates. So we'll go a bit high and use a 5% hurdle rate as our discount rate rather than our real cost of money of about 3%. Now we can proceed. Since the pipe is essentially certain to fail within 40 years, we might well set the most likely failure of this pipe at 20 years out. The cost of failure is $20,000. The present value of a $20,000 benefit to be received 20 years from now at our 5% hurdle rate is $7,538 per Example 2 above. Thus the benefit of renewal is $7,538. The cost of renewal via spot repairs is $5,000, so that seems quite worth doing. Relining will cost $25,000, so that s not a good idea at all. Verdict: Do the spot repairs immediately. - 4 -
An annuity approach The simple approach above doesn t take into account that relining will yield benefits for longer than spot repairs. Maybe using an annuity approach will help with that. Based on our pipe people's consensus is that the pipe is almost certain to fail within 40 years, there is on average a 2.5% chance of failure each year. So the community's risk exposure is 2.5% of $20,000 each year, or $500 per year. Yes, this still seems a clumsy way to look at risk and ignores some of the detail in our pipe people s consensus, but we'll address that in Part 3. If we renew the pipe, the benefit is the avoidance of this $500 per year cost for however many years the renewal is effective. In other words, the benefit is an annuity. Now we have two analyses to do, one for spot repairs and one for relining. Excel gives us our answers very quickly, just as in Example 3 above: The benefit of spot repairs is a 20-year annuity of $500 per year (20 years because that s how long spot repairs will have a benefit). That's worth, today, $6,231 at our hurdle rate of 5%. Since that's more than the $5,000 cost, the spot repairs still look like a good investment. The benefit of relining is a 40-year annuity, again of $500 a year. That's worth, today, $8,580, so relining brings quite a bit more benefit than spot repairs. However, we have to pay $25,000 for that benefit. Not a good idea. So once again spot repairs look like a good investment. We re gradually gaining a bit more faith in our analysis (although some rough edges still remain). Stay Tuned... We're way beyond the matrix now and maybe even closing in on the "truth," even if some more work still lies ahead of us. In Part 3 we'll deal with that pesky issue of how to deal with pipe failure probabilities and expected failure costs. Are they really level from year to year? Somehow that doesn't seem quite right. Exploring this issue will show us something else we may be able to start to puzzle out not just whether and how to renew the pipe but when to do it. A hint: It may not be when we think! We're way beyond the matrix now and maybe even closing in on the "truth," even if some more work still lies ahead of us. Until next time. Interested? Bookmark Ken Harlow s Asset Management Page: http://www.bcwaternews.com/assetmgt/ - 5 -