USING LIFE CYCLE COSTING AND SENSITIVITY ANALYSIS TO SELL GREEN BUILDING FEATURES

Transcription

1 USING LIFE CYCLE COSTING AND SENSITIVITY ANALYSIS TO SELL GREEN BUILDING FEATURES INTRODUCTION Alan Chalifoux, P.E. 1 The title, and basic theme, of this article probably will raise the ire of many design professionals. We all know and preach that sustainable design requires an integrated design approach, and that the design works together as a whole. A sustainably-designed building cannot be cut back in piecemeal fashion and expected to provide the benefits for which it is touted. However, as design professionals we know and experience regularly the wrenching effects of last-minute Value Engineering (VE) efforts undertaken to bring a project back to within an Owner s stated budget. During the typical VE exercises, the Owner looks at (supposed discrete) elements of the design and appraises each for its cost effectiveness. The Owner scans down the line items on the Bid Tabulation (or latest design cost estimate) and asks Where can I save money? His perspective is that of someone ordering off an à la carte menu. The bottom line is simply the sum of all the elements. Ensuing discussions of the integrated design and how it cannot be violated usually end up with the Owner s glazed-over look, and his ultimate response, again, comes forward: Where can I save money? This paper describes how a little basic sensitivity analysis can be used to show the appropriateness of the original design and can stave off the often ravaging effects of the typical VE process. It also shows that such sensitivity analysis is necessary if one is to obtain a good understanding of the design options available and the relative merit of each. First, let s review with basic tools of sustainable Design: (a) Building Energy Simulation (BES) using computer modeling and (b) Life Cycle Costing (LCC) techniques. These are basic to any Sustainable Design Professional s tool kit. We will also see how the two of these are used in conjunction with each other to create a BES/LCC model that allows one to quantify design decisions. Owners are not familiar with BES, LCC, or the combination of these into a BES/LCC model, certainly not to the degree that design professionals are. Owners need to be educated in all these areas so that they can be made aware of the value of green design. BUILDING ENERGY SIMULATION (BES) VIA COMPUTER ANALYSIS The mathematics associated with accurate calculation of expected energy usage in a building is not trivial. We are all familiar with simple methods of determining energy savings associated with specific energy conservation techniques. The basic methodology used in simple methods is to assume a certain power draw for what one describes as the baseline technology and a certain power draw for the alternate technology. One then assumes/approximates the hours that the energy consuming equipment operates over the course of a year. The cost of energy is then applied, yielding the basic equation: (E Baseline E Alternate ) * (Operation Hours/Year) * (Energy Cost) = Energy Cost Savings/Year Units common to this calculation are: [kwh kwh] * [Hours/Year] * $/kwh = $/Year Where: E Baseline = Energy Consumption of Baseline Technology E Alternate = Energy Consumption of Alternate Technology While this method provides a quick, simple means of obtaining a rough estimate of energy savings potential, it does not provide any real approximation of the physical processes involved in building energy usage. 1. Eta Engineers, LLC., Mr. Chalifoux may be reached at (217) or alan@etaengineers.com. Volume 1, Number 2 39

2 BES is generally recognized as providing the best means of comparing the energy ramifications of building design alternatives. The physical processes by which heat migrates into, or out of, today s buildings, or the ways that heating/cooling are produced from fuel, are complicated mathematical problems requiring the solution of hundreds (sometimes thousands) of simultaneous differential equations. The computer is the only tool capable of accomplishing this task. However, BES should not be regarded as being a guarantee in predicting future energy consumption of a building. BES programs are generally organized into three major sections: 1. Building Loads, which calculates the heating/ cooling required to keep the rooms/zones at the temperatures desired by the occupants 2. Air Handling Systems ( Systems ), which calculates the energy required to move the heating/ cooling (calculated in the Loads section) around the building 3. Central Plants, which calculates the fuel required (and resultant cost) to produce the heating/cooling requirements calculated in the Systems section BES programs follow a general linear progression through these three sections, iterating within each section to calculate results for that section. Results from Loads are passed onto the Systems section, and results from the Systems section are passed onto the Central Plants section. Results from the Central Plant section are output to show the BES User how much it will cost to operate the building. The Loads input in a BES model starts with entering the physical geometry of the building: wall areas and respective orientations (N, S, E, W, etc.), window areas and orientations, roof areas and slopes, etc. One also enters the physical construction of each of these elements, layer by layer (the wall sections, roof sections, etc.) and the optical properties of the glass. Most BES programs will have libraries of common building materials as well common built-up wall sections (e.g., 2 4 wood stud wall with clapboard siding on the outside and sheetrock on the inside). Once the physical geometry is entered, the next step is to enter the Internal Loads, i.e., lights, people, and office-type equipment in each room or zone of the building. It is here that the BES user often has to make numerous assumptions regarding occupancy. While building codes will often dictate the maximum occupancies that one must design for, the average daily occupancies and schedules generally can never be known ahead of time; one must make assumptions regarding these. Under the Loads section, the BES User also enters some basic information about the desired temperatures in each room/zone of the building (room setpoints ). The BES User also enters infiltration rates (air leakage into a building) in this section. Infiltration is one of the least understood and difficult-to-quantify aspects of building energy use. As such, this data entry incorporates a lot of assumptions on the part of the BES User. The BES User then moves onto entering Systems data. Here again there is ample room for interpretation on the part of the BES User. Specifically, there is often ample leeway for interpretation regarding the control of the Systems equipment, i.e., how it is turned on and off, and how it is modulated in between its off position and its maximum on position. There is also quite a selection of equipment types (e.g., forward-curved versus backward-curved versus backward-inclined fans) which necessitates further assumptions. Finally, in the Central Plants section it is necessary to continue making assumptions regarding equipment type and function. LIFE CYCLE COSTING OVERVIEW Life Cycle Costing (LCC) methodology centers around one central concept: money has time value. Stated otherwise, as a general rule, a dollar received next year is not worth what that same dollar is worth today. This is due to inflation, the (often unfortunate) economic phenomenon that says that prices will rise. Next year s dollar will not buy as much as today s dollar will. The following discussion provides a primer on cash flow analysis and was taken from the textbook Engineering Cost Analysis (Collier and Ledbetter 1982, Harper & Row Publishers). Money can be owned. It can be rented, too. The rental fee is called interest. Any purchase (or savings) that occurs over time will likely have an associated interest rate, since the money used for the purchase (or deposited into a savings account of some sort, and used by someone else for a purchase) is rented. Calculating the amount money garnered/disbursed over time due to interest is basically what LCC methodology does. 40 Journal of Green Building

3 Simple interest compounded annually is a concept that we all are familiar with. Say we borrow $1,000 at 8% interest, which we are responsible for paying in full at the end of a year after the loan is disbursed. We will pay $1,080. Example 1 $1, Principle (borrowed money) $ Interest due after 12 months $1, Total Payment due at the end of the First Year This concept becomes a little more complicated if we change the compounding period to something other than one year, say every half year: $1, Principle $ Interest earned (but unpaid) after 6 months $ Interest due after 12 months $ % times the unpaid $40.00 interest from the first Compounding Period $1, Total Payment due at the end of the First Year More elaborate calculations of interest payments are made understandable through cash flow diagrams. These diagrams present money flows on a time line, and help one visualize more complicated interest payments. The cash flow diagram for the borrower in Example 1 would look like Figure 1a. The horizontal axis shows the time period we are dealing with (one year). An arrow pointing up denotes money coming in (payments received or income). An arrow pointing down denotes money going out (disbursements). The P represents the present time, and the F is used to refer to time in the future. One can see that the future payment includes the original $1,000 borrowed as well as the $80.00 due in interest. Also, common parlance in LCC uses i to denote interest rate and n to denote number of completed borrowing periods. The lender s cash flow diagram for Example 1 would look the opposite of the borrower s cash flow diagram. It would show $1,000 cash paid out at time zero, and $1,080 coming back in at the end of year 1. This is illustrated in Figure 1b. Let us now look at cash flow equivalency in Example 2. In this example we extend the repayment period of Example 1 out over four years at the same interest, with an annual compounding period (n = 4), and different plans for payback of principle. The cash flow analysis and cash flow diagram shown in Figure 2a would result for a plan that had the borrower paying back the principle at the end of the loan. One can take the same set of terms as shown in Figure 2a and change the schedule for payback of principle so that there will be an equal payment of FIGURE 1A. Example 1 cash flow diagram: Single lump sum payment, borrower s perspective. Volume 1, Number 2 41

4 FIGURE 1B. Example 1 cash flow diagram: Single lump sum payment, lender s perspective. FIGURE 2A. Example 2 cash flow diagram: Single lump sum principle payment, borrower s perspective. FIGURE 2B. Example 2 cash flow diagram: Equal principle payments, borrower s perspective. 42 Journal of Green Building

5 FIGURE 2C. Example 2 cash flow diagram: Single lump sum principle + interest payment, borrower s perspective. principle (i.e., $250) at the end of each year. The cash flow diagram shown in Figure 2b results. Finally, one can take the same borrowed principle as shown in Figure 2a, and set the payback terms such that there will be a one and only payment of principle and accumulated interest at the end of the loan period. This yields the cash flow diagram shown in Figure 2c. The three preceding cash flow diagrams are equivalent to each other. What this means is that the $1,000 in hand today is equivalent to any of the three repayment schedules. This is the power of constructing cash flow diagrams; it allows one to compare financing alternatives. Extending the tool of cash flow diagrams to a string of equal annual payments allows one to calculate the present worth (the value in today s dollar) of a series of annual payments. The formula used to calculate this present worth (neglecting the intervening mathematical derivation), is as follows: P = A{[(1 + i) n 1)]/[i(1 + i) n ]} (EQN 1) Where: P = Present Worth of the Series of Payments A = Amount of each Annual Payment i = Interest Rate n = Number of Compounding Periods A generic cash flow diagram for EQN1 would look like Figure 3a. Figure 3a shows the equivalency of the future stream of payments, A, to the present single lump sum, P. We can change the cash flow diagram slightly FIGURE 3A. Cash flow diagram: Present worth of a stream of future equal payments, borrower s perspective. Volume 1, Number 2 43

6 and reverse the direction of the A arrows, while maintaining the positive direction of the arrow P, and the cash flow diagram becomes Figure 3b. This now represents the Present Value P (i.e., the value in today s dollars) of n equal annual payments at an interest rate of i. The value P is equivalent to the series of payments in the amount of A. This cash flow diagram becomes the basic means by which we execute life cycle cost analysis of green building strategies. In other words, the series of future equal annual payments A (the anticipated income stream) is equivalent to having P dollars in your pocket today. The only difference is that the future annual income stream is actually the annual utility cost savings predicted by running BES models. The Net Present Value (NPV) of any investment is the difference between today s cost of that investment, minus the Present Value of the stream of future annual payments you will receive from that investment. Casting this definition in terms of the cash flow diagram shown in Figure 3b generates Figure 4. The next step is to understand the concept of Rate of Return (ROR). Stressing this concept to building owners (and other persons with decisionmaking authority on your green building projects) is the key to obtaining their later buy-in to green design strategies. ROR is defined as the interest rate at which the future stream of payments exactly equals the initial investment required to achieve that stream. Thus, if we set the Present Worth P equal to the initial payment ( investment ) C and solve for i, we have calculated the ROR for that investment. This is illustrated in Figure 5. The initial investment C is calculated; it is the estimated cost of implementing the design strategy. We set it equal to the stream of annual payments. Math- FIGURE 3B. Cash flow diagram: Present worth of a stream of future equal payments. FIGURE 4. Cash flow diagram: Calculation of NPV. 44 Journal of Green Building

7 FIGURE 5. Cash flow diagram: Calculation of ROR. ematically we are solving EQN1 for i, given that all the other variables are known. Set C = P P = A{[(1 + i) n 1)]/[i(1 + i) n ]} (EQN 1) Where: C = Cost of Implementation P = Present Worth of the Series of Payments A = Amount of each Annual Payment i = Interest Rate n = Number of Compounding Periods One can use iterative methods to solve this equation. Most spreadsheet programs have an imbedded function that will solve for i, given all the other parameters. The last bit of terminology to master is Incremental Rate of Return (IROR), sometimes referred to as Incremental Internal Rate of Return. IROR refers to situations where the Owner is undertaking a major outlay of cash (e.g., putting up a building), and has several competing options he can finance (e.g., several design alternatives). He looks at each, calculates the incremental cost difference for each, and, given his chosen n (life expectancy of the investment), he calculates the incremental rate of return. THE BES/LCC MODEL Once the BES work is completed, its results have to be coupled with LCC to calculate the IROR of specific design strategies. The procedure to do this is as follows: 1. Define a Base Case Building. This building incorporates all design elements that the Design Professional can reasonably assume will be included in the building. Use BES to develop an annual utility cost for the building. 2. Define a set of incremental design upgrades. Assign a first cost premium to each. This is the incremental first cost associated with implementing that upgrade. 3. Using the previously developed BES model, simulate each of the design upgrades and calculate the annual utility costs associated with each. 4. Using your LCC tools ( home grown spreadsheet or professionally-marketed LCC calculators), enter the incremental first cost, the annual utility cost savings, and calculate the IROR for each design option. SENSITIVITY ANALYSIS Once the IROR for each design option is calculated, the role of sensitivity analysis often becomes clear. Sensitivity analysis can be defined as: A procedure to determine the sensitivity of the outcomes of an alternative to changes in its parameters (as opposed to changes in the environment). If a change in a parameter results in relatively large changes in the outcomes, the outcomes are said to be sensitive to that parameter. This may mean that the parameter has to be determined very accurately or that the alternative has to be redesigned for low sensitivity. ( vub.ac.be/asc/sensit_analy.html) Stated more directly about buildings: In engineering economics, sensitivity analysis measures the economic impact resulting from alternative values of uncertain variables that affect the economics of the Volume 1, Number 2 45

8 project. When computing measures of project worth, for example, sensitivity analysis shows just how sensitive the economic payoff is to uncertain values of a critical input, such as the discount rate or project maintenance costs expected to be incurred over the project s study period. (H.K. Marshall, as presented in Technology Management Handbook. Chapter 8.12, CRC Press LLC, Boca Raton, FL, Dorf, R. C., Editor, 8/59 63 p., 1999, and Engineering Handbook. Chapter 187, CRC Press, Inc., Boca Raton, FL, Dorf, R. C., Editor, p., 1996, ( We have reviewed the assumptions inherent in BES work. In addition to these assumptions, there is also a great variance in construction prices (the value C in Figure 5 above) due to the natural fluctuations in the economic marketplace. There is always an uncertainty of future interest rates. The reader can thus see that the prediction capability of any BES/LCC model is open to reasonable question. Therefore, in formulating the BES/LCC models of building design options, the designer has to try to make conservative assumptions, i.e., assumptions that do not have the potential to skew the simulation out of the realm of possibilities. Of all the assumptions made in the BES/LCC modeling, there are several that are very difficult (if not impossible) to determine: 1. Cost of utilities (electricity, natural gas, fuel oil, etc.) over the life expectancy of the design element 2. Life expectancy of the design element 3. First cost of the design element The above parameters have the potential to skew results dramatically. As such, it has been my policy to make very conservative guesstimates when entering these parameters. Specifically, unless there is compelling evidence otherwise, my company s standard analysis uses: 1. The current cost of utilities is used over the life expectancy of a project. This is conservative because it is highly doubtful that energy cost increases will match the general inflation rate. They will likely exceed general inflation. 2. The life expectancy of the design element is taken to be 20 years. This is short for many design elements. Most have appreciably longer life expectancies. This assumption is conservative in that the longer the life expectancy (n in our cash flow diagrams), the higher the IROR. 3. First cost estimations are always undertaken so that any errors will be on the high side. This is conservative in that the higher the first cost the lower the IROR. However, taking the above as our base analysis, we have had success in explaining to the Owner the conservatism of our assumptions and in performing a little sensitivity analysis to show the Owner the resulting IROR if we change some of our assumptions. THE PROCESS OF EDUCATING THE OWNER The Design Professional who focuses on sustainability has to be able to sell the product in a reasonable and quantitative sense. Start by appraising the Owner. If he (she) is talking about building sustainably, he needs to understand the value of LCC techniques. If he is locked into using only Simple Payback as his sole metric for determining suitability, he is not a candidate for developing a building that has the advantages of sustainable design. Simple Payback is a poor metric to appraise the investment one makes when constructing a building. The recurring question asked by Owners locked into the Simple Payback mentality is When do I get my money back? Responses to that question should stress the time value of money. I often respond to that question by asking the client the rhetorical question, If you invest in the [Stock] Market, do you ask when you get your money back? No, of course you don t; you want to know how well your money is working for you while it is in the market, i.e., what kind of interest is it earning for you while it is invested. Follow this reasoning with some basic discussion of the time value of money and how, as a rational person, he cannot disregard this when making decisions about his building. Also stress that he is developing a better product, and it will be more competitive in the marketplace. Once the time value of money is accepted, LCC techniques should be explained. It has been a long time since most of us have graduated college, and the formulae that were once second nature to each of us are likely to have long faded into distant memory. I have found that even the most astute commercial real estate entrepreneurs actually enjoy being taken through a brief review of LCC techniques. 46 Journal of Green Building

9 Your brief (yes, keep it very brief ) summary of the basic LCC technique follows: 1. Money has a time value. Due to inflation, a dollar tomorrow will not be worth a dollar today. 2. Cash flow analysis provides a means of appraising different options while accounting for the time value of money. Show a cash flow diagram to the Owner and refresh his memory of how one can calculate the present value of a future payment. 3. Move on to describe the next level of complexity in cash flow analysis, the present value of a stream of annual payments. 4. Show how one uses the above cash flow diagrams to calculate the Incremental Rate of Return for a building element. 5. Discuss with the Owner the rising cost of fossil-fuel based energy (e.g., utility-supplied electricity and natural gas). Let the discussion wander into the cost of gasoline; everyone can relate to this. Discuss how the cost of these energy sources will only increase over time, at a rate faster than inflation. 6. Explain what sensitivity analysis is: Investigation into how projected performance varies along with changes in the key assumptions on which the projections are based. (Source: com/4490/sensitivity_analysis.html) 7. One of the key assumptions made in using the above LCC technique is that no costs rise faster than inflation. However, energy prices will. We do not know exactly how fast they will rise, but we do know that they will rise. Explain that what happens in this scenario is that the IROR will be even higher than the value calculated using an energy cost that does not escalate faster than inflation. It is now that you pull out a graph summarizing the results of your sensitivity analysis. Show the Owner that increased energy costs will raise his IROR. This usually will help him see the benefits of your design decision. Volume 1, Number 2 47

10 As a simple example of the above, consider the situation I was presented with on an actual project. The green design to remodel an existing building included increasing wall insulation. However, once budget first costs were generated, the Owner started to question every aspect of the design, including the added wall insulation. There were two major variables in this situation: first cost variance and possible variance (increase) in the cost of natural gas. I developed a graph that showed how IROR changed with changing (first) cost of construction and higher costs of natural gas. The graph plots the IROR (of increased wall insulation) as a function of first costs, for a life of 20 years. The graph plots IROR for a foreseeable range of first costs, given that actual costs will not be known until bid day. It also generates a family of curves, each curve showing the IROR versus first costs for a particular cost of natural gas. The lowest curve shows IROR if, over the next 20 years, natural gas prices stay at the $0.90/therm the owner is presently paying. Given that this constant price is very unlikely, I increased the cost of natural gas to $1.10/therm and $1.30/therm (both still very conservative guesses given that we were using a life cycle of 20 years) and plotted the IROR for each of these scenarios. Upon review, the Owner saw his improved IROR for two very conservative guesstimates (i.e., erring on the low side) of what average natural gas prices will be. He became convinced that the wall insulation was a good investment and let it be implemented. The above simple example shows that sensitivity analysis can be used to generate a range of potential LCC and IROR scenarios. While such financial projection is never a guarantee, the Building Design Professional can present this range of scenarios to an Owner to help him develop a level of comfort in design decisions. With this level of comfort established, sustainable design can proceed past the incessant Value Engineering process. 48 Journal of Green Building