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Comment PDF Business & Economics

Cost Engineering: Time Value of Money

By Alfred Chiu |

Deciding whether to put a project on the fast track entails risks. Some observations are presented here to help minimize risks and maximize profits


cost engineeringTime is money!” my mother used to tell me, whenever she caught me reading comic books or staring at the TV. That was the warning for me to get back to doing something with monetary or socially redeeming value. My solution to this problem was to do the required tasks as quickly as possible. I guess that is why today, I want to run all of my projects on a fast track. I want to have that extra time, to go back to reading.


Of course in the grown-up business world, more time to sit around is a poor reason for putting a project on the fast track. A better justification is needed for the potential added expense and the certainty of increased risk of taking that route. The question that must be answered is how much “time” is really worth for each project. How much can one save by completing a project sooner or, alternatively, starting a project later to achieve the same end date.


The answer to these questions began to appear at the end of the 1800s [1]. A method that is known today as net present value (NPV) was developed, which finally allowed engineers, businessmen and government agencies, to quantitatively evaluate the financial merits of a project. This was a very important step because it became possible to determine which competing projects deserved to be developed and which ones can be set aside until the underlying business conditions improved. Embedded in this method was the recognition that “time has an economic value,” the importance of cash flow, and the effect of depreciation and taxes [2].


This article addresses only the issue of economic value. A couple of simplified examples of the impact of a fast track execution are included. The other issues of cash flow projection and accounting chicanery relating to tax laws are equally important, but not addressed here.


Using NPV calculation, it is shown that a fast-track project can achieve a small percentage savings in project execution. However, where an opportunity exists, the early completion of a project can have huge positive impact due to the positive cash flow that can be obtained from the operation of a new unit.


 


What is net present value?


The method of net present value (NPV) is a deceptively simple quantification using a formula whereby the cash flow for a project is “discounted” as it takes place over the life of the project. Cash flow that occurs today is counted at face value, whereas, cash flow that occurs some months or years from today would be discounted by multiplying it by a factor that is derived from the effect of interest rate compounded over that time span. This can be expressed as Equation (1):


CE_1217_FR4_GSO_Eq1  (1)


 


Where:


PV = present value; equivalent cash flow in the current period n = 0


F = cash flow occurring in the future after n periods


i = periodic interest rate


n = number of periods counting from present, 1 to the future, n


[Note: Equation (1) is based on cash flow occurring at the end of each period. The same formula can be used for beginning period cash flow, as during project execution by substituting the exponent for a given period with “ n – 1” instead of “ n”].


The NPV of a project is then simply a summation of the cash flow from those periods representing the service life of the project:


 Print  (2)


 


The reader will note that this discount factor is nothing more than the inverse of the periodic interest compound factor. If one were to consider the PV as a bank deposit, multiplying it with the compound interest factor yields the future value of that deposit.


For a project that required an investment of capital today, the investor first suffers a negative cash flow up through the start of period n = 1. For a large multi-year project, the required cash flow during project execution can increase the cost by several percentage points due to inflation. Project budgeting accommodates this by including an escalation factor into the cost estimate.


Assuming that the project is a wise decision, the future cash flow will pay back the investment with interest. That is: the net present value is a positive number, and hopefully a rather large one.


This article does not dwell on the art of cash-flow projection for a project other than to note that it is somewhat akin to fortune telling. I am sure that there is a book deal in there if one looks hard enough.


 


What interest rate to use?


The decision on the value of the periodic interest rate to insert into the Equation (2) is a critical one to be made by corporate management. This is a determination of what it will cost the company to secure the funds for the project. A high interest rate means that only the most profitable projects will be able to demonstrate financial profitability. On the other hand, if an overly optimistic interest rate (that is a low value) is used, then investments would be made in projects that will not return a profit. Grant notes that frequently, the calculation is made with an interest rate that is too low [ 2].


At a minimum, the interest rate used should be higher than the general market cost of borrowing. It should take into consideration the cost issuing the debt instrument. Other factors that go into determining the interest rate include: the financial condition of the company, the state of the world economy, the monetary policy of various central banks in the world, the micro economics of the specific market segment, the demographics of market place and so on. If the reader concludes that this, too, is like fortune telling, well, it may be. Regardless, it behooves the business team to make a thorough review of the selection process. Even if a company is well funded with cash, the use of the cash should be an equivalent market-based decision. As the saying goes, “You don’t want to throw good money after bad.”


Once the interest rate is determined, it is important to perform a sensitivity analysis to see how varying the interest and projected cash flow will impact the project profitability. This exercise would be part of the risk analysis prior to the project investment decision and continually updated over the life of the project.


 


Two examples


Comparing two projects with different start dates.Example One illustrates the principle of time value by comparing two projects — Case 1A and Case 1B — with identical costs and required completion date. In Case 1A, the project is completed in 30 months. In Case 1B, the same project is completed in 22 months. Due to the shorter time required to execute the project, Case 1B shows a delayed start time that is eight months later than Case 1A. To simplify this discussion, during the execution phase of both projects, all cash flow is uniform over time. In actual practice, most projects are heavily front-end loaded due to the need for material acquisition and other contract commitments. This aspect favors delayed project start. Another simplification is to leave out the impact of inflation. During periods of abnormally high inflation, it may be beneficial to spend the cash on a project as early as possible. In those circumstances (example circa 1981), business decisions on investments are very complex and cannot be addressed in this short article. The use of a spreadsheet allows the inflation impact on future costs to be easily included. The effect on both cost and cash flow can be accommodated by the predicted inflation rate for that period. The caution here is that simple does not necessarily equate to accurate.


The results of the calculations for the two cases, carried out in an Excel spreadsheet, are shown in Table 1. It can be seen that by delaying the start of the project, there is a net present value benefit of $10 million. The negative sign is for cash flow for the project during execution phase. While this is a relatively small amount in the total cost of the project, the reader is reminded that 1) it can represent more than 20% of the project home office and startup cost; and 2) the effect of delaying the expenditure of $80 million over the first eight months can be significant in business cash flow management.


t1


Comparing two projects with different end dates. Example Two illustrates the hidden time value of money for two projects with identical costs and start dates, but with one (Case 2A) having a 30-month duration and one (Case 2B) having a 22-month duration.


The same assumptions are used as in the previous example (Case 1A and 1B). In addition, a positive cash flow based on an investment capital amortization period of 36 months, at 15% interest, is added after project completion. With eight months of early cash flow, the shorter schedule project has an advantage over the longer duration project by more than $54 million. Even though the higher rate of expenditure is required for the shorter schedule, the early cash flow during the execution phase is more than offset by the following eight months of early operation (Table 2).


 t2


Final remarks


The above discussion of NPV shows it can be a useful tool to quantify the relationship of cash flow and the time when it takes place. But one must remember the most important rule of engineering: “garbage in = garbage out.” The simple Equation (2), consisting of two variables, has embedded in both variables a myriad of complex assumptions. These should be tested with sensitivity analysis prior to and during the execution phase of the project. A positive note of project acceleration is the fact that the overhead burden on a project is largely a function of the execution duration. If the schedule is reduced by 25%, it is very conceivable that the overhead burden will also come down accordingly, thus offsetting the cost of labor overtime.


 


References



1. Jones, T.W. and Smith, J.D., An Historical Perspective of Net Present Value and Equivalent Annual Cost, The Accounting Historians Journal, Vol.9, No. 1, 1982, pp. 103–110 (www.jstor.org/stable/40697714).




2. Grant, E.L., Ireson, W. G., and Leavenworth, R.S., “Principles of Engineering Economy,” 7th ed., J. Wiley and Sons, New York, 1982.



Author


IMG_0274Alfred Chiu is a project manager with S & B Engineers and Constructors Ltd. (7825 Park Place Blvd. Houston, TX 77087; Phone: 713-845-4156; Email: achiu@sbec.com). Chiu is a registered professional engineer in the state of Texas. He received his B.E.Ch.E. degree from the City College of New York, and an executive M.B.A. degree from the University of Houston. Chiu has 39 years of experience in petroleum refining, chemicals and water processing. Before joining S & B, he worked for Union Carbide Corp., Lummus Co. and Stone and Webster Engineering Corp.


 


For additional articles on cost engineering, see Part 1, “Integrating Technology and Economics,” on pp. 35–46, as well as others in the CE archives at www.chemengonline.com (for example, Considerations for Estimating the Costs of Pilot-Scale Facilities, Chem. Eng., December 2016, pp. 38–46).

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