Argentum Solutions, Inc.
Sterling guidance on corrosion and materials degradation
| Potential-pH Diagrams |
 |
|
| Intelligent Tools |
 |
|
 |
|
 |
|
| Corrosion Calculator |
 |
|
| Corrosion Economics Estimator |
 |
|
|
David C. Silverman |
|
Corrosion has costs. Mitigation of corrosion has costs. Alternative approaches to circumventing corrosion have costs that vary with approach. Unless the business makes a profit from corrosion protection, very rarely are corrosion costs offset by income. While corrosion technology can address which technique or material can prevent corrosion, it cannot address which technique or material makes most economic sense in the given situation. Sometimes the most corrosion resistant material or best corrosion inhibition technology does not make the most economic sense. In fact, doing nothing has sometimes made the most economic sense. Money is the resource that pays these costs. Business success requires the effective use of all resources including money. Using the time value of money concepts is the easiest way to assess the economics of corrosion-related alternatives. Money has an intrinsic value. As such it has a value today called the Present Value (PV) and a value at some point in the future called the Future Value (FV). The value of money lies in its ability to be used to benefit the owner. But, using money has a cost. This cost is the amount of additional dollars that could be earned by investing that same money so that someone else could use it to benefit them. That cost is the interest rate (i) or the value that the other individual places on the money for his/her use. From a purely economic view the maximum benefit would be achieved when the future value is maximized independent of the way it is reached. The future value of the two benefits after the length of time the money is in use (n) would have to be compared to determine the best economic use. The future value of the "loan" is calculated by  (1)This future value would be compared to the future value calculated for to benefit to the user. The approach with the higher future value is the best economic choice for the number years the money is in use (n). Usually when trying to compare corrosion mitigation or equipment replacement costs, the future value (cost) is known and the question that must be answered is What is the value in today’s dollars of a sum of money to be spent (or received) in the future?. A comparison of the future value in today’s dollars provides one economic comparison among choices. The question is nothing other than reverse compounding. Instead of an interest rate, one uses the discount rate. The equation that expresses the relationship is  (2)In equation (2), the variable i is the discount rate. It can be defined as the rate of return available on an investment of equal risk to that investment choice that is being discounted back to a present value from a known future value. Again, the compounding period is n. Corrosion mitigation or equipment replacement alternatives normally require more than one payment. One must consider the lifetime costs to get a true picture of actual expenditure. Such costs can include testing, capital expenditure, maintenance, repair, and depreciation of capital (a credit). Some costs are one time costs (capital or isolated repairs) and some are periodic (maintenance and some types of repair). Maintenance can be considered a periodic cost since often it can be budgeted on a yearly basis. Equations (1) and (2) may only have to be used once for single expenditures. But, for periodic expenditures they would have to be used on a yearly basis with the variable n changing depending on the year. The future value for a series of such constant periodic payments (PMT) can be written as  (3)where n is the total time for the payments and t is the time at which each payment is made. In equation (3) each payment is assumed to occur at the end of each period. FINCALC makes this assumption as well for this type of payment. This equation simplifies to the following  (4)Equation (4) can be used to determine the future value of series of equal payments (or income) for a time period n at an interest rate i. Equation (4) is negative when the payment signifies monetary outflow. They will often appear as negative values in FINCALC. One is usually interested in the present value of these periodic payments in order to compare costs. Since equation (2) would be used a number of times, the present value of a series of periodic future payments can be written as  (5)where n is the total time for the payments and t is the time at which each payment is made. In equation (5) each payment is again assumed to occur at the beginning of the period. This equation simplifies to the following  (6)Equation (6) can be used to determine the present value of series of equal payments (or income) for a time period n at an interest rate i. Equation (6) is negative when the payment signifies monetary outflow. An additional method for comparing value is to transform the present value into a stream of equal payments with time. This transformation can be useful when, for example, a capital expenditure for new equipment is being compared to periodic maintenance and repair of an existing facility. The equation to use is equation (6) transformed so that the payment is a function of the present value as  (7)Once again, this function is usually negative in corrosion-related problems because the payments are an outflow, not an inflow. 2. Application to Corrosion Economics Equations (1) - (7) apply individually to a single cash flow. In corrosion economics the cost of corrosion is comprised of multiple cash flows. Research, development, and testing for the project can occur before and even while capital expenditures are made. Maintenance can begin at some point in the future once capital is in service. Periodic and isolated repairs occur. Periodic maintenance and repairs can be budgeted to grow with time. Tax deductions occur yearly and are a credit against costs. Finally, at the end of the project, the equipment might have a salvage value (credit) if not all of the value has been eliminated by depreciation. The depreciation schedule itself may or may not last the lifetime of the equipment. The schedule may change with time. The result is uneven cash flows. But, the equations can be used together to construct these complex cash flows. FINCALC operates in that manner. Each item is treated as a separate cash flow. The present value of each item is be determined individually for a number of values of the discount rate. Since all present values are on the same basis, they are summed to get the present value of the entire project. Finally, that sum is annualized into a set of equally spaced payments for further comparison.Following is a simple example of how the equations can be joined to provide the needed information. Suppose one has an existing steel vessel which has to be replaced because of corrosion. A new vessel from steel would cost $10000 but would probably require maintenance and repair starting in the second year of $1000 per year. The vessel would last five years and would be replaced in kind. That vessel would have the same maintenance schedule. Neither vessel would have a salvage value. A 304ss vessel would cost $30000, would not require maintenance, and would have a salvage value of $5000. It would last 10 years. The question is which option is better. The discount rate is 8% and the tax rate is 48%. A simple straight line depreciation is used. FINCALC give the option of two schedules, the simple straight line or a 200% declining balance reverting to a straight line. Carbon Steel Vessels Present Value of first Vessel = -$10000 (Assume the capital payment occurs at the beginning of the first year) Present Value of Simple Straight Line Depreciation = $3833 Each year $2000 can be depreciated (($10000-0)/5). Since this amount is a tax deduction, its value is actually 48% of $2000 or $960 per year. This $960 is like an annuity paid out over 5 years. 
Present Value of Maintenance = -$1595 Assume the payment stream starts at the beginning of the second year. It runs for 4 years. The present value at the beginning of the second year is 
(Note that since the costs are a tax deduction and that deduction becomes a credit.) PV2 is actually the future value at the beginning of year 2. The present value at year 1 is needed. For this case,  .
The total present value of the first vessel = -$7762. The second vessel is identical to the first vessel except that this -$7762 is the future value at the beginning of year 6. Equation (2) with n equal to 5 is used to find this value at the beginning of year 1. In addition, while the maintenance is identical to the that of the first vessel, it must be discounted back to the beginning of the first year. The total present value for the second vessel is -$6368. The present value of the entire carbon steel option is the sum of these two or -$14130. Stainless Steel Vessel Present value of stainless steel vessel = -$30000. Present Value of Simple Straight Line Depreciation = $8052 Each year $2500 can be depreciated (($30000-$5000)/10). Since this amount is a tax deduction, its value is actually 48% of $2500 or $1200 per year. This $1200 is like an annuity paid out over 10 years. 
Present Value of Salvage = $2316 At the end of 10 years, the vessel is sold for scrap for $5000. It has a future value at the end of 10 years of $5000. Equation (2) with n equal to 10 give the present value . The present value of the stainless steel option = -$30000+$8052+$2316=-$19632. This value is greater than the carbon steel option so from an economic standpoint, the two carbon steel tank option is the better choice. Equivalent Annual Cost The present values of the two options can be converted to an equivalent annual cost over the 10 years by equation (7) where the interest is 8%. 
Carbon Steel = -$2106 Stainless Steel = -$2926 This example is fairly simple but gives a flavor for the calculation. It does not take account of research, development, and testing to determine the best way to maintain the steel or to determine that 304ss does not corrode. It does not make provision for isolated repairs that could be more likely with steel. It does not make provision for other possible expenses, or leakage or loss that might occur with the less corrosion resistant material. FINCALC itself allows for a limited number of such options. Previous Page: Using FINCALC-a step-by-step procedure |
|
David C. Silverman, Ph.D. - Primary Consultant |