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Houston Energy Management Present Worth Factor for Single Cash Flow Excel Task

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Instructor Handout MENG 4350/5342 Energy Management Module 4 – Economic Analysis Learning outcomes Course 1. Perform economic analysis of energy management projects. Module 1. Apply concepts of mathematic of interest. 2. Use economic definitions for project assessment. 3. Evaluate projects using life-cycle cost (LCC) analysis. Learning resources Required LR-R1 Module 4 – Economic Analysis (Instructor handout) Additional LR-A1 ASHRAE Service Life Estimates (available on CANVAS) LR-A2 Life-Cycle Costing Manual for the Federal Energy Management Program, NIST Handbook 135, 1995 edition. PDF available on CANVAS. Self-assessment ✓ Develop an Excel Worksheet to reproduce the results of the problem given in the Project Assessment section of the Module 4 – Instructor handout. Note: you can get ideas of format and check your work by reviewing the instructor’s worksheet posted on CANVAS. ✓ Can you answer the following question? Q1 New equipment is required in the facility where you are working as the Energy Manager. Two options are available for consideration for the new equipment, option A and option B. Both options use the same fuel. The information known for both options is equally accurate. The administration has commissioned you to present a report on the analysis of both options. Known information: Option A: Period of analysis: 10 years (equal to the useful life of equipment) Net present value: $149,044 1 Instructor Handout MENG 4350/5342 Energy Management Option B: Period of analysis: 10 years (equal to the useful life of equipment) Discount rate: 6% Fuel escalation rate: 4% Capital cost: $50,000 Estimated energy cost: $10,000/yr (5% energy savings with respect to Option A) Estimated maintenance cost: $1000/yr One-time replacement parts needed at end of year 5th: $2,000 a) Find the net present value of Option B. b) Which option would you recommend and why? 2 Instructor Handout MENG 4350/5342 Energy Management Module 4 – Economic Analysis An energy audit leads to the proposal of energy-saving opportunities that must be both technically feasible and economically attractive. Therefore, the audit report must present the economic justification that would allow owners or administrators make the decision of its implementation. Because it is common to find multiple technologies that meet the requirements for a retrofit, and each of the different options would have different values for initial cost, operation costs, and maintenance costs, it is necessary an economic analysis to determine the benefits of each alternative to provide enough information to make the right decision. Mathematics of Interest The interest rate (𝑖) is a factor that allows for knowing the value of money over time (n, number of years). Its use however, depends on the way in which the cash flow occurs. When the interest rate is used to calculate the present value of future flows, it is called the discount rate. The use of a cash flowchart, shown below, it is helpful for a better understanding and application of the concepts relating to interest. It represents all the cash flows for each period of time throughout the life of the project. A cash flowchart takes into account incomes, which are represented by arrows pointing upwards, and payments, represented with arrows pointing down. In a cash flowchart, P represents the present flow, F represents the future flow, A represents a uniform series of flows, and G represents a gradient series of flows: Incomes (+) G A F Time P Payments (-) Simple interest: is the interest affecting only the original amount (single flow). • Capitalization factor: find F given P: F 𝐹 = 𝑃 ∙ (1 + 𝑛 ∙ 𝑖) P • Present worth factor: find P given F: P 𝑃 = 𝐹 ∙ (1 + 𝑛 ∙ 𝑖)−𝑖 F 3 Instructor Handout MENG 4350/5342 Energy Management Compound interest: is the interest applied to the original amount and any interest accumulated in previous years (single flow and interests). • Capitalization factor (F/P, i, n): find F given P: F 𝐹 = 𝑃 ∙ (1 + 𝑖)𝑛 P • Present worth factor (P/F,i,n): find P given F: P 𝑃 = 𝐹 ∙ (1 + 𝑖)−𝑛 F Uniform Series Cash Flows: is a uniform series of cash flow that occurs when cash flows are made each year and all they are for the same amount. • Compound amount factor (F/A,i,n): find F given A: F (1 + 𝑖)𝑛 − 1 𝐹 =𝐴∙ 𝑖 A • Sinking fund factor (A/F,i,n): find A given F: F 𝐴=𝐹∙ 𝑖 (1 + 𝑖)𝑛 − 1 A • Capital recovery factor (A/P,i,n): find A given P: A 𝐴=𝑃∙ 𝑖 ∙ (1 + 𝑖)𝑛 (1 + 𝑖)𝑛 − 1 P 4 Instructor Handout MENG 4350/5342 Energy Management • Present worth factor (P/A,i,n): find P given A: P A (1 + 𝑖)𝑛 − 1 𝑃 =𝐴∙ 𝑖 ∙ (1 + 𝑖)𝑛 Gradient series: is a series that occurs when the amount of flow for any period is greater than the previous flow in a constant amount. • Uniform series factor (A/G,i,n): find A given G: A • 1 𝑛 𝐴=𝐺∙൤ − ൨ 𝑖 (1 + 𝑖)𝑛 − 1 Present worth (P/G,i,n): find P given G: P • G G 𝑃=𝐺∙ 1 (1 + 𝑖)𝑛 − 1 1 ∙ቈ − 𝑛቉ ∙ (1 + 𝑖)𝑛 𝑖 𝑖 Present worth of an escalating series: find P given a growth of the annuity A1 (first year annuity) at an escalation rate e: 1+𝑒 1+𝑒 𝑛 𝑃 = 𝐴1 ∙ ቈ1 − ൬ ൰ ቉ 𝑖𝑓 𝑖 ≠ 𝑒 𝑎𝑛𝑑 𝑃 = 𝐴1 ∙ 𝑛 𝑖𝑓 𝑖 = 𝑒 𝑖−𝑒 1+𝑖 Definitions for project analysis End-of-year convention The end-of-year convention means that all cash flows occurring during a specific year are modeled as occurring at the end of the year. Discount rate As mentioned in previous equations, when the interest rate is used to calculate the present value of future flows, it is called the discount rate. In other words, a discount rate is an interest rate used to relate/discount future cash flows to the present value. In general, the discount rate considers the possible growth of available money due to earnings, the risk or uncertainty of the anticipated future cash flows, and the variation in purchasing power due to inflation. Hereafter, for previous equations, the nomenclature for a discount rate will be 𝑑 instead of 𝑖. 5 Instructor Handout MENG 4350/5342 Energy Management Inflation Inflation is a familiar concept of money value change over time. It is understood that most goods and services that are bought or received today will cost more in the future because of inflation, which also means that money loses purchasing power. Life-cycle cost (LCC) analysis can be done by considering cash flows in constant dollars (purchasing power does not change over time) or in current or nominal dollars (actual purchasing power for the year the cash flows are expected to occur in the future). The NIST Handbook 135 recommends that analysis be performed with constant dollars using two methods to arrive at constant dollars amounts in an LCC analysis: Method 1: “Estimate future costs and savings in constant dollars and discount with a “real” discount rate, i.e., a discount rate that exclude the rate of inflation.” Method 2: “Estimate future costs and savings in current dollars and discount with a “nominal” discount rate, i.e., a discount rate that includes the rate of inflation.” The following expression is used to compute the real discount rate (𝑑𝑟 ) (or interest rate) using a nominal discount rate (𝑑) and inflation rate (𝑘): 𝑑𝑟 = 1+𝑑 −1 1+𝑘 This value of real discount rate, as it is logical, must be less than the nominal discount rate because the value of money over time decreases with inflation. To illustrate that both methods yield the same present value results, Table 1 shows an example 1+𝑑 with the real discount rate (3%) found using 𝑑𝑟 = 1+𝑘 − 1 and the known nominal discount rate (6.09%) and inflation (3%). Table 1
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