Lesson 8 - Basic Methods for Making Economy Studies.pdf

Engineering Economy BASIC METHODS FOR MAKING ECONOMY STUDIES These are the basic methods or patterns for making economy studies:  Minimum Attractive Rate of Return Method  Presen...

Engineering Economy BASIC METHODS FOR MAKING ECONOMY STUDIES These are the basic methods or patterns for making economy studies:  Minimum Attractive Rate of Return Method  Present Worth Method  Future Worth Method  Annual Worth Method  Internal Rate of Return Method  External Rate of Return Method  Payback Period Method  Benefit/Cost Ratio Method 1. The Minimum Attractive Rate of Return (RoR) method The rate of return on the capital invested is given by the formula, 𝑛𝑒𝑡 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑟𝑜𝑓𝑖𝑡 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 = 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 A rate of return (RoR) is the net gain or loss of an investment over a specified period, expressed as a percentage of the investment’s initial cost. When calculating the rate of return, you are determining the percentage change from the beginning of the period until the end. Key Takeaways:  The rate of return (RoR) is used to measure the profit or loss of an investment over time.  The metric of RoR can be used on a variety of assets, from stocks to bonds, real estate, and art.  The effects of inflation are not taken into consideration in the simple rate of return calculation but are in the real rate of return calculation.  The internal rate of return (IRR) takes into consideration the time value of money The applications of RoR method is controlled by the following conditions: A single investment of capital at the beginning of the first year of the project life and identical revenue and cost data for each year. The capital invested is the total amount of capital investment required to finance a project, whether equity or borrowed. 2. The Present Worth method A process of obtaining the equivalent worth of future cash flows BACK to some point in time. If the present worth of the net cash flows is equal to, or greater than, zero, the project is justified economically. It is used extensively in making economy studies in the public works field, where long- lived structures are involved. SEA – General Engineering Department Page 1  Engineering Economy 3. The Future Worth method It is used particularly in an investment situation where we need to compute the equivalent worth of the project at the end of its investment period like in building a nuclear power plant, where it is tie consuming. In such situation, it is more common to measure the worth of the investment at the time of commercialization. It is exactly comparable with the Present Worth method except that all cash inflows and outflows are compounded forward to a reference point in time called the future. If the future worth is equal to, or greater than, zero, the project is justified economically. 4. The Annual Worth method Annual Worth (AW) Analysis is defined as the equivalent uniform annual worth of all estimated receipts (income) and disbursements (costs) during the life cycle of a project. In this method, the interest on the original investments (sometimes called minimum required profit) is included as a cost. If the excess of annual cash inflows over annual cash outflows is not less than zero, the proposed investment is justified. This method is covered by the same limitation as the rate of return pattern a single initial investment of capital and uniform revenue and cost throughout the life of the investment. 5. The Internal Rate of Return method The internal rate of return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments. The internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a project equal to zero. IRR is sometimes referred to as "economic rate of return" or "discounted cash flow rate of return." The use of "internal" refers to the omission of external factors, such as the cost of capital or inflation, from the calculation. It is important for a business to look at the IRR as the plan for future growth and expansion. The formula and calculation used to determine this figure follows. where: Ct=Net cash inflow during the period t Co=Total initial investment costs IRR=The internal rate of return t=The number of time periods To calculate IRR using the formula, one would set NPV equal to zero and solve for the discount rate (r), which is the IRR. Because of the nature of the formula, however, IRR cannot be calculated analytically and must instead be calculated either through trial-and-error or using software programmed to calculate IRR. Generally, the higher a project's internal rate of return, the more desirable it is to undertake. IRR is uniform for investments of varying types and, as such, IRR can be used to rank multiple prospective SEA – General Engineering Department Page 2  Engineering Economy projects on a relatively even basis. Assuming the costs of investment are equal among the various projects, the project with the highest IRR would probably be considered the best and be undertaken first. 6. The External Rate of Return method The external rate of return (ERR)is the rate of return on a project where any “excess” cash from a project is assumed to earn interest at a pre-determined explicit rate. Computing an exact ERR is difficult: The ERR affects project balances, which affect the ERR. To get an approximate ERR: 1. Take all net receipts forward at the MARR to the time of the last cash flow. 2. Take all net disbursements forward at the unknown rate i (approximate ERR) to the time of the last cash flow. 3. Set FW(receipts) = FW(disbursements) and solve for i. The ERR method should be used whenever multiple IRRs are possible. Unfortunately, it is sometimes hard to know in advance when there are multiple IRRs. However, most investments will have a cash flow structure which excludes multiple IRRs. Simple investment: an investment characterized by one or more periods of cash outflows, followed by one or more periods of cash inflows. If a project is a simple investment, it will have at most one positive IRR. If a project is not a simple investment, there may be more than one IRR. If the sign of successive cash flows changes X times, there may be up to X IRRs. Use an ERR computation if you have found multiple IRRs with a plot, or if you are not sure. 7. The Payback Period method It is the length of time required to recover the first cost of an investment from the net cash flow produced by that investment for an interest rate of zero. 8. The Benefit/Cost Ratio Method A benefit-cost ratio (BCR) is a ratio used in a cost-benefit analysis to summarize the overall relationship between the relative costs and benefits of a proposed project. BCR can be expressed in monetary or qualitative terms. If a project has a BCR greater than 1.0, the project is expected to deliver a positive net present value to a firm and its investors. Key Takeaways:  A benefit-cost ratio (BCR) is an indicator showing the relationship between the relative costs and benefits of a proposed project, expressed in monetary or qualitative terms.  If a project has a BCR greater than 1.0, the project is expected to deliver a positive net present value to a firm and its investors.  If a project's BCR is less than 1.0, the project's costs outweigh the benefits, and it should not be considered. SEA – General Engineering Department Page 3  Engineering Economy Examples: 1. An investment of P270,000 can be made in a project that will produce a uniform annual revenue of P185,400 for 5 years and then have a salvage value of 10% of the investment. Out-of-pocket costs for operation and maintenance will be P81,000 per year. Taxes and insurance will be 4% of the first cost per year. The company expects capital to earn not less than 25% before income taxes. Is this a desirable investment? What is the payback period of the investment? b. By annual worth method SEA – General Engineering Department Page 4  Engineering Economy SEA – General Engineering Department Page 5  Engineering Economy SEA – General Engineering Department Page 6  Engineering Economy References: Blank, L. & Tarquin, A. (2018). Engineering Economy (8th Ed.). McGraw-Hill Education. Sullivan, W., Wicks, E. & Koelling, C. P. (2014). Engineering Economy (16th Ed.). Pearson Education South Asia Pte Ltd. Sta. Maria, H. (2000). Engineering Economy (3rd Ed.). National Book Store. Arreola, M. (1993). Engineering Economy (3rd Ed.). Ken Incorporated. Investopedia at https://www.investopedia.com/terms/r/rateofreturn.asp Dr Abdelaziz Berrado, Al Akhawayn University, EGR2302-Engineering Economics at http://www.aui.ma/personal/~A.Berrado/EGR2302/EGR2302_Ch05.pdf http://facstaff.cbu.edu/~gmcginni/classes/CE%20314%20Engineering%20Economy/PowerPoint/Chapter %206.pdf https://www.coursehero.com/file/p7vh2ik/The-external-rate-of-return-ERR-is-the-rate-of-return-on-a- project-where-any/ SEA – General Engineering Department Page 7