Isye 220 Engineering Economy Mock Final Northern Illinois Un
Isye 220 Engineering Economy Mock Final1northern Illinois Universit
Suppose you wish to accumulate $10,000 in a savings account 4 years from now, and the account pays you an interest rate of 5% per year, how much money must be deposited today?
What value of X makes these two cash flows equivalent assuming an interest rate of 10%?
The operating cost of a small machine is $800 in year one, $900 in year two, $1000 in year three, increasing by $100 per year through year ten. At an interest rate of 8% per year, determine the equivalent annual worth of the machine.
What is the future worth of an equal quarterly payment series of $2,500 for 10 years, if the interest rate is 9%, compounded monthly?
What is the capitalized cost of $10,000 for every 5 years forever, starting now at an interest rate of 10% per year?
Consider a project with a first cost (investment) of $250,000, an annual O&M cost of $50,000, annual revenue of $160,000, and a salvage value of $40,000 after a 10-year life. Find the annual worth of the project assuming an interest of 13% per year.
A permanent scholarship fund is started through a donation of $100,000. If five scholarships of $5,000 each are awarded each year beginning ten years from now, what is the rate of return ‘i’ for the invested money?
If a company invests $10,000 and receives $2,775 per year for five years, what is the rate of return on the investment?
Paper For Above instruction
Engineering economy plays a vital role in the decision-making process for investment projects and financial planning across various industries. It involves the systematic evaluation of the economic merits of proposed investments or projects, emphasizing techniques such as present worth analysis, future value calculations, and cost-benefit assessments. This paper explores several foundational principles of engineering economy, illustrating their applications through practical examples and decision-making scenarios.
Introduction
Engineering economy aims to facilitate rational decision-making by quantifying costs and benefits over time, often considering factors such as interest rates, inflation, and project lifespan. The core techniques include calculating present value, future worth, and annual equivalent costs or benefits, which allow comparisons among alternatives. These methods are essential for engineers, financial analysts, and managers engaged in evaluating projects and ensuring optimal resource allocation.
Calculating Present Value for Future Goals
One common concern involves computing the initial deposit required to reach a specific savings goal. For example, to accumulate $10,000 after four years at an interest rate of 5%, the present value (PV) can be determined using the formula:
PV = FV / (1 + i)^n
where FV is the future value, i the interest rate, and n the number of periods. Substituting values gives:
PV = $10,000 / (1 + 0.05)^4 ≈ $8,227.65.
This calculation underscores the importance of starting early and investing appropriately to meet financial targets.
Equivalence of Cash Flows and the Value of X
Determining the value of X that renders two cash flows equivalent requires equating their present or future values, depending on the context. Assuming an interest rate of 10%, the equivalence condition may involve solving for X in equations such as:
PV = CF1 + X / (1 + i)^n = CF2 + ...
This approach helps in evaluating investment trade-offs, lease vs. buy decisions, or comparing alternative cash flow streams.
Equivalent Annual Worth (EAW) of Operating Costs
The operating cost profile of a machine, increasing annually, can be converted into an equivalent annual worth to facilitate comparison with other alternatives or investment options. Using the capital recovery factor and the uniform series present worth factor, the calculation involves summing the discounted costs and then amortizing over the machine’s lifespan at the given interest rate. For the machine with costs escalating from $800 to $1,000 over ten years, the EAW quantifies the cost per year that is equivalent in value over its operational life.
This method aids in understanding ongoing expenses and making cost-effective procurement decisions.
Future Value of an Annuity with Compound Interest
Monthly compounded interest affects the future value of regular payments. The future value (FV) of a series of quarterly payments of $2,500 over 10 years at a 9% annual nominal interest rate compounded monthly can be computed using the future value of an annuity formula, adjusted for the periodic interest rate and number of periods:
FV = PMT * [(1 + i/m)^{nt} - 1] / (i/m)
where PMT is the payment, i the annual nominal interest rate, m the number of compounding periods per year, n the number of payments per year, and t the total years.
This calculation highlights the effects of compounding frequency on investment growth.
Capitalized Cost of Perpetual Series
The capitalized cost represents the present worth of a perpetual series of costs or cash flows, calculated as:
Capitalized Cost = Cash Flow per period / Interest Rate
For a scenario of $10,000 every five years forever at 10% interest, the present value of this perpetuity is:
Capitalized Cost = $10,000 / 0.10 = $100,000.
This measure assists in evaluating the long-term financial viability of perpetual projects or investments.
Cost and Revenue Analysis over a Project’s Life
Evaluating a project involving initial investment, operational costs, revenues, and salvage value requires comprehensive analysis. The annual worth (AW) can be calculated by considering the capital recovery cost, annual cash flows, and the discounted value of salvage. Using the given figures, and assuming a 13% interest rate, the analysis helps determine whether the project’s annual benefits outweigh associated costs, guiding investment decisions.
Interest Rate of Return in Scholarship Funds
The rate of return (IRR) on a scholarship fund can be computed by solving for ‘i’ in the equation equating present value of the fund and the future disbursements. This involves iterative calculations or financial calculator usage to find the interest rate that makes the net present value of all cash flows zero. Accurate determination of IRR informs donors and administrators about the fund’s growth potential.
Investment Return Calculation
Similarly, the rate of return on an investment such as $10,000 generating $2,775 annually over five years is obtained by solving the annuity interest rate formula, which provides insight into the profitability of the investment.
Conclusion
Engineering economy principles, including present worth, future value, annual worth, and rate of return calculations, provide essential tools for analyzing financial decisions. These methods facilitate comparisons of alternative projects, investments, and operational strategies, enabling informed, economically sound choices. As technological and economic environments evolve, mastery of these tools remains critical for engineers, financial analysts, and decision-makers.
References
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