9.1 Time value of money and economic decision-making
4 min read•august 15, 2024
is a crucial concept in engineering economics. It helps engineers understand how the worth of money changes over time, considering factors like inflation and . This knowledge is essential for making informed decisions about long-term projects and investments.
In this section, we'll explore key TVM principles and their applications in engineering. We'll cover present and calculations, annuities, and economic analysis techniques like NPV and IRR. These tools are vital for evaluating project feasibility and making sound financial choices.
Time Value of Money in Engineering
Fundamental Principles of TVM
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Time value of money (TVM) dictates that present money holds greater value than future money due to its earning potential
Key factors influencing TVM in engineering economics
Inflation erodes purchasing power over time
Opportunity cost represents foregone alternative investments
Risk increases with longer time horizons
Discounting compares cash flows at different times by converting future values to present equivalents
Interest rates represent cost of capital or required return on investments in TVM calculations
TVM principles crucial for
Capital budgeting decisions
Equipment replacement analysis
Project financing evaluations
Applications in Engineering Economics
Long-term investments in engineering projects necessitate TVM for accurate valuation
TVM enables fair comparison of projects with different cash flow timings
Capital budgeting uses TVM to assess long-term project profitability
Equipment replacement decisions factor in time value of future cost savings
Project financing evaluations incorporate TVM to determine loan affordability and terms
Risk assessment in engineering projects considers time-dependent uncertainties
Present Value, Future Value, and Annuities
Present and Future Value Concepts
(PV) determines current worth of future cash flows using
Future value (FV) projects current funds' worth at future date given and time
calculations account for interest on principal and accumulated interest
Time diagrams visually represent cash flows, aiding in TVM problem setup and solution
allows comparison of cash flows at different times by converting to common basis
PV formula: PV=FV/(1+r)n where r is interest rate and n is number of periods
FV formula: FV=PV∗(1+r)n
Annuities and Cash Flow Series
Annuities represent series of equal payments or receipts at fixed intervals
Present value of formula: PVA=PMT∗[(1−(1+r)−n)/r] where PMT is payment amount
Future value of annuity formula: FVA=PMT∗[((1+r)n−1)/r]
considers payments at beginning of periods, while assumes end-of-period payments
represent infinite series of equal payments, valued using PV=PMT/r
and perpetuities incorporate payment growth rates in calculations
Solving for unknown variables (interest rate, time, payment amount) crucial in TVM equations
Economic Feasibility of Engineering Projects
Net Present Value and Internal Rate of Return
(NPV) calculates difference between present value of cash inflows and outflows
Positive NPV indicates profitable project
NPV formula: NPV=∑t=0n(1+r)tCFt where CF_t is cash flow at time t
(IRR) determines discount rate at which NPV becomes zero
IRR > required rate of return indicates profitable project
IRR calculated through iterative process or financial calculators
Other Economic Analysis Techniques
(BCR) compares present value of benefits to present value of costs
BCR > 1 indicates economically viable project
BCR formula: BCR=PV of CostsPV of Benefits
calculates time to recover initial investment
Simple payback ignores time value of money
Discounted payback considers TVM in recovery period calculation
(LCCA) considers all project costs over entire lifespan
Includes initial, operational, maintenance, and disposal costs
Enables comprehensive comparison of alternatives with different cost structures
Sensitivity and Risk Analysis
examines impact of variable changes on project feasibility
Variables may include interest rates, costs, revenues, or project duration