Time value of money is the principle that a monetary unit available today is not economically equivalent to the same unit received in the future. In engineering projects, this difference exists because capital has a cost, can be allocated to alternatives, is affected by inflation, and is exposed to uncertainty. Therefore, CAPEX, OPEX, benefits, replacements, revenues, maintenance costs, and residual value need to be compared at the same valuation date before supporting a decision.<\/p>\n\n\n\n
This principle is the mathematical foundation of present value, future value, discounted cash flow, NPV, annuities, perpetuities, and several economic evaluation methods. It also explains why two projects with the same nominal total benefits can have different economic values when the timing of the cash flows is not the same.<\/p>\n\n\n\n
In engineering, the issue is not only financial. The physical schedule determines when capital is disbursed; commissioning determines when benefits begin; ramp-up affects the speed of cash generation; delays postpone returns; early replacements consume cash sooner than expected. Time value of money converts these timing differences into measurable economic differences.<\/p>\n\n\n\n
Time Value of Money \u2014 TVM \u2014 is the principle that relates value, time, and rate of return.<\/p>\n\n\n\n
The CFA Institute treats TVM as a foundation for valuing future cash flows through present value and for determining implied returns from known prices and cash flows. The central logic is that cash flows occurring on different dates cannot be added directly before they are converted to the same point in time.<\/p>\n\n\n\n
If $1 million can earn 10% in one year, having $1 million today is economically different from receiving $1 million one year from now.<\/p>\n\n\n\n
This is the opportunity-cost component. Capital available now can fund another project, reduce debt, remunerate investors, or generate a return in an alternative investment.<\/p>\n\n\n\n
When prices rise, the same nominal amount buys fewer goods and services in the future.<\/p>\n\n\n\n
Receiving money in the future depends on the cash flow actually occurring. The discount rate may reflect part of systematic risk, while specific risks may also be addressed in cash flows and scenarios.<\/p>\n\n\n\n
Capital available today provides flexibility to respond to opportunities and obligations. Funds tied up in a project reduce financial flexibility.<\/p>\n\n\n\n
They are inverse operations.<\/p>\n\n\n\n
Future value projects what a current amount becomes after a given period at a compounding rate.<\/p>\n\n\n\n
FV = PV \u00d7 (1 + i)^n<\/strong><\/p>\n\n\n\n where:<\/p>\n\n\n\n If $1 million earns 10% p.a. for three years:<\/p>\n\n\n\n FV = 1,000,000 \u00d7 (1.10)^3 = $1,331,000<\/strong><\/p>\n\n\n\n Present value works in the opposite direction.<\/p>\n\n\n\n PV = FV \/ (1 + i)^n<\/strong><\/p>\n\n\n\n A cash flow of $1.331 million in year 3, discounted at 10% p.a., is equivalent to $1 million today.<\/p>\n\n\n\n The equivalence depends on the rate adopted.<\/p>\n\n\n\n Consider two benefits:<\/p>\n\n\n\n Adding them as R$ 2 million ignores that the second cash flow is unavailable for five years.<\/p>\n\n\n\n For a correct comparison, both need to be converted to the same valuation date.<\/p>\n\n\n\nPresent value<\/h3>\n\n\n\n
Why Cash Flows from Different Dates Cannot Be Added Directly<\/h2>\n\n\n\n