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AALL1002 Engineering Economics

Core ideas

  • Engineering economics compares technical alternatives using money, time, and risk considerations.
  • A rupee today is worth more than a rupee later because of earning potential and opportunity cost.
  • Cash-flow direction matters: inflows are positive, outflows are negative by common convention.

Discount rate, interest, and time value of money

Future value of present amount \(P\) at interest rate \(i\) for \(n\) periods:

\[ F = P(1+i)^n \]

Present value of future amount \(F\):

\[ P = \frac{F}{(1+i)^n} \]
  • Discounting converts future cash to present worth.
  • A higher discount rate lowers the present worth of future benefits.

Project cash flow

  • Cash-flow diagrams show amount, sign, and timing of expenses and benefits.
  • Initial capital cost is often a large early outflow.
  • Operation, maintenance, salvage value, tax effect, and depreciation impact should be considered where relevant.

Discounted payback period

  • Payback period is the time needed to recover initial investment.
  • Discounted payback uses discounted cash inflows, not raw inflows.
  • A shorter discounted payback is usually preferred, but it ignores benefits after the cutoff once recovery occurs.

Net present value

\[ NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+i)^t} \]
  • Accept an independent project if \(NPV > 0\) at the chosen discount rate.
  • For mutually exclusive alternatives, the one with the higher acceptable NPV is generally preferred when lives and assumptions are comparable.
  • NPV is usually the most reliable primary decision rule under standard assumptions.

IRR and MARR

  • Internal rate of return (IRR) is the discount rate that makes \(NPV = 0\).
  • Minimum attractive rate of return (MARR) is the firm's hurdle rate or required minimum return.
  • Decision rule: accept if \(IRR \ge MARR\), subject to cash-flow-pattern caveats.

Decision-rule caveats

  • Multiple IRRs may occur with nonconventional cash flows.
  • IRR can be misleading for mutually exclusive projects of different scale or timing.
  • NPV is generally more dependable than IRR when rankings conflict.
  • MARR must be chosen consistently before evaluation.

Comparison of alternatives

Rule Good use Main caution
Payback Liquidity emphasis Ignores later benefits
Discounted payback Better than simple payback Still ignores far-future value after cutoff
NPV Primary value measure Needs discount-rate estimate
IRR Intuitive percentage return Ranking conflicts and multiple-IRR cases

Depreciation

  • Depreciation allocates asset cost over useful life for accounting and tax purposes.
  • It is not the same as market value decline, though related in practice.
  • Straight-line depreciation is the simplest exam-ready method.

Straight-line annual depreciation:

\[ D = \frac{C-S}{n} \]
  • \(C\): initial cost.
  • \(S\): salvage value.
  • \(n\): useful life.

Taxation system in Nepal

  • Engineering-economics comparisons should use cash flows consistently on a before-tax or after-tax basis. An elementary after-tax relation is:
\[ CF_{\mathrm{after-tax}}=CF_{\mathrm{before-tax}}-T_{\mathrm{cash}}. \]
  • Depreciation is noncash, but an allowable depreciation deduction reduces taxable income. Where the deduction is fully usable, the simplified depreciation tax shield is \(D\,t\), where \(D\) is allowable depreciation and \(t\) is the applicable marginal tax rate.
  • Stable categories that may affect a Nepal project include income tax, VAT or other indirect taxes, customs/excise, and withholding. Whether a payment is recoverable, deductible, capitalized, exempt, or applicable depends on current law and project facts.
  • Compare after-tax cash flows with a consistently selected after-tax discount rate; do not subtract tax again from a cash-flow series that is already after tax.
  • Exact Nepal tax rates, thresholds, depreciation classes, and statutory rules are time-sensitive.
  • Exact current Nepal tax slabs and depreciation schedules must be marked VERIFY against current official law/rules before memorization.

Recognition cues for project planning and scheduling

  • "Discount rate that makes NPV zero" means IRR.
  • "Required minimum acceptable return" means MARR.
  • "Present worth of all inflows and outflows" means NPV.
  • "Recovery period using discounted cash flows" means discounted payback.

Common traps in project planning and scheduling

  • Simple payback and discounted payback are not the same.
  • A project with positive accounting profit can still have poor NPV.
  • Higher IRR does not always imply better project choice when scales differ.
  • Depreciation is a noncash charge, but it can affect taxes and therefore cash flow.

One-step examples for project planning and scheduling

  • If \(P=1000\), \(i=10\%\), and \(n=2\), then \(F = 1000(1.1)^2 = 1210\).
  • If a project's NPV at MARR is positive, it passes the NPV rule.
  • For \(C=100000\), \(S=10000\), and \(n=5\), straight-line depreciation is \(18000\) per year.

Project-planning-and-scheduling revision box

NPV is usually the strongest decision rule. IRR is the rate where NPV becomes zero. MARR is the acceptance threshold. Discounted payback accounts for time value, simple payback does not. Nepal tax details are time-sensitive and must be officially verified before memorizing exact numbers.