Cash-flow timeline explorer
Enter signed cash flows (negative for outlays, positive for receipts). The diagram rescales arrow lengths using a logarithmic stretch so both small and large amounts remain visible.
| Period t | Net cash flow |
|---|
Interactive Engineering Economics Learning Platform
PW · AW · IRR · Cash Flow · Risk Analysis — Learn, Practice, Analyze, Apply
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Symbol & convention glossary
Cash Flow Basics
| Symbol | Meaning | Typical units | Conventions |
|---|---|---|---|
| P | Present worth (lump sum at t = 0 or at the valuation instant). | Currency (e.g., USD). | Single payment unless paired with an annuity factor. |
| F | Future worth—a one-time cash flow at the end of period n. | Currency. | Uses the same period index as n for i. |
| A | Uniform amount per period (“annuity” payment). | Currency per period. | Ordinary annuity: payments at each end of period (default). |
| S | Salvage value—estimated resale value at end of asset life. | Currency. | Treated as inflow at period n unless specified otherwise. |
| NCF | Net cash flow—receipts minus disbursements in a period. | Currency per period. | Positive = inflow (receipt); Negative = outflow (disbursement). |
Time & Interest Parameters
| Symbol | Meaning | Typical units | Conventions |
|---|---|---|---|
| i | Interest (or discount) rate per interest period. | Dimensionless per period (enter 0.08 for 8%). | Discrete compounding unless stated continuous r. |
| n | Number of compounding (or payment) periods in the model. | Integer periods. | Must match the timing of i and each cash flow arrow. |
| t | Time index—period number in cash flow timeline. | Integer period index (0, 1, 2, ..., n). | t = 0 is the present; t = n is the final period. |
| r, m | Nominal rate per year (r) and compounding periods per year (m). | r as decimal/year; m as count. | Periodic rate iperiod = r/m. |
Gradient & Special Cash Flows
| Symbol | Meaning | Typical units | Conventions |
|---|---|---|---|
| G | Arithmetic gradient step—cash flows increase by G each period after a base. | Currency per period. | Requires the textbook's "0, G, 2G, …" pattern. |
Value Metrics
| Symbol | Meaning | Typical units | Conventions |
|---|---|---|---|
| NPW / NPV | Net Present Worth / Net Present Value. | Currency. | Sum of discounted cash flows at MARR. Accept if NPW ≥ 0. |
| AW | Annual Worth—equivalent uniform annual amount. | Currency per period. | AW = EUAB - EUAC. Accept if AW ≥ 0. |
| EUAC | Equivalent Uniform Annual Cost. | Currency per period. | Converts all costs to equivalent uniform annual amount. |
| EUAB | Equivalent Uniform Annual Benefit. | Currency per period. | Converts all benefits to equivalent uniform annual amount. |
| CR | Capital Recovery—annual cost to recover initial investment. | Currency per period. | CR = P(A/P,i,n) - S(A/F,i,n). |
Decision Criteria
| Symbol | Meaning | Typical units | Conventions |
|---|---|---|---|
| MARR | Minimum Attractive Rate of Return. | Dimensionless per period (decimal). | Hurdle rate for accept/reject decisions. Used as i in PW/AW analysis. |
| IRR | Internal Rate of Return. | Dimensionless per period (decimal or percent). | Interest rate where NPW = 0. Accept if IRR ≥ MARR. |
| ΔIRR | Incremental Internal Rate of Return. | Dimensionless per period (decimal or percent). | IRR on incremental cash flow between alternatives. Accept increment if ΔIRR ≥ MARR. |
Engineering Economics Calculators
Present Worth Calculator
Chart showing how present value changes over time.
Annual Worth Calculator
Chart showing annual worth distribution over time.
IRR Estimator (5 Periods)
Chart showing cash flows and cumulative NPV.
EUAC Calculator
Chart showing annual costs and equivalent uniform annual cost.
Interest Factor Calculator
Chart showing how interest factors change with time.
Quantitative models & cash-flow laboratory
Simple vs compound terminal wealth
Compare two textbook benchmarks at integer years: simple Fk = P(1 + ik) versus compound Fk = P(1 + i)k. Adjust the table and the paths update.
| Principal P ($) | |
|---|---|
| Interest rate i (per year, %) | |
| Horizon n (years) |
Plotted at k = 0,1,…,n. Same i anchors both curves for a controlled comparison.
Challenge
🎯 8 Economic Intuition Traps
Identify common mistakes and learn correct engineering economics tools!
Completed
1/5
Accuracy
100%
Mastery
20%
1
Lifespan Illusion
2
IRR Ranking
3
Sunk Cost
4
Nominal Rate
5
EUAC Mistake
6
Gradient Error
7
NPW Curve
8
Compounding
📂 Case File
#001
The IRR Trap
The boss excitedly says: "Project A has IRR 28%, crushing B's 15%!"