A CASH FLOW IS ANY MOVEMENT OF MONEY INTO OR OUT OF A PROJECT, RECORDED WITH THE TIME AT WHICH IT OCCURS. CASH INFLOW (+) — revenue, savings, salvage value, loans received CASH OUTFLOW (−) — capital cost, operating cost, maintenance, taxes, loan repayments NET CASH FLOW = inflow − outflow, for each period THE CASH FLOW DIAGRAM is the standard notation, and drawing it correctly is usually the first two marks of any economics question: · A HORIZONTAL LINE is the time axis, marked in periods (usually years). · ARROWS UPWARD are INFLOWS (receipts). · ARROWS DOWNWARD are OUTFLOWS (payments). · Arrow LENGTH is roughly proportional to the amount. · TIME 0 IS THE PRESENT — normally the moment the initial investment is made. A machine costing 100,000 that returns 30,000 a year for five years and is then scrapped for 10,000: 30k 30k 30k 30k 30k ↑ ↑ ↑ ↑ ↑ ↑ 10k salvage ───────────┼────┼────┼────┼────┼───────▶ time 0 1 2 3 4 5 │ ↓ 100,000 THE END-OF-PERIOD CONVENTION — the assumption that makes all of this tractable: ALL CASH FLOWS WITHIN A PERIOD ARE TREATED AS OCCURRING AT THE END OF THAT PERIOD. Revenue arriving continuously through year 3 is treated as a single lump at the end of year 3. THIS IS AN APPROXIMATION, and it is slightly conservative — it discounts money as though it arrived later than it did. It is adopted because modelling every transaction on its actual date would add enormous complexity for a change that is small relative to the uncertainty in the forecasts themselves. NOTE THE ASYMMETRY: THE INITIAL INVESTMENT IS AN EXCEPTION, PLACED AT TIME 0 — the BEGINNING of year 1 — because it is spent before anything can be earned. THE CATEGORIES OF PROJECT CASH FLOW: 1. INITIAL INVESTMENT (capital cost), at t = 0 land, buildings, plant, machinery, installation, engineering fees, initial working capital 2. OPERATING CASH FLOWS, during the life + revenue or cost savings − labour, materials, energy, maintenance, insurance 3. TERMINAL CASH FLOWS, at the end + SALVAGE VALUE (or − disposal cost, if removing the asset costs money) + recovery of working capital 4. PERIODIC NON-ANNUAL FLOWS a major overhaul in year 7, a replacement of a component in year 10 — these are placed at their own points and are a favourite exam complication THE FOUR STANDARD CASH FLOW PATTERNS, which the formulae in the next topic are built to handle: P — a SINGLE PRESENT amount at t = 0 F — a SINGLE FUTURE amount at t = n A — a UNIFORM SERIES (annuity): the same amount at the end of every period from 1 to n G — a GRADIENT SERIES: an amount increasing by a constant G each period (arithmetic) or by a constant percentage (geometric)

A WORKED CONSTRUCTION — a small hydropower scheme, since that is the Nepali engineer's standard example: Capital cost Rs 100,000 thousand at t = 0 Annual revenue Rs 42,000 thousand Annual O&M cost Rs 12,000 thousand Turbine overhaul, year 5 Rs 15,000 thousand Salvage at year 10 Rs 20,000 thousand YEAR INFLOW OUTFLOW NET CASH FLOW ────────────────────────────────────────── 0 0 100,000 −100,000 1 42,000 12,000 +30,000 2 42,000 12,000 +30,000 3 42,000 12,000 +30,000 4 42,000 12,000 +30,000 5 42,000 27,000 +15,000 ← overhaul year 6 42,000 12,000 +30,000 7 42,000 12,000 +30,000 8 42,000 12,000 +30,000 9 42,000 12,000 +30,000 10 62,000 12,000 +50,000 ← includes salvage ────────────────────────────────────────── THE POINT OF THE TABLE IS THE LAST COLUMN. Everything that follows in this section — payback, NPV, IRR — operates on that single column of net figures, so an error there propagates into every subsequent calculation. BUILD THE TABLE FIRST AND CHECK IT BEFORE DISCOUNTING ANYTHING. THE RULES FOR DECIDING WHAT BELONGS IN A CASH FLOW — each one is a standard exam trap: 1. ONLY INCREMENTAL FLOWS COUNT. Include a cost only if it CHANGES as a result of the decision. An existing salary that will be paid whether or not the project proceeds is not a project cost. 2. SUNK COSTS ARE IRRELEVANT. Money already spent — a feasibility study, a preliminary design, land bought years ago — CANNOT BE RECOVERED BY ANY FUTURE DECISION AND MUST BE EXCLUDED. THIS IS THE HARDEST RULE TO FOLLOW IN PRACTICE, because abandoning a project after spending 20 million feels like wasting 20 million. It is not: THE 20 MILLION IS GONE IN EITHER CASE, and the only question is whether the REMAINING spending is justified by the REMAINING returns. The psychological failure has a name — the SUNK COST FALLACY — and it keeps doomed projects alive everywhere. 3. OPPORTUNITY COSTS MUST BE INCLUDED. If a project uses land the company already owns, the cash flow must charge it at the price the land could have been sold or leased for. Owning something does not make it free — it means the revenue it could have earned is being given up. 4. DEPRECIATION IS NOT A CASH FLOW. It is an accounting allocation, and no money moves when an asset is depreciated. BUT IT AFFECTS CASH FLOW INDIRECTLY THROUGH TAX, because it reduces taxable income: after-tax cash flow = (revenue − cash expenses − depreciation)(1 − t) + depreciation This is developed in the depreciation and taxation topics. 5. FINANCING FLOWS ARE NORMALLY EXCLUDED from the project evaluation. Interest and loan repayments belong to the FINANCING decision, not the INVESTMENT decision, and the cost of capital enters through the discount rate instead. Including both would count it twice. 6. WORKING CAPITAL is an outflow when tied up at the start and an inflow when released at the end. It is not consumed — merely locked away for the project's life. 7. INFLATION MUST BE HANDLED CONSISTENTLY: either forecast cash flows in CURRENT (inflated) rupees and discount at a NOMINAL rate, or forecast in CONSTANT rupees and discount at a REAL rate. MIXING THE TWO IS A COMMON AND SERIOUS ERROR that systematically understates or overstates a project's value.