TWO KINDS OF PROJECT SET, and the distinction determines the entire method: INDEPENDENT — accepting one does not affect the others. Accept EVERY project with NPV > 0, subject to the budget. MUTUALLY EXCLUSIVE — only ONE can be chosen. This is the case of designing a bridge as steel OR concrete, or heating a building by electricity OR gas. THE ANALYSIS IS ENTIRELY DIFFERENT: NPV > 0 is no longer sufficient, because several alternatives may clear the bar and only one may be selected. THE ALTERNATIVE ALWAYS TO INCLUDE, and the one most often forgotten: THE DO-NOTHING ALTERNATIVE. Doing nothing has a cash flow of zero and therefore an NPV of zero. IF EVERY ALTERNATIVE HAS A NEGATIVE NPV, DO-NOTHING WINS, and the correct engineering recommendation is not to proceed. An analysis that omits it can only ever conclude "build something", which is not analysis. Note the exception: WHERE THE PROJECT IS MANDATORY — a legal safety requirement, a regulatory compliance upgrade — do nothing is unavailable, and the comparison is between costs only, choosing the LEAST NEGATIVE. THE THREE EQUIVALENT METHODS. All give the same ranking when applied correctly, so choose by convenience: 1. PRESENT WORTH (PW / NPV) METHOD Convert everything to a present value; choose the highest NPV, or for cost-only alternatives the lowest present cost. REQUIRES EQUAL LIVES, or an adjustment — see below. 2. ANNUAL WORTH (AW / EUAC) METHOD Convert everything to an equivalent uniform annual amount: AW = PW × (A/P, i, n) THE EASIEST METHOD FOR UNEQUAL LIVES, because an annual figure is already life-neutral. For cost-only comparisons this is the EQUIVALENT UNIFORM ANNUAL COST (EUAC), which is the standard measure in infrastructure appraisal. 3. RATE OF RETURN METHOD Compare by INCREMENTAL analysis, as derived in the IRR topic. NEVER by comparing IRRs directly. ── THE UNEQUAL LIVES PROBLEM ─────────────────────────────── THE CENTRAL DIFFICULTY OF THIS TOPIC, and a near-certain exam question. A present worth comparison over different periods is INVALID, because a project running 10 years naturally accumulates more value than an equally good one running 5 years. Comparing their raw NPVs rewards longevity rather than quality. THE TWO CORRECT REMEDIES: (a) LEAST COMMON MULTIPLE (REPEATABILITY) METHOD Assume each alternative is REPEATED until both span the same period — the LCM of their lives. A 3-year and a 5-year alternative are compared over 15 years: A repeated 5 times, B repeated 3 times. THE ASSUMPTION BEING MADE — and it must be stated — IS THAT EACH ALTERNATIVE CAN BE REPLACED BY AN IDENTICAL ONE AT THE SAME COST. That is reasonable for a pump and unreasonable for a computer system, whose replacement will be cheaper and better. (b) ANNUAL WORTH METHOD — usually preferable. Compute the EUAC of each over its OWN life and compare directly. NO REPETITION NEEDS TO BE ASSUMED EXPLICITLY, though mathematically it embeds the same assumption. IT IS FAR LESS ARITHMETIC, which is why it is the practical choice. (c) STUDY PERIOD (PLANNING HORIZON) METHOD Fix a common period of analysis — say 10 years — and assign a realistic ESTIMATED SALVAGE VALUE to any alternative still in service at the end. Used when repetition is genuinely implausible. A WORKED UNEQUAL-LIVES COMPARISON, at i = 10%: ALTERNATIVE A: cost 60,000, annual O&M 12,000, life 3 years, no salvage ALTERNATIVE B: cost 90,000, annual O&M 8,000, life 5 years, no salvage BY THE ANNUAL WORTH METHOD: A: EUAC = 60,000(A/P,10%,3) + 12,000 = 60,000(0.40211) + 12,000 = 24,127 + 12,000 = Rs 36,127 per year B: EUAC = 90,000(A/P,10%,5) + 8,000 = 90,000(0.26380) + 8,000 = 23,742 + 8,000 = Rs 31,742 per year CHOOSE B — it costs Rs 4,385 per year less. NOTE THAT B HAS THE HIGHER CAPITAL COST AND STILL WINS, because its longer life spreads that cost over more years and its running cost is lower. COMPARING FIRST COSTS ALONE — the instinct of every inexperienced client — WOULD HAVE CHOSEN A AND BEEN WRONG.

LIFE CYCLE COST (LCC) is the total cost of ownership over the whole life, and it is the framework this topic exists to teach: LCC = INITIAL COST + OPERATING COST + MAINTENANCE COST + REPLACEMENT / OVERHAUL COSTS + DISPOSAL COST − SALVAGE VALUE all discounted to present worth. THE POINT OF LCC IS THAT THE INITIAL COST IS OFTEN THE SMALLEST PART. For a building over 30 years, the construction cost is typically a minority of the total, with energy and maintenance dominating; for a pump, the electricity to run it over ten years commonly exceeds its purchase price several times over. THE DESIGN CONSEQUENCE: DECISIONS MADE IN THE FIRST FEW PER CENT OF A PROJECT'S SPEND COMMIT THE REMAINING NINETY PER CENT. Choosing a cheaper, less efficient pump saves a little once and costs a great deal every year afterwards — which is why LCC belongs at the design stage, when the commitment is still open, rather than at the procurement stage, when it is not. THE OTHER COMPARISON CRITERIA an engineer will meet: BENEFIT-COST RATIO (B/C) — the standard method for PUBLIC projects, required by most government and donor agencies: B/C = PW of benefits / PW of costs Accept if B/C > 1. For mutually exclusive public projects, USE THE INCREMENTAL B/C RATIO — comparing B/C ratios directly repeats exactly the scale error that comparing IRRs does. THE PRACTICAL DIFFICULTY IS DEFINING THE BENEFITS. A road's benefits include time saved, fuel saved, accidents avoided and trade enabled — each requiring a monetary value for things not traded in a market, including, unavoidably, a value for a human life. THE ANALYSIS IS ONLY AS CREDIBLE AS THOSE VALUATIONS. CAPITALIZED COST — the present worth of a cost continuing FOREVER: CC = A / i Used for perpetual public assets: bridges, dams, embankments, endowments. At 8%, a Rs 200,000 annual maintenance obligation has a capitalized cost of Rs 2,500,000 — a striking way to show a client what an apparently modest recurring commitment is really worth. PAYBACK — as covered, supplementary only. THE NON-ECONOMIC FACTORS, which an exam answer should close with because they are part of professional judgement: · SAFETY and regulatory compliance — often not negotiable at any price · ENVIRONMENTAL IMPACT, increasingly monetised but not entirely · reliability and availability of spares and skills LOCALLY — decisive in Nepal, where an imported machine with no service network can be worthless the day it fails · flexibility to expand or change use · social acceptability and displacement AN ALTERNATIVE THAT WINS ON EUAC BUT CANNOT BE MAINTAINED LOCALLY IS NOT THE BETTER ALTERNATIVE. The economic analysis informs the decision; it does not make it.