THE PAYBACK PERIOD IS THE TIME REQUIRED FOR THE CUMULATIVE CASH INFLOWS TO EQUAL THE INITIAL INVESTMENT. SIMPLE (UNDISCOUNTED) PAYBACK, for uniform annual returns: PAYBACK = INITIAL INVESTMENT / ANNUAL NET CASH INFLOW Rs 100,000 invested, returning Rs 30,000 a year: payback = 100,000 / 30,000 = 3.33 YEARS FOR UNEVEN CASH FLOWS, accumulate year by year and interpolate within the year in which the cumulative total turns positive: PAYBACK = (full years before recovery) + (unrecovered amount at the start of that year) / (cash flow during that year) THE FATAL FLAW OF SIMPLE PAYBACK: IT TREATS A RUPEE RECEIVED IN YEAR 5 AS EQUAL TO A RUPEE RECEIVED IN YEAR 1. That contradicts everything in the time value of money topic. Consider two projects, each costing 100,000 over three years: PROJECT A: 60,000 / 30,000 / 10,000 → payback 2.0 yrs PROJECT B: 10,000 / 30,000 / 60,000 → payback 3.0 yrs SIMPLE PAYBACK PREFERS A, and it is right to — but only by accident, because it happens to notice the timing here. Change B's figures to 30,000 / 30,000 / 40,000 and simple payback still says 3 years, treating that as identical to any other 3-year recovery regardless of how front- or back-loaded it is. THE FIX — DISCOUNTED PAYBACK: DISCOUNT EACH YEAR'S CASH FLOW TO PRESENT VALUE FIRST, THEN ACCUMULATE. The question becomes "how long until the PRESENT VALUE of the returns equals the investment?", which is the economically meaningful version.

THE STANDARD EXAMPLE, carried through this whole section: Investment Rs 100,000 at t = 0 Net cash inflow Rs 30,000 per year for 5 years Discount rate i = 10% ── SIMPLE PAYBACK ────────────────────────────────────────── 100,000 / 30,000 = 3.33 YEARS ── DISCOUNTED PAYBACK ────────────────────────────────────── YEAR CASH FLOW P/F(10%,n) DISCOUNTED CUMULATIVE ───────────────────────────────────────────────────────── 0 −100,000 1.0000 −100,000 −100,000 1 30,000 0.9091 27,273 −72,727 2 30,000 0.8264 24,793 −47,934 3 30,000 0.7513 22,539 −25,394 4 30,000 0.6830 20,490 −4,904 5 30,000 0.6209 18,628 +13,724 ───────────────────────────────────────────────────────── RECOVERY OCCURS DURING YEAR 5. Interpolating: discounted payback = 4 + 4,904 / 18,628 = 4 + 0.263 = 4.26 YEARS COMPARE: 3.33 years undiscounted against 4.26 discounted. THE DISCOUNTED FIGURE IS ALWAYS LONGER — necessarily so, since every discounted inflow is smaller than the raw one. THE 0.93-YEAR DIFFERENCE IS THE COST OF WAITING, which simple payback pretends does not exist. AND NOTE THE INTERNAL CHECK, which is worth pointing out because it links the two topics: THE FINAL CUMULATIVE FIGURE, +13,724, IS EXACTLY THE PROJECT'S NPV. Discounted payback and NPV are the same calculation read at different points — NPV asks "what is the total at the end?", discounted payback asks "when did the running total cross zero?". A SECOND EXAMPLE WITH UNEVEN FLOWS, since exams prefer them: Investment 50,000; returns 15,000 / 20,000 / 25,000 / 10,000 at 12%. YEAR FLOW P/F(12%) DISCOUNTED CUMULATIVE ──────────────────────────────────────────────── 1 15,000 0.8929 13,393 −36,607 2 20,000 0.7972 15,944 −20,663 3 25,000 0.7118 17,795 −2,868 4 10,000 0.6355 6,355 +3,487 ──────────────────────────────────────────────── discounted payback = 3 + 2,868/6,355 = 3.45 YEARS (simple payback = 3 + 10,000/10,000... no: cumulative undiscounted is 15+20+25 = 60,000 > 50,000 at year 3, so simple payback = 2 + 15,000/25,000 = 2.60 YEARS) AGAIN THE DISCOUNTED FIGURE IS SUBSTANTIALLY LONGER — 3.45 against 2.60 — and the gap widens as the discount rate rises.

THE ADVANTAGES, which explain its persistence: 1. IT MEASURES LIQUIDITY AND RISK EXPOSURE. Payback answers "how long is my capital at risk?", which NPV does not answer at all. For a firm with limited cash or operating somewhere politically or economically unstable, THAT IS THE BINDING CONSTRAINT. 2. IT IS SIMPLE TO COMPUTE AND TO EXPLAIN. A board, a household or a client understands "it pays for itself in four years" immediately. 3. IT FAVOURS EARLY CASH FLOWS, which are inherently more certain — a year-2 forecast is far more reliable than a year-9 one. 4. IT IS A USEFUL SCREENING FILTER: reject anything over the cut-off quickly, then apply NPV to the survivors. THE DISADVANTAGES — and the first is decisive: 1. IT IGNORES ALL CASH FLOWS AFTER THE PAYBACK POINT. This is the criticism that matters. Consider: PROJECT X: cost 100,000, returns 50,000/yr for 3 years → payback 2 years, total return 150,000 PROJECT Y: cost 100,000, returns 40,000/yr for 10 years → payback 2.5 years, total return 400,000 PAYBACK PREFERS X. NPV PREFERS Y OVERWHELMINGLY. PAYBACK SYSTEMATICALLY DISCRIMINATES AGAINST LONG-LIVED PROJECTS — which is to say against infrastructure, against research, and against exactly the investments an engineer is most often evaluating. 2. THE CUT-OFF PERIOD IS ARBITRARY. Why four years and not five? There is no theory behind the threshold. 3. IT DOES NOT MEASURE PROFITABILITY. A project can pay back quickly and still destroy value. 4. IT CANNOT RANK MUTUALLY EXCLUSIVE PROJECTS reliably. 5. Simple payback additionally ignores the time value of money — which is what discounted payback repairs, leaving the other four faults untouched. THE HONEST SUMMARY, which is what an exam answer should conclude with: DISCOUNTED PAYBACK FIXES THE TIME VALUE PROBLEM AND FIXES NOTHING ELSE. It still ignores everything beyond the payback point and still uses an arbitrary cut-off. THEREFORE IT IS A LEGITIMATE SUPPLEMENTARY MEASURE — used alongside NPV to describe risk exposure — AND NOT A LEGITIMATE PRIMARY CRITERION. THE STANDARD PROFESSIONAL PRACTICE: USE NPV TO DECIDE, AND PAYBACK TO DESCRIBE. A project report states the NPV, the IRR and the payback period together, because each answers a different question: NPV asks "how much value?", IRR asks "at what rate?", and payback asks "for how long is the money exposed?"