ROI and Payback Period in Consulting Case Interviews

Oliver Wyman's water case interview, recomputed to the last rupee

The oil and gas price strategy case ends on a financial viability question. Its exact wording matters: "What are the estimated costs and revenues for entering the new market, along with the forecasted payback period and return on investment (ROI)? The client requires a five-year payback period."

The published inputs are a 10 percent market share, a daily volume of 250,000 kL, fixed annual costs of Rs 20 crore where "1 crore = 10 million", and variable costs of Rs 5 per kL. The municipal buyer pays Rs 10 per kL. Here is every line, redone by hand in the order the page poses it.

Every one of those lines matches what the firm prints, including the rounding of 11.43 to "11.4 years". That is worth saying plainly, because it is not always true of published cases. This arithmetic holds.

The return the case asks for and never computes

Read the question again and then read the answer. The word ROI appears in the prompt and never again. The firm computes revenue, cost, profit and payback, then closes with one sentence. "The estimated payback period is around 11.4 years, which is longer than the client's target of five years." No return on investment is published anywhere on the page.

So here is one, and it is ours rather than the firm's. Annual profit of Rs 17.5 crore against Rs 200 crore of capital is 8.75 percent a year. Over the five years the client cares about, the venture returns 5 times 17.5, which is 87.5 crore against 200 invested, so 43.75 percent of the capital comes back inside the window. The project misses the client's test by a wide margin, and saying by how much is more useful than saying that it misses.

That 8.75 percent has a second meaning worth having. A perpetual stream of 17.5 crore discounted at 8.75 percent is worth 17.5 over 0.0875, which is exactly 200 crore. So 8.75 percent is the rate at which this venture breaks even over an infinite horizon. At 10 percent, an endless stream of 17.5 crore is worth only 175 crore against a 200 crore outlay, so the project never clears at 10 percent no matter how long you run it. A payback of 11.4 years understates how demanding this investment is.

What volume would have passed the client's payback period test

The more useful answer to a failed criterion is the volume that would meet it. Work backwards. A five-year payback on Rs 200 crore needs annual profit of 40 crore. Fixed costs are 20 crore, so contribution has to reach 60 crore, which is Rs 600,000,000. Contribution is Rs 5 per kL, so the venture needs 120,000,000 kL a year, and over 300 operating days that is 400,000 kL a day.

Check it forward. 400,000 × 300 × Rs 5 is Rs 600,000,000, less Rs 200,000,000 of fixed cost leaves Rs 400,000,000, which is 40 crore, and 200 divided by 40 is 5 years exactly.

Now put that in the client's language. 400,000 kL a day against the 250,000 assumed is 60 percent more volume. The case's own sizing question puts total Bangalore demand at 2,500,000 kL a day, so the venture needs 16 percent of the market rather than the 10 percent assumed. That is a sentence a partner can act on, and it took one division more than the firm's own answer.

Two projects, where ROI and payback pick different winners

The two measures disagree in a way that is easy to demonstrate and easy to get backwards, so here it is with numbers you can check.

Project A costs 100 and returns 50 a year for three years. Project B costs 100 and returns 25 a year for ten years.

Five measures, and payback and the annualized return prefer A while the other three prefer B. Nothing here is a mistake in any of the five. They are answers to different questions, and the question the client is actually asking decides which one you should lead with.

Read the last row carefully, because it is the one that moves the decision most. Discounted at 12 percent, B is worth roughly twice A, and B is the project payback rejects first.

What a payback period silently assumes

Two assumptions, both invisible in the arithmetic.

Everything after the cutoff is worth nothing. Project B above earns for six years after it has repaid its capital, and payback gives those six years no weight at all. On a long-lived asset that is a severe distortion.

Money inside the period is worth its face value. Discount project B at 12 percent and its payback stretches. The discounted inflows reach 100 somewhere between year five and year six, because the five-year annuity factor at 12 percent is 3.60 and the six-year factor is 4.11, and the project needs 4.00 to cover its outlay. Discounted payback therefore lands near 5.8 years against a stated 4.0, roughly 45 percent longer.

Circular A-94, the US federal guidance on benefit-cost analysis, treats a rate-of-return figure as useful rather than decisive, and says it earns its keep "particularly when budgets are constrained". That is the honest case for payback too. When a client cannot fund two good projects, the one that releases its cash sooner funds the next one, and that is a real advantage no NPV column shows.

A return whose numerator is not money

Gupta Strategists publishes a case asking for "the (public) return on investment" of a water filtration project, and its published answers compute one in life-years. The line reads "DALYs saved per euro = DALYs / Investment = 119,700/300,000 ≈ 0,4", and the firm adds a reading of it: "With 2,5 euros spent on the project someone will live an extra year.". Both hold: 119,700 over 300,000 is 0.399, the tilde declares the rounding, and one over 0.4 is 2.5.

The interesting part is the denominator. The firm's 300,000 euros is the total investment, and it includes 196,000 of grant money plus 60,000 from third parties. The foundation itself put up 44,000. Divide the same 119,700 life-years by 44,000 and the return is 2.72 DALYs per euro, which is nearly seven times the published figure.

Neither number is wrong. Return on total resources deployed and return on the sponsor's own money answer different questions, and choosing between them is the whole of the analysis. This is the discipline every ROI needs: say what is in the denominator before you quote the percentage, because a reader will assume the denominator you did not name.

How we score a return answer, and whose scale this is

No consulting firm publishes a marking scheme for quantitative work. Oliver Wyman publishes a full worked case and no weighting; Gupta publishes model answers and no weighting. The hundred points below are ours, written by us and read out of src/lib/grading/rubrics.ts. They are what our own grader measures. No firm has seen them.

The four questions that settle which of ROI and payback to use

Ask them in this order and the choice of measure stops being a matter of taste.

1. What is scarce? If cash is the binding constraint, payback is the client's real criterion and a strong long-run return will not help them. If capital is available and the horizon is long, lifetime return and discounted value are the right frame and payback will reject good projects.
2. What is in the denominator? Total capital, the sponsor's own equity, cumulative cash deployed, or the incremental spend over a base case. Four denominators, four percentages from one project.
3. Over what period is the return measured? Per year, over the life, or to a fixed date.
4. Has the client already stated a criterion? If so, the analysis is a comparison against their number and not a search for the best measure.

Ask what is scarce. The answer to that one question decides which column of the table above you lead with, and it is usually available for the asking. Where the horizon is long and the timing uneven, the comparison belongs on discounted value instead.

Oliver Wyman's client had already answered question four by stating a five-year requirement, which is why the case ends where it does. Gupta's case answers question two in the opposite direction, choosing total resources deployed over the sponsor's own contribution, and the choice moves the headline figure by a factor of nearly seven. Neither firm explains its choice, and in an interview you should explain yours.

Drilling both ROI and payback

Compute both on every investment case you meet, and then compute the third thing neither measure gives you: the volume, price or cost level at which the answer flips. That is the number a client uses.

The habit that pays off fastest is the reverse calculation shown above. Given a criterion the project fails, find the input value that would satisfy it. It is one division, it turns a rejection into a condition, and almost nobody does it. Where the question is about a volume with no time dimension at all, break-even analysis is the tool, and the same reverse move applies there.

The weights above and the reasoning behind them sit on how an answer is assessed. The math drill reports the four dimensions separately and names the first to fix, which is how a Units problem stops being mistaken for carelessness. Nothing here is behind a sign-up, and every figure above is reproducible from the two firm pages linked in the text.