NPV in Case Interviews: The Discount Rate Decides It

Discount factors worth carrying into a case interview

You will not be given a factor table and you will not have a calculator. Four rates cover almost every case you will meet, and sixteen numbers cover four rates. Every factor below is rounded to two decimals, which is all a case needs.

Two shortcuts make the rest recoverable. A perpetual stream is worth its annual amount divided by the rate, so a dollar a year forever at 10 percent is worth ten dollars today. And the rule of 72 works on discounting as well as growth: at 12 percent, 72 over 12 is 6, so a dollar six years out is worth roughly half a dollar. The precise factor is 0.51, which is close enough to say out loud without apology.

Say the approximation as an approximation. Calling 0.507 "roughly a half" is a case skill. Calling it "a half" without the word roughly is an error, and a reader redoing the arithmetic will find the gap.

One project, three rates, two signs

Take a project that costs 100 today and returns 30 a year for five years, each payment arriving at year end. Undiscounted, the five payments total 150, so the project returns 50 on 100 and looks comfortable.

Now discount. The five-year annuity factor is the sum of the five yearly factors, so it is 4.10 at 7 percent, 3.60 at 12 percent, and 2.99 at 20 percent.

Read the column rather than any one row. The project is worth 23 at 7 percent, worth 8 at 12 percent, and destroys 10 at 20 percent. The rate nobody in the room can source has moved the recommendation from clear yes to no, and the crossing point is the internal rate of return, which sits near 15 percent here. At 15 percent the annuity factor is 3.35 and at 16 percent it is 3.27, so the factor that would make NPV zero, 100 over 30 or 3.33, falls just above 15 percent.

The 20 percent row is the one candidates skip, and it is the one that matters. A venture-grade hurdle rate turns a project with a 50 percent undiscounted return into a value-destroying one, without any change to the forecast.

The only discount rate we found published, and a regulator owns it

No consulting firm publishes a rate. We read four firm cases with full figures and none of them names one. Bain's Coffee Shop Co. case goes closest: its better answer says a stronger response "would take into account how long it would take for her to recoup the cost to open the store", and that "we'd want to understand more about our friend's investment timeline". Timing is raised. No rate is given.

A rate is published, though, and it belongs to the US Office of Management and Budget. Circular A-94 carries the instruction in full: "Constant-dollar benefit-cost analyses of proposed investments and regulations should report net present value and other outcomes determined using a real discount rate of 7 percent." The next sentence gives the reason. "This rate approximates the marginal pretax rate of return on an average investment in the private sector in recent years."

That is a real rate for public projects, and transplanting it into a corporate case is a choice you would have to defend. It is still the most useful anchor available, because it is dated, reasoned and checkable, and because 7 percent is the low end of what a company would use. Against it, the market rate for riskless money on 29 September 2026: the Treasury par yield curve closed at 4.58 percent for one year, 5.06 for five, 5.26 for ten and 5.59 for thirty. Those are nominal. A corporate hurdle rate sits above them by whatever the equity risk is judged to be, and no public source will hand you that judgment.

The terminal assumption outweighs the forecast you spent the time on

Add a terminal value to the project above. Suppose the business is sold at the end of year five for 100.

At 7 percent, 100 in year five is worth 100 times 0.71, so 71.3. The NPV becomes 23.0 plus 71.3, which is 94.3. Of that 94.3, the terminal lump contributes 71.3, which is 76 percent, so roughly three quarters of the value sits in a single assumption about a sale five years out.

At 20 percent, the same 100 is worth 40.2, and the NPV goes from minus 10.3 to plus 29.9. The terminal assumption has flipped the sign back, at the rate where the operating forecast had already failed.

That is the whole argument for saying out loud which input the answer turns on. Five years of carefully reasoned revenue growth moved the answer by less than one number nobody defended. Naming it costs a sentence: "three quarters of this NPV is the exit assumption, so I would test that before revisiting the growth rate."

Real and nominal, and why mixing them is silent

Circular A-94 states the rule flatly: "Nominal and real values must not be combined in the same analysis." It is worth repeating because the error leaves no trace in the arithmetic. Every multiplication is correct and the answer is wrong by roughly the inflation rate compounded over the horizon.

A concrete version. Forecast cash flows at current prices, then discount them at a nominal rate that already contains expected inflation, and you have charged inflation twice. Over ten years, the gap between the 7 percent factor of 0.51 and the 10 percent factor of 0.39 in the table above is three points of rate and roughly a quarter of the value, because 0.39 over 0.51 is 0.76. Declare which basis you are in, in the first sentence, and stay there.

The same circular is also careful about the internal rate of return, and its caution is worth borrowing: it "does not generally provide an acceptable decision criterion", though it "does provide useful information, particularly when budgets are constrained or there is uncertainty about the appropriate discount rate." That is exactly the case situation. You do not know the rate, so quoting the rate at which the answer breaks even is more honest than quoting a single NPV.

How we score an NPV answer, and whose scale this is

No consulting firm publishes a marking scheme for quantitative work, and none of the four published cases we read comes with one. 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 on a numerical answer. No firm has seen them.

Five case interview moves when there is no calculator

1. Round the cash flows before discounting. 28 becomes 30. The factors are two-digit approximations already, so precision in the flows buys nothing.
2. Write the factor row once, for the rate you were given, and reuse it.
3. Sum the factors into an annuity factor when the flows are level. One multiplication replaces five.
4. Compute the NPV at a second rate, higher than the first, and see whether the sign holds.
5. Report the sign, the rough magnitude, and the rate that would change your mind. In that order.

Step four is the one that separates an answer from a number. It costs one extra multiplication when the flows are level, and it converts an invented input into a stated range.

Step one deserves more defense than it usually gets, because rounding feels like cheating. It is not. The factors in the table above are already rounded to two decimals, and the cash flows in a case were made up by whoever wrote the case. A forecast of 28.4 discounted by a factor of 0.7130 carries five digits of apparent precision on top of two guesses. Round both, and the answer keeps the accuracy it actually had while becoming sayable aloud, which is the binding constraint in an interview.

What to say in a case interview when you cannot compute it

Sometimes the flows are uneven, the horizon is long, and there is no clean factor. Say what the answer depends on instead of forcing a figure. "At any rate under about 15 percent this is positive, and above it negative, so the question becomes whether this client's cost of capital is above or below 15." That is a complete answer to a decision question, and it is often the better one.

There is a second version of this, for when the case gives you a rate you think is wrong. Do not argue about it. Compute at the rate you were handed, then add one line: "at 12 percent this clears, and it would stop clearing somewhere around 15, so if the real hurdle for a project this uncertain is higher than 15 this recommendation reverses." You have accepted the interviewer's input and shown its consequence, which is the move the Circular's own sensitivity instruction describes.

Where the decision is about volume rather than timing, discounting is the wrong tool and break-even analysis is the right one. Where the client has named a time limit rather than a rate, the comparison runs on return and payback, which is undiscounted and therefore disagrees with NPV in predictable ways.

Drilling discounting

Build the factor table from memory once a day for a week and it stops being something you look up. Then practice the second half, which is harder and scored higher: after every NPV you compute, name the rate that flips it and the single input carrying the most value.

Then drill the failure you have not met yet. Uneven cash flows are common in cases and almost nobody practices them, because level flows let you use an annuity factor and feel fast. Take a stream like 10, 40, 60, 60, 40 and discount it flow by flow. It is five multiplications and one sum, and the point is to learn that the early years barely matter. At 12 percent, the first two years of that stream contribute 8.9 and 31.9, while years three to five contribute 42.7, 38.1 and 22.7. Front-loaded costs and back-loaded benefits are what discounting is for, and you cannot feel that from level flows.

The weights above and the reasoning behind them sit on how an answer is assessed. The math drill returns the four dimensions separately and names the first thing to fix, which is how you find out whether your losses are arithmetic or interpretation. Nothing on this page sits behind a sign-up, and every figure above can be rebuilt from the two government sources linked in the text.