Discount
Divide each year's cash by (1 + r) once per year of waiting.
- Year 1 at 10%
- × 0.91
- Year 5 at 10%
- × 0.62
How to calculate NPV, case interview math, worked
To calculate NPV, divide each year's cash flow by (1 + r) raised to the number of years until it arrives, add them up and subtract the upfront cost. If the result is above zero, the investment earns more than the discount rate. In a consulting case you rarely need more than round discount factors, one shortcut for even cash flows and cash ÷ rate for cash that lasts forever. Soreno, an AI voice interview practice app for consulting, investment banking and other finance candidates, runs free case math drills with no sign-up, and full mock cases where the interviewer checks your math out loud.
Updated
- The formula
- Sum of cash ÷ (1 + r)^t, minus cost
- t is the number of years until the cash arrives
- Perpetuity
- Cash ÷ rate
- Growing: next year's cash ÷ (rate minus growth)
- Worked cases
- 2, every step shown
- Invented by us, math checked two ways
- Free practice
- No sign-up
- Timed case math drills in your browser
What is NPV, and how do you calculate it?
NYU Stern's Aswath Damodaran defines net present value as the sum of the present values of all cash flows from a project, including the initial investment, and gives the rule: accept if NPV is above zero. His primer gives three reasons a future dollar is worth less than one today: people prefer to spend now, inflation erodes money, and a promised payment might not arrive. The discount rate captures all three.
Add
Sum the discounted cash flows into one present value.
- Even cash
- Cash × sum of the factors
- 5 years at 10%
- Factors sum to 3.79
Subtract
Take off the upfront cost, which is not discounted.
- Year 0
- Cost counts in full
- Result
- That is the NPV
Decide
Above zero, it beats the discount rate. Below, it doesn't.
- Then ask
- What would flip the sign?
- Say
- The answer, then the risk
The mental math method (ours)4 shortcuts
In our experience, interviewers expect round numbers. These four tricks cover almost every NPV step in a consulting case.
Round factors
Learn five numbers at 10%
At 10%, a dollar 1 to 5 years out is worth about 0.91, 0.83, 0.75, 0.68, 0.62 today. Multiply each year's cash by its factor and add. For $1 million, $2 million and $3 million in years 1 to 3, that is 0.91 + 1.66 + 2.25, about $4.82 million.
Even cash
Annuity shortcut
When the cash is the same every year, add the factors once and multiply. At 10%, 5 years of factors add to about 3.79 and 6 years to about 4.35.
Forever
Perpetuity: cash ÷ rate
Damodaran defines a perpetuity as a constant cash flow at regular intervals forever, and values his console bond example as $60 ÷ 0.09, about $667. A growing perpetuity is next year's cash ÷ (rate minus growth), and he notes growth has to be less than the rate for it to work.
Halving
Halving time: rule of 72
Damodaran's primer gives the rule of 72 for how fast money doubles: 72 ÷ the rate. Run it backward for discounting: at 8%, cash 9 years out is worth about half today.
Worked case 1: Bayside Hotels renovation (ours)5 steps
Bayside Hotels, an invented chain, can spend $12 million renovating its rooms. The work adds $3 million of cash profit a year for 6 years, then the rooms need redoing. The client uses a 10% discount rate. Should it go ahead? This case and every number in it are invented by Soreno for practice.
Lay out the cash
$12 million now, $3 million a year for 6 years
Payback alone is 4 years, inside the 6 year life. That says it gets its money back, not whether it beats 10%.
Discount
Factors add to about 4.35
At 10%, years 1 to 6 are worth about 0.91, 0.83, 0.75, 0.68, 0.62, 0.56. Even cash, so add them once: about 4.35.
NPV
About +$1.05 million
$3 million × 4.35 is $13.05 million, less the $12 million cost: about +$1.05 million. Exact factors give $13.07 million and +$1.07 million, so the rounding costs little.
Stress it
Life and rate both matter
If the rooms need redoing after 5 years, NPV turns negative, about $630,000 below zero. At a 12% rate it is still positive, about +$330,000. The rate that brings NPV to zero is about 13%.
Recommend
Go ahead, if the rooms last six years
Renovate: it clears a 10% rate by about $1.07 million. The risk is the life of the work, not the rate, so ask what the last renovation lasted before you commit.
Worked case 2: Fairway Grocers loyalty program (ours)4 steps
Fairway Grocers, an invented chain, can spend $20 million on a loyalty program. The customers it keeps add $2.4 million of cash profit next year, growing 2% a year after that, with no end date. The rate is 10%. Is it worth it? This case and every number in it are invented by Soreno for practice.
Spot the shortcut
Cash that grows forever
No end date and steady growth: a growing perpetuity. Next year's cash ÷ (rate minus growth).
Value it
$2.4 million ÷ 0.08 = $30 million
At 10% with 2% growth, the program is worth $30 million today. Less the $20 million cost, NPV is +$10 million.
Stress it
Still +$4 million with no growth
With no growth at all it is $2.4 million ÷ 0.10 = $24 million, an NPV of +$4 million. It breaks even if next year's extra profit is only $1.6 million: the cost × (rate minus growth).
Recommend
Launch, and track kept customers
Launch it. The value rests on the $2.4 million of first year profit, so measure how many customers the program really keeps in its first year before adding more spend.
From NYU Stern (Damodaran): A Primer on the Time Value of Money, NYU Stern (Damodaran): capital budgeting notes, Microsoft Support: NPV function and Microsoft Support: XNPV function.
Free case math drills
Timed questions on percentages, growth, break-even, margins and big numbers, the arithmetic every NPV step rests on. Free, runs in your browser, nothing is saved.
Set up
A 10-question timed set
Do the math in your head or on paper, type the answer and press Enter. You see right or wrong straight away, then your score and average time per question.
Two questions from each type: percentages, growth rates, break-even, margins and large numbers. Answers within 1% count as correct.
When does NPV come up in a consulting case interview?
In our experience, as one step in an investment decision, with round numbers, not a model. Here is what we listen for.
Spot when it's needed
Upfront money for cash later: a new factory, a renovation, make or buy, a program with ongoing savings. If the cash comes over several years, the timing matters.
Say the setup first
State the cost, the yearly cash, how long it lasts and the rate before you multiply. The interviewer can correct an input before you do the math.
Round, then say so
Use two decimal factors and the shortcuts, and tell the interviewer you are rounding. Being close and fast beats exact and slow.
Turn the number into a decision
Positive or negative, what it means for the client, and which input would flip it. That last line is where most of the credit is.
7 interview questions with an NPV step
The first four are consulting cases. The last three are where finance interviews take it further. Under each is what a strong answer does.
Consulting cases
An investment decision with cash over several years.
A manufacturer is deciding whether to build a second factory. How would you evaluate the investment?
Sets out the cost, the yearly cash from new capacity and the factory's life, then gives a rough NPV and the input that could flip it. Practice it, see a model answer
A carmaker is deciding whether to keep making a key component in-house or buy it from a supplier. How would you approach it?
Compares the cash cost of each path over the same years, discounted, and adds the risks that numbers miss. Practice it, see a model answer
A coffee chain is opening a new store. How many cups a day does it need to sell to break even?
Starts with yearly break-even, then asks whether the store earns back its fit-out over the lease once the cash is discounted. Practice it, see a model answer
A private equity firm is considering buying a regional chain of dental clinics. How would you assess the deal?
Values the clinics' steady cash with a quick perpetuity check before getting into growth and exit. Practice it, see a model answer
Where finance interviews go further
DCF questions, beyond case math.
Walk me through a DCF.
Projects free cash flow, discounts it at WACC, adds a terminal value and bridges to equity value. Practice it, see a model answer
How do you calculate terminal value in a DCF?
Gives both methods, growing perpetuity and exit multiple, and checks one against the other. Practice it, see a model answer
What is WACC and how do you calculate it?
Weights the cost of debt after tax and the cost of equity by their shares of the capital. Practice it, see a model answer
Common NPV mistakes in case interviews
Discounting the upfront cost
Money spent today is already in today's dollars. Only the later cash gets divided by (1 + r).
Using profit instead of cash
NPV runs on cash. If the case gives profit after depreciation, ask whether to add it back.
Growth at or above the rate
Cash ÷ (rate minus growth) blows up as growth nears the rate. If growth looks close to the rate, the forever assumption is wrong.
Payback as the answer
Payback says when the money comes back, not whether the project beats the rate. Use it as a quick check, then give the NPV.
Ignoring how long it lasts
In the Bayside case, one year less of life turns a positive NPV negative. Ask about the life before the rate.
Building a banking DCF
A consulting case wants an NPV in a minute or two. Free cash flow builds, WACC and terminal multiples belong in finance interviews.
Do the math out loud
Soreno's AI interviewer runs a full case, hands you the numbers when you ask, checks your math as you go and scores the session. Start your free week.
Questions people ask
What is the NPV formula?
NPV = cash in year 1 ÷ (1 + r) + cash in year 2 ÷ (1 + r)² + ... + cash in year n ÷ (1 + r)^n, minus the upfront cost. r is the discount rate. If NPV is above zero, the investment beats the rate.
How do you calculate NPV in Excel?
Use =NPV(rate, value1, value2, ...). Microsoft says the values must be equally spaced and arrive at the end of each period, so leave out a cost paid today and add it after. For Bayside, =NPV(10%, 3, 3, 3, 3, 3, 3)-12 gives about 1.07, in millions. If the dates are uneven, use XNPV.
How do you calculate NPV quickly in a case?
Round the discount factors to two places, use the annuity shortcut when the cash is the same every year, and cash ÷ rate when it never ends. At 10%, five years of even cash is worth about 3.79 times one year's cash.
What discount rate should I use in a case interview?
Ask the interviewer, or say the rate you are assuming and why. Damodaran's primer says the rate reflects the preference for spending now, inflation and the risk the cash won't arrive, so riskier projects get a higher rate.
What is the difference between NPV and IRR?
NPV is a dollar figure at a given rate. IRR is the rate that sets NPV to zero, as Damodaran's notes put it, so you accept a project if IRR is above the discount rate. In the Bayside case, NPV is about $1.07 million at 10% and IRR is about 13%.
What is a perpetuity?
A constant cash flow at regular intervals forever. Its present value is cash ÷ rate. If it grows at a steady rate, use next year's cash ÷ (rate minus growth), with growth below the rate.
What is a good NPV?
Any NPV above zero. It means the project earns more than the discount rate. Between two projects, the higher NPV adds more value, so also say which input could flip the sign.
What is the difference between PV and NPV?
PV is what future cash is worth today. NPV is that PV minus the cost of getting it.
Is NPV the same as a DCF?
A DCF uses the same discounting to value a whole company, with projected free cash flow, WACC and a terminal value. Consulting cases rarely go that far. For banking interviews, see our walk me through a DCF question.
Do I need a calculator for NPV in a case interview?
Usually not. In our experience, case math is done on paper with round numbers. The factors and shortcuts on this page cover nearly every NPV step a consulting case asks for.