NPV and payback, interview style
Cases about investments ask whether money spent now comes back later. Interviewers keep the math light, often giving you discount factors.
- Payback: investment / yearly cash. Simple and easy to explain, but it ignores everything after payback and the timing of money.
- NPV (net present value): today's value of future cash minus the investment. Multiply each year's cash by its discount factor and add them. Positive NPV: the project beats the required return.
- Perpetuity: cash C every year forever, at rate r, is worth C / r. Growing at g: C / (r - g).
- Annuity: the same cash for n years: cash × annuity factor (given).
Watch the sign of year 0 (the investment is negative) and whether a rate is given as a percent or a decimal. For the spreadsheet side, the Finance course covers NPV and IRR functions.
Invest $1,000 now; get 400, 500, 600 over three years; factors 0.91, 0.83, 0.75
PV = 400 × 0.91 + 500 × 0.83 + 600 × 0.75 = 364 + 415 + 450 = 1,229
NPV = 1,229 - 1,000 = 229
Discount each year, add them up, subtract the investment.