Learning objectives
When you have finished, you can:
- Explain time value of money from first principles, as opportunity cost rather than magic or mere inflation, and move any cash flow to any date with
FV = PV·(1+r)^nandPV = FV/(1+r)^n, at any compounding frequency. - Convert any quoted rate into an effective annual rate (EAR) and refuse to compare loans or deposits on quoted APRs, including India's flat-rate loan trap and monthly-quoted credit-card rates.
- Price and build annuities both ways: PV and FV, ordinary and due. Compute an EMI from scratch, construct a full loan amortization schedule, and quantify the effect of a prepayment.
- Derive the perpetuity and growing-perpetuity (Gordon) formulas from the geometric series, state precisely why the formula demands
g < rand uses next year's cash flow, and demonstrate how PV explodes as g approaches r. - Deploy NPV as the master decision rule and articulate why it dominates every alternative: value additivity, currency units, correct opportunity-cost logic.
- Catch every IRR trap in the wild: multiple IRRs from sign changes (and construct such an example yourself), scale blindness, the reinvestment assumption, ranking conflicts and crossover rates. Compute MIRR, XNPV, and XIRR correctly.
- Convert real↔nominal exactly via Fisher
(1+r_nom) = (1+r_real)(1+π), know when the approximationr_real ≈ r_nom − πis safe, and never mix real cash flows with nominal rates, with the India-vs-US inflation contrast internalized. - Implement all of it in a spreadsheet: PV, FV, PMT, RATE, NPER, NPV (and its off-by-one trap), IRR, MIRR, XNPV, XIRR, EFFECT, NOMINAL, IPMT/PPMT, fast enough to pass a timed exam with a blank workbook.
Prerequisites & connections
Builds on. Module 0.04's financial-literacy bootcamp (compounding met informally; now we formalize it), M1.08 (debt mechanics: you have seen amortization from the accounting side; now you build it from the pricing side), M2.03 (ROIC: the return side of the value equation, to which you now add the time side), M2.04 (free cash flow: the thing we will be discounting from M3.04 onward).
Feeds into. Everything. M3.02–3.03 construct the discount rate r that is treated as given here. M3.04–3.05 discount forecast FCF streams: the growing annuity is your explicit forecast period, the growing perpetuity is your terminal value, and reverse DCF is Gordon run backward. M3.06's multiples are compressed TVM (P/B ≈ (ROE−g)/(r−g) is Gordon algebra, and you will derive it there). M3.07's key-value-driver formula is a growing perpetuity with reinvestment made explicit. M3.09's LBO returns are IRR/MOIC, with every IRR caveat above attached. M7 (macro) picks up Fisher and runs it through currencies and central banks. Even M9's hurdle-rate discipline is the same opportunity-cost logic applied to your own portfolio.
The one-sentence version of this module. A rupee today and a rupee in 2036 are different goods with different prices, and the discount rate is the exchange rate between them, set by what your money could otherwise earn.
4.1 A rupee today is not a rupee next year: the first principle
Start with what time value of money is not. It is not primarily about inflation. It is not a convention finance professors imposed. It is about opportunity cost: the oldest idea in economics wearing a formula.
Suppose I owe you ₹1,00,000 and offer to pay either today or exactly one year from now. Even in a world with zero inflation and zero risk, you should insist on today. Why? Because ₹1,00,000 today can be put to work. Park it in a one-year Government of India security yielding, say, 7%, and in a year you hold ₹1,07,000. The rupee today is worth more because it has an earning alternative. Whoever asks you to wait is asking you to give up that alternative, and must compensate you for it.
That is the entire theory. Everything else is arithmetic:
FV = PV × (1 + r)^n
PV= present value, the amount todayFV= future value, the amount at time nr= the rate per period, the return your next-best alternative of equivalent risk offersn= number of periods