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.
Say I owe you ₹1,00,000 and offer to pay either today or 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. Anyone who asks you to wait is asking you to give that alternative up, and they have to compensate you for it.
What is the time value of money formula?
That's all the theory you need. 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
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Why (1+r)^n and not 1 + r·n? Because each period's earnings start earning too. ₹100 at 10% becomes ₹110 after year one. In year two you earn 10% on ₹110, and the original ₹100 is no longer the base. That reinvestment-of-earnings effect is compounding, and no piece of arithmetic will matter more to you as an analyst. Take 7.1%, the Public Provident Fund rate of recent years. At that rate ₹1 becomes ₹7.83 in 30 years. Simple interest, 1 + 0.071×30, would give you ₹3.13. The gap between the two is earnings on earnings, and it's most of the outcome. PPF resets quarterly, so check the current rate on the National Savings Institute or India Post site.
Discounting is compounding run backward. Rearrange the same equation:
PV = FV / (1 + r)^n
Nothing new has happened. You've only solved for the other variable. "What is ₹1 crore received in 2036 worth today?" is the same question as "what deposit grows to ₹1 crore by 2036?" At 8%, PV = 1,00,00,000 / 1.08^10 = ₹46.32 lakh. Take that literally. If someone offers you a contract paying ₹1 crore in ten years, and your alternative is a comparable 8% instrument, the contract is worth ₹46.32 lakh today. Pay less and you beat your alternative. Pay more and you trail it.
What is a discount factor?
The discount factor as a price. Define DF(t) = 1/(1+r)^t, the value today of one rupee arriving at time t. Here it is at r = 12%, a common Indian equity hurdle that you'll learn to justify when you build the cost of capital:
| t (years) | 1 | 2 | 3 | 5 | 7 | 10 |
|---|---|---|---|---|---|---|
| DF at 12% | 0.8929 | 0.7972 | 0.7118 | 0.5674 | 0.4523 | 0.3220 |
Look at the last cell. At a 12% opportunity cost, a rupee ten years out is worth 32 paise today. So terminal-value assumptions matter a great deal, and distant "story" cash flows have to be enormous to justify high prices.
Discount factors also trade. A zero-coupon bond is a discount factor you can buy. A US Treasury STRIP paying $1,000 in 10 years and priced at $656.38 is the market telling you DF(10) = 0.6564, which is a 4.3% rate (656.38 × 1.043^10 = 1,000). When you discount, you're pricing future money the way the bond market already does. You just pick the rate to match your cash flow's risk.
How do you avoid mistakes and check your TVM answers?
Two habits that prevent 90% of errors:
- Draw the timeline. Time 0 is today. Under the end-of-period convention, a cash flow labeled "year 3" arrives at the end of year 3 unless the problem says otherwise. Every worked solution in the time value of money module starts with a timeline, and yours should too. In real work, most TVM mistakes are cash flows placed on the wrong date. Wrong formulas are the smaller problem.
- Match the rate to the period. If cash flows are monthly, r must be a monthly rate and n a count of months. An annual rate with monthly periods is the most common beginner error there is, and the page on compounding frequency is the cure.
Mental math anchor: the Rule of 72. Money doubles in roughly 72 / (rate in %) years. At 8%, about 9 years against an exact 9.01. At 12%, about 6 against 6.12. At 18%, about 4 against 4.19. It works very well between about 4% and 20%. It makes you the person who can say, mid-meeting, "a 12% compounder quadruples in twelve years" without touching a keyboard. Sanity-check every spreadsheet answer against it.
Where r comes from (for now). For now the discount rate is given. Treat it as the return on the next-best comparable alternative. What "comparable" means (risk, currency, duration) is the subject of the cost-of-capital work that comes next. One rule holds even now: the rate must match the cash flow. That means matching its risk. It also means matching its currency and its inflation basis, which the real-versus-nominal section will hammer home.