Time value of money and NPV
Why a rupee today and a rupee later are not the same, and how a discount rate links the two
Market rates as on 1 September 2026
Verified 12 October 2026
For training and education only. Not investment advice.
Trainer notes
Ask the room: would you take ₹1,00,000 today or ₹1,00,000 three years from now? Everyone picks today. Then ask: ₹1,00,000 today or ₹1,25,000 in three years? Opinions will split. Keep the question open; slide 4 gives a way to answer it.
A rupee today is worth more than a rupee a year from now.
Today's rupee can be put to work and earn something by next year. When prices rise, next year's rupee also buys less. So amounts must be compared at one date.
Trainer notes
Two separate reasons: money can earn a return while you wait, and inflation wears down what it buys. A third, for the notes only: a future payment may not arrive at all. The statement assumes a positive rate of return, which is the usual case.
Four words to know first
Future value
What a sum today grows to at a yearly rate r over n years. FV = PV × (1 + r)^n.
Present value
What a future sum is worth today at that rate. PV = FV ÷ (1 + r)^n.
Discount rate
The yearly rate r used to bring future money back to today. Somebody chooses it.
NPV
Net present value: the present value of the money coming in, minus the money going out today.
Take-away: (1 + r)^n means (1 + r) multiplied by itself n times. At 8% for 3 years: 1.08 × 1.08 × 1.08.
Trainer notes
These formulas assume interest is added once a year. With monthly or quarterly compounding the same idea holds but the rate and the number of periods are adjusted. Use the word 'assumed' whenever a rate is mentioned in this deck.
Forward and back with one rate
THE SET-UP
Amount today: ₹1,00,000.
Assumed rate: 8% a year, added once a year.
Period: 3 years.
- After 1 year: ₹1,00,000 × 1.08 = ₹1,08,000. After 2 years: ₹1,08,000 × 1.08 = ₹1,16,640.
- After 3 years: ₹1,16,640 × 1.08 = ₹1,25,971.20. In one step: ₹1,00,000 × 1.259712 = ₹1,25,971.20. This is the future value.
- Going back: ₹1,25,971.20 ÷ 1.259712 = ₹1,00,000. This is the present value of ₹1,25,971.20 due in 3 years.
- So at 8%, ₹1,25,000 in 3 years is worth ₹1,25,000 ÷ 1.259712 = ₹99,229.03 today, a little under ₹1,00,000.
Result: Compounding moves money forward in time. Discounting moves it back. One rate does both.
Illustration with an assumed rate of 8% a year. Not a forecast; returns are not assured.
Trainer notes
1.08 × 1.08 × 1.08 = 1.259712. This answers the opening question only for someone whose rate is 8%. At 7% the same ₹1,25,000 is worth ₹1,02,037.23 today, which is more than ₹1,00,000. The answer depends on the rate, which is the subject of the next slide.
The discount rate is an assumption
| Present value (₹) | |
|---|---|
| 4% | 67,556 |
| 6% | 55,839 |
| 8% | 46,319 |
| 10% | 38,554 |
| 12% | 32,197 |
Read the chart
- The future amount is the same in each bar: ₹1,00,000 in 10 years.
- Discounted at 4% a year it is worth ₹67,556.42 today. At 12% it is worth ₹32,197.32.
- No bar is 'the' answer. Each is correct for its rate.
- The higher the rate and the longer the wait, the smaller the present value.
Illustration: ₹1,00,000 ÷ (1 + r)^10 for each rate. Assumed rates, not forecasts of any return.
Trainer notes
Values: 4% ₹67,556.42; 6% ₹55,839.48; 8% ₹46,319.35; 10% ₹38,554.33; 12% ₹32,197.32. The discount rate is not looked up; it is chosen by the person doing the sum, usually from what the money could earn elsewhere at similar risk. The statement about the wait holds for any rate above zero.
Net present value of a small project
A shop pays ₹5,00,000 today for a machine. Assumed extra cash it brings in, discounted at 10% a year.
| When | Cash flow | Divide by | Present value at 10% |
|---|---|---|---|
| Today | − ₹5,00,000 | 1 | − ₹5,00,000.00 |
| End of year 1 | + ₹2,00,000 | 1.10 | + ₹1,81,818.18 |
| End of year 2 | + ₹2,50,000 | 1.21 (1.10 × 1.10) | + ₹2,06,611.57 |
| End of year 3 | + ₹2,00,000 | 1.331 (1.10 × 1.10 × 1.10) | + ₹1,50,262.96 |
| Net present value | + ₹38,692.71 |
Illustration with an invented project and assumed figures. Inflows total ₹5,38,692.71 in today's money; less the ₹5,00,000 outlay, NPV = ₹38,692.71.
Trainer notes
Check: 1,81,818.18 + 2,06,611.57 + 1,50,262.96 = 5,38,692.71. A positive NPV means that, at 10%, the forecast inflows are worth more today than the outlay. It does not mean the cash will arrive as forecast. Cash flows are placed at year ends to keep the sum simple.
Same project, a different rate
THE SAME CASH FLOWS
Pay ₹5,00,000 today.
Receive ₹2,00,000, ₹2,50,000 and ₹2,00,000 at the end of years 1, 2 and 3.
- No discounting: ₹6,50,000 − ₹5,00,000 = ₹1,50,000. This treats a rupee in year 3 as equal to a rupee today.
- At 10%: inflows are worth ₹5,38,692.71 today. NPV = ₹5,38,692.71 − ₹5,00,000 = + ₹38,692.71.
- At 15%: ₹1,73,913.04 + ₹1,89,035.92 + ₹1,31,503.25 = ₹4,94,452.21. NPV = ₹4,94,452.21 − ₹5,00,000 = − ₹5,547.79.
- The project did not change. The rate did, and the answer moved from positive to negative.
Result: A positive NPV holds only for the rate used. Show the answer at more than one rate.
Illustration with an invented project and assumed figures. Not a forecast.
Trainer notes
At 15% the divisors are 1.15, 1.3225 and 1.520875. Somewhere between 10% and 15% the NPV is exactly zero; that rate is called the internal rate of return (IRR). Do not suggest which rate is 'right' for a real business; that is a judgement for its owners.
Where the same idea turns up
The price of a bond
A bond is a set of future payments. Its price is their present value. A ₹1,000 bond paying ₹100 a year for 3 years, discounted at 8%: ₹92.59 + ₹85.73 + ₹873.22 = ₹1,051.54.
A goal calculation
₹10,00,000 is needed in 10 years. At an assumed 8% a year, ₹10,00,000 ÷ 1.08^10 = ₹4,63,193.49 set aside today would reach it. At an assumed 6%, the amount is ₹5,58,394.78.
Take-away: In both, future rupees are brought back to today at a chosen rate. A new rate gives a new answer.
Illustrations with assumed figures. The rates are assumptions, not expected returns. Returns are not assured.
Trainer notes
Bond: ₹100 ÷ 1.08 = ₹92.59; ₹100 ÷ 1.1664 = ₹85.73; ₹1,100 ÷ 1.259712 = ₹873.22. For a bond the discount rate is the yield the market asks for; see the deck 'Bond prices and yields'. Goal: a lower assumed rate means more must be set aside today. A goal calculator works this way, usually with monthly instalments in place of one lump sum.
Market rates in view
A discount rate often starts from a bond yield plus an allowance for risk. Rates change; check the date.
- INDIA 10-YEAR G-SEC YIELD
- 6.96%Yield on the 6.94% GS 2036, the 10-year government bond, on 1 September 2026.
- RBI POLICY REPO RATE
- 5.50%Raised from 5.25% on 7 Oct 2026 (5.25% on 1 Sep 2026).
- CPI INFLATION
- 4.82%Year-on-year for August 2026 (provisional). RBI's target is 4%, within a band of 2% to 6%.
Sources: RBI Current Rates (10-year yield 6.9570%, 1 Sep 2026); RBI Monetary Policy Statement, 7 Oct 2026; MoSPI CPI press release, 14 Sep 2026.
Trainer notes
None of these is 'the' discount rate. A government bond yield is a common starting point for cash flows that are near certain; uncertain cash flows are usually discounted at a higher rate. Inflation matters for what the money will buy. Refresh these at each month-end, using market figures that are at least 30 days old. Market figures are shown with a lag of at least 30 days, in line with SEBI's norms on price data used for education.
When the rate is chosen carelessly
Too low for a project
Distant inflows are overvalued, and a weak project shows a positive NPV. The machine above passes at 10% and fails at 15%.
Too high for a goal
The amount needed today looks small. At an assumed 15%, ₹10,00,000 in 10 years needs ₹2,47,184.71 today; at 8%, ₹4,63,193.49.
Mixing in inflation
Cash flows that include price rises need a rate that includes inflation. Mixing the two kinds distorts the answer.
One rate for unlike risks
Uncertain cash flows are usually discounted at a higher rate than near-certain ones. One rate for both hides the risk.
Take-away: State the rate, say why it was chosen, and show the answer at a second rate.
Illustration with assumed rates. The rates are assumptions, not expected returns. Returns are not assured.
Trainer notes
₹10,00,000 ÷ 1.15^10 = ₹2,47,184.71. On the second point: a plan built on a high assumed return leaves a shortfall if returns turn out lower, and returns are not assured. A mutual fund distributor shows the calculation at more than one assumed rate and does not present any of them as likely.
Four things people get wrong
Misconception'₹1 crore in 20 years is ₹1 crore.'
What is trueDiscounted at 6% a year it is worth ₹31,18,047.27 today. Compare amounts only at the same date.
Misconception'NPV is a fact about the project.'
What is trueIt is the result of forecast cash flows and a chosen rate. Change either one and the NPV changes.
Misconception'A positive NPV is a sure gain.'
What is trueIt says the forecast inflows are worth more than the outlay at that rate. Forecasts can turn out wrong.
Misconception'The discount rate is the inflation rate.'
What is trueInflation is one part. The rate usually also reflects what the money could earn elsewhere and the risk taken.
Trainer notes
₹1,00,00,000 ÷ 1.06^20 = ₹31,18,047.27. The 6% is an assumed rate for illustration. On the fourth point: discounting by inflation alone answers a narrower question, namely what a future sum will buy in today's prices.
Check yourself
Question 1: What does ₹50,000 grow to in 2 years at 10% a year, added once a year? And what is the present value of ₹60,500 due in 2 years at the same rate?
Answer: ₹50,000 × 1.10 × 1.10 = ₹60,500. The present value of ₹60,500 due in 2 years at 10% is ₹60,500 ÷ 1.21 = ₹50,000. Compounding and discounting are the same sum run in opposite directions.Question 2: A project costs ₹1,00,000 today and pays ₹60,000 at the end of year 1 and ₹60,000 at the end of year 2. What is its NPV at 10% a year?
Answer: ₹60,000 ÷ 1.10 = ₹54,545.45. ₹60,000 ÷ 1.21 = ₹49,586.78. Total ₹1,04,132.23. NPV = ₹1,04,132.23 − ₹1,00,000 = ₹4,132.23.Question 3: A plan to reach ₹10,00,000 in 10 years assumes 15% a year. What happens to the amount needed today if 8% is assumed instead, and how would you put this to a client?
Answer: It rises from ₹2,47,184.71 to ₹4,63,193.49. The rate is an assumption, not a promise; returns are not assured. Show the calculation at more than one rate so the client sees how much rests on the assumption.
Sources and disclaimer
Sources for the figures in this explainer
- 10-year government bond yield (6.94% GS 2036, 6.9570% on 1 Sep 2026): Reserve Bank of India, Current Rates, rbi.org.in (page archived 2 Sep 2026).
- Policy repo rate 5.50% from 7 Oct 2026: RBI Monetary Policy Statement, Press Release 2026-2027/1264.
- CPI inflation 4.82% for August 2026 (provisional, base 2024=100): MoSPI press release dated 14 Sep 2026.
- Inflation target of 4% with a band of 2% to 6%, 1 April 2026 to 31 March 2031: Government of India notification of March 2026.
- Every other figure in this deck is an illustration computed from assumed amounts and rates: the shop, the machine, the bond and the goal are invented.
This material is for training and investor education only. It is not investment, tax or legal advice and is not a recommendation to buy, sell or hold any security or scheme. Examples use assumed figures unless a source and date are shown. Mutual fund investments are subject to market risks; read all scheme related documents carefully. Trustner Asset Services Pvt. Ltd. is an AMFI-registered Mutual Fund Distributor (ARN-286886).