Present value
What a sum of money due in the future is worth today, found by discounting it back at the rate the money could earn: PV = FV ÷ (1 + r)^n.
In plain language
If you need a sum of money later, you do not need to put that whole sum aside now. Money set aside today can be invested and will grow. Present value answers the question: how much is enough today?
It is the mirror image of future value. Future value carries today's money forward by compounding; present value carries tomorrow's money back by discounting. Same equation, opposite direction.
In retirement planning the workbook uses present value twice — to see how little needs to be invested now for a known future sum, and, in its Excel form, to turn a stream of retirement income into the single corpus that will fund it.
How it works
Three inputs decide it:
- FV — the future sum required
- r — the rate of return the money will earn, per period
- n — the number of periods
A higher rate or a longer period gives a smaller present value, because the investment does more of the work.
In Excel the workbook uses the PV function. For a single future sum the inputs are Rate, Nper and FV. For a stream of income, as in the retirement corpus, the inputs are Rate, Nper, PMT and Type — the monthly income as PMT, Type = 1 for payment at the beginning of each period. Excel returns the answer as a negative number, and the workbook explains why: the sign indicates the outflow as funds are invested.
When the income being funded rises with inflation, the rate used is not the nominal return but the inflation-adjusted (real) rate, divided by 12 for monthly periods.
The formula
PV = FV ÷ (1 + r)^n
Excel, single sum: PV(Rate, Nper, , FV)
Excel, income stream: PV(Rate, Nper, PMT, , Type)
A worked example
A single sum — the workbook's Box 1.1. Mr X will need Rs 25,526 five years from now. A 5-year bank FD gives a post-tax 8 percent.
PV = 25,526 ÷ (1.08)^5 = Rs 17,372
Excel returns −Rs 17,372. He invests Rs 17,372 today, not Rs 25,526.
An income stream — the workbook's corpus case. Rani needs Rs 1,50,215 a month from 60 to 80 (240 months). The corpus earns 8 percent against 6 percent inflation, a real rate of 1.89 percent.
PV(1.89%/12, 240, 1,50,215, , 1) = Rs 3,00,48,832
Sensitivity to the rate (illustrative). A family needs Rs 10 lakh in 10 years for a goal:
| Rate assumed | Present value |
|---|---|
| 7% | 10,00,000 ÷ (1.07)^10 = Rs 5,08,349 |
| 0% (money kept idle) | Rs 10,00,000 |
The return assumption roughly halves the sum required today — which is also why the workbook warns that unrealistic return estimates leave the corpus short.
Why NISM asks about it
Chapter 1, section 1.2.1, introduces present value with the formula and the PV function in Box 1.1. Chapter 3, section 3.2.7 and Box 3.1, uses it to compute the retirement corpus by the deterministic method. Expect a direct discounting computation, a question on which Excel inputs are required, and the conceptual point that the negative sign in Excel's output denotes an outflow.
Common exam traps
- Present value is smaller than future value whenever the rate is positive. An answer larger than the future sum is wrong.
- The negative sign is a convention, not a loss. Excel shows −17,372 because the money is invested.
- Use the real rate when the income inflates. The corpus calculation discounts at 1.89 percent, not at the nominal 8 percent; using 8 percent would badly understate the corpus.
- Monthly periods need a monthly rate. 1.89 percent ÷ 12 with 240 months — not 1.89 percent with 20 periods.
- Type matters for a stream. Payment at the beginning of the month (
Type = 1) gives a larger present value than payment at the end. - Present value is not the Present Value factor — the factor is the 1 ÷ (1 + r)^n multiplier alone, before it is applied to a sum.
Where this is taught
- Series XVII · Chapter 1: Fundamental Concepts in Retirement Planningintroduced here
- Series X-A · Chapter 2: Time Value of Moneyintroduced here
Related terms
- InflationA sustained general rise in the price level, which erodes what a rupee buys — and the reason a nominal return has to be deflated before it means anything.
- PV functionThe spreadsheet function that converts a stream of future payments into the single lump sum needed today — the tool the workbook uses to size a retirement corpus and a life insurance cover.
- Real rate of returnThe return on an investment after the effect of inflation has been removed — what the money actually buys more of, as against the nominal percentage the product advertises.
- Time value of moneyThe principle that the same sum of money is worth different amounts at different points on a timeline, because money held today can be invested and because inflation erodes what it will buy.
- Future valueWhat a sum of money invested today will be worth at a future date once returns have been earned and reinvested — the compounding half of the time value of money.
- Spot rateThe true return on money invested today for one stated term with no interim cash flow — read straight off a zero-coupon instrument, and the only rate a cash flow should be discounted at.
- NPER functionThe Excel function that returns how many periods a loan takes to clear, given the rate, the instalment and the amount outstanding — the workbook's tool for the period of the loan.
- Ordinary annuityA series of equal payments falling at the end of each period — the default form of annuity, and the one every standard present value and EMI calculation assumes.
- Deterministic methodThe simplest way to calculate a retirement corpus — one fixed inflation rate and one fixed return throughout, giving a single definite corpus figure but ignoring how the sequence of returns can hurt a portfolio.
- Two-step education fundingThe workbook's method for funding a multi-year education goal from one set-aside: inflate each year's fee to the year it falls due, then discount the later years back to the set-aside date.
- Annuity dueAn annuity whose payments fall at the beginning of each period rather than the end, which makes it worth more than an otherwise identical ordinary annuity.
- PerpetuityA constant cash flow received every period with no end date. Its present value is simply the cash flow divided by the discount rate: PV = C / r.
- Frequency of compoundingHow often interest is calculated and added within a year — monthly, quarterly or annually — and the reason the same annual rate delivers a different actual return depending on the frequency chosen.