Present value:
what a future payment is worth to you today

Why a later rupee is worth less than a rupee now

Offered ₹10,00,000 today or ₹10,00,000 in five years, almost everyone takes it now. Today's money can be invested, spent, or used to retire a loan, and prices usually rise in the meantime. Present value (PV) turns that instinct into a calculation: it states what a future amount is worth in today's terms.

The tool that makes the conversion is the discount rate. It stands for the return you could earn elsewhere, or the cost of borrowing, or the pace of inflation, depending on the question you are asking. Choosing it is the hardest part; the arithmetic is simple.

Three ideas sit underneath the maths. First, a payment's size is not its value; its value depends on when it arrives. Second, the further away the payment, the more it is reduced. Third, riskier or less certain payments are reduced more. Once those are clear, the formula is only a way of writing them down.

PV and future value are the same relationship read in opposite directions. Compounding grows an amount forward; discounting brings it back.

The discounting formula

The denominator is the same growth factor used in future-value work. Dividing by it undoes the growth. If ₹100 grows to ₹110 in one year at 10%, then ₹110 a year from now has a present value of ₹100.

When there are several payments, discount each one separately and add the results. A loan or a bond is nothing more than a stream of such amounts.

Worked example: ₹10,00,000 due in five years

A reasonable check: at 7% money doubles in roughly ten years, so five years should cut the value by a bit more than a quarter. The result, 71.3% of face value, passes.

The same ₹10,00,000 payable in ten years at 7% is worth only ₹5,08,349. Doubling the wait takes off more than ₹2 lakh because each extra year multiplies the discount again.

Choosing a discount rate that makes sense

• Opportunity cost: the return you could realistically get on a comparable-risk alternative, such as a bank deposit or index fund.
• Borrowing cost: if you would otherwise be paying off a loan at 11%, then 11% is the price of waiting.
• Inflation: using the expected inflation rate gives value in today's purchasing power.
• Risk premium: riskier payments, such as a customer promise to pay, deserve a higher rate than a bank guarantee.

The rate swings the answer more than most people expect. The next table shows the same ₹10,00,000 due in five years at four different rates.

Several payments, and the rate that makes two offers equal

A stream of payments is discounted one amount at a time. Suppose you are promised ₹50,000 at the end of each of the next three years and you use an 8% discount rate.

Discounting also answers a comparison question: at what rate are two offers equal? If someone offers ₹7,00,000 now or ₹10,00,000 in five years, the break-even rate is (10,00,000 ÷ 7,00,000)^(1/5) − 1 = 7.39%. If you can reliably earn more than that elsewhere, take the money now; if not, waiting is the better deal.

Where discounting shows up

• Settlements and lump sums: converting a stream of promised payments into a single figure today.
• Project evaluation: net present value subtracts the up-front cost from the discounted inflows.
• Valuing a business or property: expected future cash flows, discounted at a rate reflecting risk.
• Pension and annuity choices: comparing a lump sum now with a guaranteed monthly income.

In every case the result is only as good as the cash-flow forecast and the rate. A small change in the rate on a long-dated payment can move the value by tens of percent, so it is wise to test two or three rates and see how wide the range is.

Present value as a purchasing-power check

Discounting is not only for investors. Any future sum can be read against inflation by using the expected price rise as the discount rate. At 6% a year, a payment of ₹10,00,000 received in five years has the purchasing power of ₹7,47,258 today, so about ₹2.5 lakh of its apparent value is eroded by rising prices.

The same logic works in reverse for goals. A target of ₹10,00,000 for a child's course starting in five years is not a ₹10,00,000 goal in today's money; it is whatever amount buys what ₹7,47,258 buys now, if prices rise 6% a year. Be explicit about whether a figure is in today's money or in future money, because mixing the two is the commonest reason a plan falls short.

Mistakes that skew the answer

• Mixing periods: using an annual rate with a number of months.
• Forgetting that the rate must be a decimal in the formula: 7% is 0.07.
• Treating a nominal rate as a real one, so inflation is counted twice or not at all.
• Discounting a payment that has already been taxed with a pre-tax rate.

Another trap is treating the discount rate as a forecast. It is a hurdle: a statement that you would only accept a delayed payment if it beats that return. Setting it too low makes distant payments look attractive, and a long project can seem worthwhile only because the rate was chosen generously.