NISM-Series-XV: Research Analyst · Valuation Principles

Time Value of Money and Discounting for NISM Research Analyst

Updated 11 October 2026 · Fact-checked

Time value of money means ₹1 today is worth more than ₹1 later, because money can earn a return. Future value = PV × (1 + r)ⁿ. Present value = FV ÷ (1 + r)ⁿ. You solve questions by fixing the rate, the period and the cash flow pattern, then picking the right formula.

Understand Time Value of Money and Discounting

Time value of money is the idea that a rupee received today is worth more than a rupee received in future. You can invest today's rupee and earn interest. You also face inflation and the risk that future cash may not arrive.

Future value (FV) tells you what money today grows to after some periods at a given rate. Present value (PV) works backwards. It tells you what a future cash flow is worth today. The process of finding PV is called discounting. The rate used is the discount rate. It reflects the return you require for the risk and time involved.

Compounding means you earn interest on past interest. The higher the rate or the longer the period, the larger the gap between PV and FV. Discounting more heavily (a higher rate) makes PV smaller. This is why a riskier cash flow is discounted at a higher rate.

An annuity is a series of equal cash flows at equal intervals for a fixed number of periods. An ordinary annuity pays at the end of each period. An annuity due pays at the start. A perpetuity is an equal cash flow that continues forever. A growing perpetuity has a cash flow that grows at a constant rate.

All valuation rests on this. The value of a share or bond is the present value of the cash flows you expect from it. Dividend discount and DCF models are applications of the same idea.

Key formulas to remember

Future value (single sum): FV = PV × (1 + r)ⁿ; r is the rate per period and n is the number of periods. Match them (e.g. half-yearly rate with half-yearly periods).
Present value (single sum): PV = FV ÷ (1 + r)ⁿ; This is discounting. Higher r or longer n gives lower PV.
Periodic rate for compounding m times a year: Periodic rate = Annual rate ÷ m; periods = years × m; Use this when the question says half-yearly, quarterly or monthly compounding.
PV of ordinary annuity: PV = C × [1 − (1 + r)⁻ⁿ] ÷ r; C is the cash flow at the end of each period. The PV sits one period before the first cash flow.
FV of ordinary annuity: FV = C × [(1 + r)ⁿ − 1] ÷ r; Value is at the time of the last payment.
Annuity due adjustment: Annuity due value = Ordinary annuity value × (1 + r); Applies to both PV and FV. Each payment is one period earlier.
PV of perpetuity: PV = C ÷ r; First cash flow is one period from now. r must be a rate per period of the cash flow.
PV of growing perpetuity: PV = C₁ ÷ (r − g); C₁ is the next period's cash flow. Valid only when r > g.
Effective annual rate: EAR = (1 + Annual rate ÷ m)ᵐ − 1; More frequent compounding gives a higher EAR for the same stated rate.

How to solve Time Value of Money and Discounting questions

Use this order for any time value question. It stops you mixing up rates, periods and formulas.

1Draw a timeline. Mark each cash flow and when it occurs.
2Decide what is asked: value today (PV) or value later (FV).
3Identify the pattern: single sum, annuity, perpetuity or growing perpetuity.
4Convert the rate and number of periods to the same unit, based on the compounding frequency.
5Pick the formula. Check the timing: ordinary annuity or annuity due.
6Substitute the values and calculate carefully.
7Check reasonableness: PV must be below FV for a positive rate, and a perpetuity PV must exceed any single payment's PV.

Quickest way: Option elimination with direction and size checks

When to use it: Use this when options are numerical and you are short of time or cannot do long powers.

Decide the direction first. A PV answer must be smaller than the total of future cash flows. An FV answer must be larger than the amount invested.
For perpetuities, divide directly: C ÷ r. No power is needed.
For two or three years, multiply step by step instead of using powers (for example 1.10 × 1.10 = 1.21).
Cross out options that break the direction check or use the wrong period count.
Do the full calculation only for the options that remain.

Common mistakes in Time Value of Money and Discounting

Using the annual rate with half-yearly or quarterly periods.
You skip the compounding line in the question.
Fix: Divide the rate by m and multiply the years by m before any calculation.
Adding cash flows from different years without discounting.
You treat all rupees as equal in value.
Fix: Bring each cash flow to the same date first, then add.
Using the perpetuity formula C ÷ r when the first cash flow is not one period away.
You do not check timing.
Fix: Find the value one period before the first cash flow, then discount it back to today if needed.
Applying (r − g) when g ≥ r, or using C₀ instead of C₁ in the growing perpetuity.
You memorise the formula without its conditions.
Fix: Check r > g. Use the next cash flow C₁ = C₀ × (1 + g) if only the current one is given.
Treating annuity due as ordinary annuity.
You miss words like 'at the beginning of each year'.
Fix: Multiply the ordinary annuity value by (1 + r) when payments are at the start of periods.
Thinking a higher discount rate raises present value.
You confuse discounting with compounding.
Fix: Remember PV = FV ÷ (1 + r)ⁿ. A bigger denominator means a smaller PV.

Worked examples

Example 1

A stock is expected to pay a fixed dividend of ₹6 every year forever, with the first dividend one year from now. If your required return is 8% a year, what is the present value of the dividend stream?

Show the solution

The pattern is a perpetuity with C = ₹6 and r = 8% = 0.08.
PV = C ÷ r.
PV = 6 ÷ 0.08 = ₹75.

Answer: ₹75

Example 2

You will receive ₹1,21,000 two years from now. The discount rate is 10% a year, compounded annually. What is its present value?

Show the solution

This is a single sum: FV = ₹1,21,000, r = 10%, n = 2.
PV = FV ÷ (1 + r)ⁿ = 1,21,000 ÷ (1.10)².
(1.10)² = 1.21.
PV = 1,21,000 ÷ 1.21 = ₹1,00,000.

Answer: ₹1,00,000

Exam tips

Read the compounding frequency and timing words (end of year, beginning of year, forever) before touching the formula.
For perpetuity questions, check whether the cash flow given is the next one or the current one when growth is involved.
Know the direction rules: higher rate lowers PV and raises FV; longer time lowers PV and raises FV.
Conceptual options often test that a riskier cash flow needs a higher discount rate and so has a lower present value.
Wrong answers cost marks in this exam, so use the direction and size checks to remove options before guessing.

Practice questions from Valuation Principles

Time Value of Money and Discounting in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Time Value of Money and Discounting: frequently asked questions

What is the difference between present value and future value?

Future value is what money today grows to after some time at a given rate. Present value is what a future amount is worth today. They use the same rate and periods but in opposite directions.

How do I calculate the present value of a perpetuity?

Divide the fixed cash flow per period by the discount rate per period. For ₹10 a year at 5%, PV = 10 ÷ 0.05 = ₹200. This assumes the first payment comes one period from now.

What is a discount rate?

It is the rate used to convert future cash flows into present value. It reflects the return you require, which depends on time, inflation and risk. A riskier cash flow gets a higher discount rate.

Why does time value of money matter for equity valuation?

The value of a share or bond is the present value of the cash flows it is expected to give. Dividend discount and DCF methods are built on discounting those cash flows.