The time value of money

11/July/2025 01:19 Share:

? Time Value of Money (TVM) – Concept

The Time Value of Money (TVM) is a fundamental financial concept that states “a rupee today is worth more than a rupee tomorrow.” This is because money has earning potential over time—it can be invested to earn interest, returns, or profits. TVM reflects the idea that receiving cash sooner allows one to invest it and generate additional income, whereas receiving it later loses this opportunity. TVM is crucial in finance for comparing investments, evaluating loan options, valuing future cash flows, and making business decisions like capital budgeting. It helps businesses and individuals in understanding the real value of future cash flows, especially when making long-term investment or financing decisions.

? Key Techniques of Time Value of Money

1. Future Value (FV)

The Future Value is the value of a present sum of money after a certain time period with interest or returns added to it. It answers the question: "How much will my money grow in the future if invested today?"

FV = PV × (1 + r)ⁿ
where:
PV = Present Value
r = Interest rate per period
n = Number of periods

Example: If you invest ₹10,000 at 10% annual interest for 3 years:
FV = ₹10,000 × (1 + 0.10)³ = ₹10,000 × 1.331 = ₹13,310

2. Present Value (PV)

The Present Value tells us how much a future amount of money is worth today, given a certain rate of return. It is the reverse of FV and is used in discounting future cash flows.

PV = FV / (1 + r)ⁿ

Example: If you’re supposed to receive ₹15,000 after 4 years, and the discount rate is 10%:
PV = ₹15,000 / (1 + 0.10)⁴ = ₹15,000 / 1.4641 ≈ ₹10,240.78

3. Annuity

An annuity is a series of equal payments made at regular intervals over a period of time. It could be in the form of monthly EMIs, rent, or pension payments. TVM is used to calculate both Present Value of an Annuity (PVA) and Future Value of an Annuity (FVA).

(A) Present Value of Annuity (PVA)

PVA = PMT × [1 - (1 + r)^-n] / r

Example: If you receive ₹5,000 annually for 5 years, and the interest rate is 8%:
PVA = 5,000 × [1 - (1 + 0.08)^-5] / 0.08 ≈ 5,000 × 3.993 ≈ ₹19,965

(B) Future Value of Annuity (FVA)

FVA = PMT × [(1 + r)ⁿ - 1] / r

Example: Investing ₹5,000 annually for 5 years at 8%:
FVA = 5,000 × [(1 + 0.08)⁵ - 1] / 0.08 ≈ 5,000 × 5.867 ≈ ₹29,335

4. Perpetuity

A perpetuity is a special type of annuity that continues forever. It is used in valuing bonds or projects with infinite cash inflows (like endowments or real estate leases).

PV = PMT / r

Example: If a project pays ₹1,000 every year forever and the required rate of return is 5%:
PV = ₹1,000 / 0.05 = ₹20,000

5. Compounding and Discounting

These are the core processes of TVM:

Compounding helps in calculating future values.
Discounting helps in finding present values.

These concepts are applied in investment decisions, EMI calculations, capital budgeting (NPV, IRR), lease evaluations, and more.

✅ Conclusion

Time Value of Money is essential for understanding the real worth of money over time. Whether you are saving, investing, or borrowing, TVM helps you compare financial alternatives and make better decisions. The use of formulas like FV, PV, annuity, and perpetuity provide a mathematical way to evaluate future cash flows in today’s terms, making them a cornerstone of modern financial management.