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Time Value of Money (TVM) is the single most important concept in Financial Management — every chapter from capital budgeting to bond valuation is built on it. The idea is simple: ₹1 in your hand today is worth more than ₹1 promised to you a year from now, because today's money can be invested to earn returns. This is asked in almost every CA Inter FM paper, either as a standalone 4–6 mark calculation or as the engine inside NPV, IRR, and lease-vs-buy problems.

There are two directions to move money through time. Future Value (FV) asks: if I invest money today, what will it grow to? Use FV = PV × (1 + r)ⁿ. Present Value (PV) asks the reverse: what is a future cash flow worth today? Use PV = FV ÷ (1 + r)ⁿ. The process of calculating PV is called discounting, and the rate used is the discount rate (also called required rate of return or cost of capital). When interest earns further interest, that's compounding — the magic that makes FDs grow faster than simple interest.

For a series of equal periodic cash flows, use annuity formulas. PV of Ordinary Annuity = A × PVIFA(r, n), where PVIFA = [1 − (1+r)⁻ⁿ] ÷ r. An ordinary annuity has payments at period-end (default assumption in exams). An annuity due has payments at period-start — multiply ordinary annuity result by (1+r). A perpetuity — equal payments forever — simplifies beautifully: PV = A ÷ r. This shows up in preference share valuation. For compounding more than once a year (semi-annual, quarterly), adjust: r becomes r/m and n becomes n×m, where m = compounding frequency. ICAI typically provides PVIF and PVIFA tables in the question — use them to save time, but know the formulas cold in case tables aren't given.

📊 Worked example

Example 1 — Future Value (Lump Sum)

Mr. Sharma deposits ₹2,00,000 in a bank FD at 10% p.a. compounded annually for 3 years. What does he receive at maturity?

| Step | Working |

|------|----------|

| Formula | FV = PV × (1 + r)ⁿ |

| Values | PV = ₹2,00,000 · r = 0.10 · n = 3 |

| Compute | (1.10)³ = 1.10 × 1.10 × 1.10 = 1.3310 |

| FV | ₹2,00,000 × 1.3310 = ₹2,66,200 |

Mr. Sharma receives ₹2,66,200 at the end of 3 years.

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Example 2 — Present Value of Annuity

Rajesh & Co. Pvt. Ltd. expects cash inflows of ₹75,000 at the end of each year for 4 years from a new machine. The required rate of return is 12%. What is the present value of these inflows?

| Step | Working |

|------|----------|

| Formula | PV = A × PVIFA(12%, 4) |

| PVIFA calc | [1 − (1.12)⁻⁴] ÷ 0.12 |

| (1.12)⁴ | 1.12 × 1.12 × 1.12 × 1.12 = 1.5735 |

| (1.12)⁻⁴ | 1 ÷ 1.5735 = 0.6355 |

| PVIFA | (1 − 0.6355) ÷ 0.12 = 0.3645 ÷ 0.12 = 3.0375 |

| PV | ₹75,000 × 3.0375 = ₹2,27,813 |

The present value of the cash inflows is ₹2,27,813.

If the machine costs less than this today, the investment creates value.

⚠️ Common exam mistakes

  • Multiplying when you should divide (or vice versa): Don't use FV = PV × (1+r)ⁿ when you need PV — discounting always divides (or equivalently, multiplies by a fraction less than 1). Ask yourself: am I moving money forward in time (multiply) or backward (divide)?
  • Applying ordinary annuity formula to annuity due problems: If the question says payments are made 'at the beginning of each year' or 'in advance,' multiply your ordinary annuity answer by (1+r). Most exam questions are ordinary annuity — don't assume due unless explicitly stated.
  • Forgetting to adjust r and n for sub-annual compounding: For 12% p.a. compounded quarterly over 2 years, use r = 3% and n = 8 — not r = 12% and n = 2. This is a very common slip that kills 2 marks.
  • Rounding PVIF/PVIFA too early: Rounding to 2 decimal places mid-calculation causes your final answer to differ from ICAI's solution. Keep at least 4 decimal places until the very last step.
  • Using perpetuity formula (A/r) for a finite annuity: Perpetuity only applies when cash flows continue forever (e.g., irredeemable preference shares). For any annuity with a fixed end date, use the proper PVIFA formula.
📖 Reference: TVM — Institute of Chartered Accountants of India
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