Time Value of Money - Video Notes

Time Value of Money (Page 2)

  • The concept that money available now is worth more than the same amount in the future because it can be used for investment or consumption.
  • Example posed: Which would you prefer - Rs 10,000 today or Rs 10,000 in 5 years? Obviously Rs 10,000 today.
  • Rationale: Money received sooner allows one to invest or consume earlier; this is the TIME VALUE OF MONEY!!

Time Value of Money (Concept overview and motivation)

  • Money now enables investment opportunities, consumption timing, and potential earnings growth.
  • The value of money changes over time due to earning capacity and consumption preferences.

Reasons for Time Value of Money (Page 3)

  • Individuals prefer current consumption to future consumption.
  • Capital can be employed productively to generate positive returns.
  • In an inflationary period, a rupee today represents a greater purchasing power than a rupee a year hence.

Time Preference Rate & Required Rate (Page 4)

  • The time value of money is generally expressed by an interest rate, typically the risk-free rate.
  • If risk is involved, a risk premium is added to the interest rate.
  • Required Rate = Risk Free rate + Risk Premium
  • The required rate of return may also be comparable with the opportunity cost of capital.

Compound Value (Page 5)

  • Definition: The ability of an asset to generate earnings, which are then reinvested to generate their own earnings. In other words, compounding refers to generating earnings from previous earnings.
  • Also known as "compound interest".
  • Interest that accrues on the initial principal and the accumulated interest of a principal deposit, loan or debt.
  • Compounding of interest allows a principal amount to grow at a faster rate than simple interest, which is calculated as a percentage of only the principal amount.

Formulas: Future Value and Present Value (Page 6)


  • FV_n = PV(1+r)^n
  • FV = Future or Compound Value
  • PV = Present Value
  • r = rate of interest

- n = number of years

(1+r)^n = the future value interest factor

  • Simple Interest
    FV = PV(1+n*r)

Compound Value of an Annuity (Page 7)

  • An annuity is an investment that you make, either in a single lump sum or through installments paid over a certain number of years, in return for which you receive back a specific sum every year, every half-year or every month, either for life or for a fixed number of years.
  • Ordinary Annuity: A series of fixed payments made at the end of each period over a fixed amount of time.
  • Annuity Due: An annuity due requires payments to be made at the beginning of the period.
  • Formulas:
    • Ordinary Annuity: FV_{ordinary} = A \frac{(1+r)^n - 1}{r}
    • Annuity Due: FV_{due} = A \frac{(1+r)^n - 1}{r} \cdot (1+r)
  • Note: The transcript shows some typographical inconsistencies; the standard forms above are used.

Sinking Fund (Page 8)

  • A sinking fund provision is a pool of money set aside by a corporation to help repay a bond issue.
  • Formulas:
    • FV = A \cdot CVAF_{n,i}
    • A = \frac{FV}{CVAF_{n,i}}
    • A = FV \cdot \frac{i}{(1+i)^n - 1}
  • Here CVAF stands for the Compound Value Annuity Factor.
  • Purpose: It helps determine the annual amount to be put in a fund to repay bonds or debentures at the end of a specified period.

Present Value (Page 9)

  • Present Value is the amount of current cash that is equivalent in value to a future cash flow (inflow or outflow) for the decision maker.
  • Discounting is the process of determining present values of a series of future cash flows.
  • The compound interest rate used for discounting cash flows is also called the discount rate.
  • Formulas:
    • FV = PV(1+r)^n
    • PV = \frac{FV}{(1+r)^n}

Net Present Value (Page 10)

  • NPV is the difference between present value of cash inflows and the present value of cash outflows.
  • NPV is used in capital budgeting to analyze the profitability of an investment or project.
  • Common representation:
    • NPV = \sum{t=0}^{n} \frac{Ct}{(1+r)^t}
    • where Ct are cash flows (C0 usually negative, representing the initial investment)
  • Alternative common form:
    • NPV = \sum{t=1}^{n} \frac{Ct}{(1+r)^t} - C_0
  • Sign convention: cash inflows are positive; cash outflows are negative.

Connections, implications, and applications

  • The time value of money underpins decision-making in investment appraisal, loan pricing, savings planning, and capital budgeting.
  • Discount rate selection reflects risk, opportunity costs, and preferences for whether consumption today or in the future is prioritized.
  • Real-world relevance: evaluating projects, pricing debt, setting financial strategy, and making informed choices about consumption vs. investment.
  • Ethical and practical implications: choosing inappropriate discount rates can bias project selection, misallocate capital, or impact debt sustainability.