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.