Time Value of Money - PowerPoint Bazaar

3.1. Basics of Time Value of Money (TVM)

The Time Value of Money (TVM) is the foundational financial concept that asserts a dollar today is worth more than a dollar in the future due to its potential earning capacity. This principle is vital in areas such as investment decision-making, retirement planning, loan amortization, and any situation involving cash flows over time.

Key Concepts:

Present Value (PV):
Present Value refers to the current worth of a future sum of money or stream of cash flows, given a specified rate of return or discount rate. It answers the question: “How much is a future amount worth today?”Formula:
PV=FV(1+r)nPV = \dfrac{FV}{(1 + r)^n}PV=(1+r)nFV
Where:
FVFVFV = Future Value
rrr = Discount rate (or interest rate)
nnn = Number of periods
Future Value (FV):
Future Value is the value of an investment after it has grown over a certain period at a given interest rate. It helps assess how much an investment made today will grow to in the future.Formula:
FV=PV×(1+r)nFV = PV \times (1 + r)^nFV=PV×(1+r)n

Discounting vs. Compounding:

Discounting:
Discounting is the process of determining the present value of a future amount. It’s used to calculate how much a future cash flow is worth today, considering the risk and time.
Compounding:
Compounding refers to the process where the value of an investment grows because earnings on an investment generate their own earnings. This concept is used to determine the future value of an investment.

3.2. Applications of TVM

The Time Value of Money plays a critical role in various financial applications:

Annuities:
An annuity is a series of equal payments made at regular intervals over a specified period. Annuities can be classified as ordinary annuities (where payments are made at the end of each period) or annuities due (where payments are made at the beginning of each period). TVM helps in calculating both the present and future value of annuities.PV of an Ordinary Annuity:
PV=P×1−(1+r)−nrPV = P \times \dfrac{1 – (1 + r)^{-n}}{r}PV=P×r1−(1+r)−n
Where PPP is the periodic payment.
Perpetuities:
A perpetuity is an annuity that lasts forever, meaning it provides an infinite stream of cash flows. The present value of a perpetuity is calculated using the formula:PV of Perpetuity:
PV=PrPV = \dfrac{P}{r}PV=rP
Where PPP is the periodic payment, and rrr is the discount rate.
Mixed Cash Flows:
Not all cash flows are equal in magnitude or timing, so TVM can be used to calculate the present or future value of mixed cash flows by discounting or compounding each individual flow.
Loan Amortization:
Loan amortization refers to the process of paying off a loan over time through scheduled, equal payments. Each payment covers both the interest and a portion of the principal. The TVM concepts of PV and discounting are essential for determining the payment amounts, as well as understanding the proportion of each payment that goes toward interest vs. principal.
Retirement Planning:
TVM plays a significant role in retirement planning, particularly in determining how much money needs to be saved today to reach a future retirement goal, how long savings will last, and how to structure withdrawals over time. TVM is used to compute the future value of investments and the present value of desired retirement withdrawals.