CFA Level I — TVM Concept Flashcards

These flashcards cover the core Time Value of Money (TVM) concepts from the CFA Level I curriculum, including formulas, relationships, and definitions for annuities, perpetuities, and compounding.

Time Value of Money

The concept that a rupee today is worth more than a rupee received in the future because today's rupee can be invested to earn a return.

Basic TVM Components

The three foundational elements: Present Value (PV), Future Value (FV), and Interest or Discount Rate (r).

Present Value (PV)

The value today of future cash flows.

Future Value (FV)

The value at a future date of money invested today.

Basic Future Value (FV) Formula

$$FV = PV \times (1 + r)^n$$

Basic Present Value (PV) Formula

$$PV = \frac{FV}{(1 + r)^n}$$

r

The interest rate or required rate of return per period.

n

The number of compounding periods.

Impact of Interest Rate on FV

Future value increases when the interest rate increases, assuming PV and the number of periods remain constant.

Impact of Discount Rate on PV

Present value decreases when the discount rate increases, assuming FV and the number of periods remain constant.

Impact of Periods on FV

Assuming the rate is positive, FV increases as the number of periods increases.

Impact of Periods on PV

Assuming the discount rate is positive, PV decreases as the number of periods increases.

Compounding

The process of earning interest on both the original principal and previously earned interest.

Simple Interest

Interest calculated only on the original principal amount.

Compound Interest

Interest calculated on the principal plus any accumulated interest from previous periods.

Discounting

The process of converting a future amount into its equivalent value today.

Discount Rate

The specific rate used to convert future cash flows into present value.

Annuity

A series of equal cash flows occurring at regular intervals for a specified number of periods.

Ordinary Annuity

A type of annuity where equal cash flows occur at the end of each period.

Annuity Due

A type of annuity where equal cash flows occur at the beginning of each period.

Relative Value: Ordinary Annuity vs. Annuity Due

Annuity due has a higher value because each payment occurs one period earlier, allowing more time for compounding.

Perpetuity

A series of equal cash flows that continues indefinitely.

PV of a Perpetuity Formula

$$PV = \frac{CF}{r}$$

PV of Perpetuity and r Relationship

As the interest rate (r) increases, the present value of a perpetuity decreases.

Growing Perpetuity

A perpetuity whose cash flows grow at a constant rate indefinitely.

Growing Perpetuity Formula

$PV = \frac{CF_1}{r - g}$ where $r > g$.

r and g Variables

In a growing perpetuity, r represents the required return and g represents the constant growth rate.

Uneven Cash-Flow Stream

A series of cash flows where the financial amounts vary from period to period.

Valuation of Uneven Cash Flows

Calculated by determining the individual PV of each cash flow and adding them together.

PV and FV Key Relationship

PV grows into FV through compounding, while FV is discounted back to PV.