Time Value Of Money

Geometric Mean (Formula)

(x*y*z)^1/n n = the number of sample

Why cash flow in the future is worth less than equivalent cash flow today?

1. People prefer consuming today to consuming in the future 2. Inflation 3. Default Risk

Cash Flow Types

1. Simple Cash Flows 2. Annuities 3. Growing Annuities 4. Perpetuities 5. Growing Perpetuities

Growing Annuity

A cash flow that grows at a constant rate for a specified period of time.

Annuity

A constant cash flow that occurs at regular intervals for a fixed period of time. There are 2 types of annuities.

Annuity Due

An annuity for which the cash flows occur at the beginning of the period. Annuity Due has its first payment occurring at t = 0 (Present).

Ordinary Annuity

An annuity that pays at the end of each period. Indexed at t=1.

Monthly home mortgage payments

Annuity

Monthly insurance payments

Annuity

Pension payments

Annuity

Regular equal deposits to a savings account

Annuity

Cash flows occur at the beginning of each period

Annuity Due

Cash Flow Additivity Principle

Can be used to solve problems with uneven cash flows by combining single payments and annuities.

Maturity Premiun

Compensates investors for the increased sensitivity of market value of debt to a change in market interest rates as maturity is extended, in general. The difference between interest rate on long term, liquid T-Bills and that on short term T-Bills reflects a positive maturity premium for longer term T-Bills.

Discounting Cash Flows

Converting future cash flows into today's dollars (present value), allowing for comparison of cash flows at different points in time.

Effective Annual Yield

Converts a t-day holding period yield to a compound annual yield based on a 365-day year.

Present Value Theory

Enables us to calculate how much a dollar sometime in the future is worth in today's terms.

We can find the EAR by finding the appropriate __

Future Value Factor

Cost of Capital

How much it costs a firm (in percentage terms) to get/maintain their debt and equity financing.

Interest Rate Theory

Interest rate can be viewed as the sum of the real Risk-Free interest rate and a set of premiums that compensate lenders for risk: default risk premium, liquidity premium, maturity premium.

Bond Equivalent Yield (BEY)

Is 2x the semiannual compounded yield. This is because US bonds pay interest semiannually rather than annually.

Perpetuity

Is a cash flow at regular intervals forever.

Growing Perpetuity

Is a cash flow that is expected to grow at a constant rate forever

Simple Cash Flow

Is a single cash flow in a specified future time period

Geometric Mean

Is always less than or equal to the arithmetic mean

Interest Rate

Is the required rate of return; r is also called the discount rate or opportunity cost

Time value of money (Formula)

It's possible to calculate an unknown variable, given the other relevant variables in this formula.

PV & FV of Annuity Due

Once you have found the PV or FV of an ordinary annuity, you can convert the discounted value to an annuity due by multiplying by 1 plus the periodic rate. This discounts the ordinary annuity by one less (or more) period.

Cash flows occur at the end of each compounding period

Ordinary Annuity

Console Bond

Perpetuity

Preferred Stock (equal payments indefinitely)

Perpetuity

Rent Payment from real estate property

Perpetuity

Periodic Interest Rate

Quoted interest rate per period; it equals the Stated Annual Interest Rate divided by the number of compounding periods per year

Stated Annual Interest Rate

Quoted interest rate that does not account for compounding within the year

Annuity Factor

Read up on this and single-payment factors

The ___ does not give a FV directly, so we need a formula for the EAR

Stated Annual Interest rate

Discount Rate Theory

The Discount Rate can be viewed as the composite of the expected REAL RETURN, expected INFLATION, and a DEFAULT RISK premium.

Effective Annual Rate (EAR)

The amount by which a unit of currency will grow in a year with interest on interest included (compounded). The interest rate expressed as if it were compounded once per year.

Bank Discount Yield

The annualized percentage discount from face value.

Time Value of Money (TVM)

The concept that money available today is worth more than the same amount tomorrow.

Opportunity Cost

The cost of money is the opportunity cost of holding money in hands instead of investing it

Present Value

The current value of future cash flows discounted at the appropriate discount rate

Cash Flow Additivity Principle

The idea that amounts of money indexed at the same point in time are additive.

Interest Rate Theory

The interest rate, r, makes current and future currency amounts equivalent based on their time value.

Discount Rate

The magnitude by which future cash flows are adjusted for inflation risk, default risk, illiquidity risk, maturity risk.

Expected Real Rate of Return

The percent of profit or loss an investor anticipates on an investment, adjusted (minus) for inflation.

Perpetuity PV

The present value of a perpetuity is A/r, where A is the periodic payment to be received forever.

Discounting Principle

The process by which future cash flows are adjusted to reflect inflation, default risk, liquidity risk, and maturity premium

Required Rate of Return (RRR)

The required rate of return (RRR) is the minimum annual percentage earned by an investment that will induce individuals or companies to put money into a particular security or project.

Real Risk-Free Rate

The theoretical rate of return of an investment with zero risk. This rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. Interest rate for 3 month T-bill is often used as the risk-free rate for US investors.

Future Value

The value of a current asset at a specified date in the future. The amount an investment grows to after one or more compounding periods.

Timeline

We can index the present as 0 and then display equally spaced hash marks to represent a number of periods into the future. This allows us to index how many periods away each cash flow will be paid.

Nominal Interest Rate

When viewed as a required rate of return on an investment, a nominal interest rate consists of: a real risk-free rate, a premium for expected inflation, and other premiums for sources of risk specific to the investment.

Annuity Present Value

You can compute the PV of an annuity by discounting EACH cash flow and adding them.

Effective Annual Yield (Formula)

[(1 + HPY)^365/t] - 1 HPY/HPR - Holding Period Return or Yield T - time