Time Value of Money

What does TVM stand for? What is it?

"time value of money" A dollar today is worth more than a dollar tomorrow

Banker's Year

*360 days* *all months have 30 days in them*

Cash Flow Sign Convention

*Cash inflows are entered as positive numbers*, and *cash outflows are entered as negative numbers*

Future Value of Annuity Equation

*FV = (PMT/r) x [(1+ r)nth - 1]* FV= The future value of the annuity stream to be paid in the future PMT = The amount of each annuity payment r = The interest rate n = The number of periods over which payments are made

FV Equation

*FV=PV(1+r)^n*

Cash flow Time Line

*Graphical representation of the operating cycle and the cash cycle*

Present Value of Annuity Equation

*PV = (PMT/r) x (1 - (1 / (1 + r)nth)* PV = The present value of the annuity stream to be paid in the future PMT = The amount of each annuity payment r = The interest rate n = The number of periods over which payments are made

PV Equation

*PV = FV/(1+r)^t*

Rule of 72

*This approximate the number of years it takes for a certain amount to doubleJ *72 divided by its annual rate of interest* (Example: In a little over seven years, $100 will double to $200 at a compound annual rate of 10 percent (72/10 = 7.2 years).

Uneven Cash Flow Stream

*multiple payments* that are *not equal* (Any series of cash flows that doesn't conform to the definition of an annuity is considered to be an uneven cash flow stream. For example, a series such as: $100, $100, $100, $200, $200, $200 would be considered an uneven cash flow stream)

Amortization Schedule

A *table that shows each loan payment* over the life of a loan, and a breakdown of the *amount of interest*, *principal paid* and the *remaining balance after each payment* has been made.

Lump Sum

A lump sum is a *single cash flow* (For example, an investment that is expected to pay $100 one year from now would have a "lump sum payment" of $100)

Perpetuity

A perpetuity is simply a type of *annuity* that has an *infinite life*. In other words, it is a *"perpetual annuity"*

Graduated Annuity

A series of *cash flows* that increases over time at a *constant rate* for a *finite number of periods* (A common example of a graduated annuity would be a lottery payout. A lottery winner (e.g., Powerball) may opt to receive their winnings as a series of 30 annual payments (the first payment is immediate, and there are 29 additional annual payments). In the case of Powerball, each payment will be 4% greater than the previous payment.)

Period

A unit of time amount of time that passes between cash flows eg. a day, a week, a month, a quarter (three months), six months, or a year.

Regular Annuity

Annuity in which payments occur at *end of each period*

Annuity

Cash payments of equal amounts over equal time intervals

Modified Internal Rate of Return

HOLD ON THIS ONE The compound average annual rate of return that is expected to be earned on an investment, assuming that the investment is held for its entire life and that the cash flows are reinvested at a rate that is different from the IRR. Typically, the reinvestment rate is assumed to be the WACC. Investments that have an MIRR that is greater than or equal to the cost of funds (WACC) should be accepted. Note that the difference between MIRR and IRR is in the assumed reinvestment rate.

Compounding Frequency

How often interest is credited to the account. Once interest is credited it becomes, in effect, principal.

Compound Interest

Interest earned on both the principal amount and any interest already earned

Discount Rate

Interest rate used to convert between future values and present values. (Note that the process of calculating present values is often referred to as "discounting" because present values are generally less than future values.)

Internal Rate of Return

Internal rate of return (IRR) is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. The *minimum return one needs to break even* on an investment. Or *opportunity cost rate of return.* If IRR is greater than your should do the project.

Nominal Rate - Define - Give 3 other terms that mean the same thing?

The *APR* stated on a *financial instrument* - 1) face 2) Stated rate 3) APR (Annual Percentage Rate)

Net Present Value

The *present value* of the future cash flows less the cost of the investment*.

Annuity Due

The first *payment is made immediately* (at period 0)

Payment

The payment is the *amount of a cash flow*

Required Return

The return that an investor believes he/she needs to earn in order to make an investment in a particular security. It is based on the *perceived riskiness of the security*, the rate of return available on alternative investments, and the investor's degree of risk aversion. It is likely that two investors looking at the same investment will have different required returns because of their differing risk tolerance. The required return, along with the size and timing of the expected cash flows, determines the value of the investment to the investor. Note that the required return is different from the yield (or promised rate of return), which is a function of the cost of the investment and the cash flows, and not of investor preferences.

Principle of Value Additivity

This fundamental principle states that *the present value (future value) of a series of cash flows is the sum of the present value (future value) of each of the individual cash flows. *I don't understand this*

Future Value

This term refers to the value of a cash flow (or series of them) at some specific future time.

Present Value

current (today's) value of a series of future cash flows. Literally translated, present value means "what is it worth right now?"

Effective Interest Rate - Define - Give Equation

interest rate calculated when results of compounding are included