Module 6: Intro to Finance- Time Value of Money and Lump Sums

A _____ provides a tool for visualizing cash flows and time. It identifies the amount and timing of astream of payments - both cash received and cash spent - along with the interest rate earned. Timelines are typically expressed in _____, but could be expressed in months, days, or any unit of time.

A timeline provides a tool for visualizing cash flows and time. It identifies the amount and timing of astream of payments - both cash received and cash spent - along with the interest rate earned. Timelines are typically expressed in years, but could be expressed in months, days, or any unit of time.

_________ is the process of determining the future value of an investment madetoday - solving for FV.

Compounding is the process of determining the future value of an investment madetoday - solving for FV.

Interest-on-interest is the interest that is earned on _____ ______ _________.

Interest-on-interest is the interest that is earned on prior interest payments.

The interest rate, r, captures the investor's _________ ____. Recall that opportunity cost is the cost of the next best opportunity foregone. By definition, the opportunity cost of capital to an investor is the ______ of _______ that is foregone when one investment is chosen instead of another.

The interest rate, r, captures the investor's opportunity cost. Recall that opportunity cost is the cost of the next best opportunity foregone. By definition, the opportunity cost of capital to an investor is the rate of return that is foregone when one investment is chosen instead of another.

inflation

a general increase in prices and a fall in purchasing power of money.

annual percentage yield (APY)

a nominal interest rate that reflects all the compound interest paid/earned in one year

lump sum

a single payment made at a particular time

discounting

determining the present value of an expected future cash flow using the discount rate. Most often we use an interest rate as a discount rate

decimal form

interest rates expressed asa percentage must be converted into decimal form when using mathematical formulas or excel sheets for TVM calcualtions

continuously compounded interest

interest that is earned constantly, and immediately begins earning interest on itself

compound interest

interest that is earned o both the initial principal and he reinvested interest earned in prior periods

percentage form

is used to input interest rates when solving TVM calculations with a financial calculator

number of periods (t)

the number of periods between the two lump sums and is consistent with the periodic rate

present value (PV)

the current value of a future cash flow

net present value (NPV)

the different between the present value of cash inflows and the present value of cash outflows. NPC is used in capital budgeting to analyze the profitability of an investment or project

Banks are required by law to display the ____ on all loans but not the ____. To find the actual amount of interest you would pay over the course of one time period, you must convert the quoted ___ to the ____.

Banks are required by law to display the APR on all loans but not the APY. To find the actual amount of interest you would pay over the course of one time period, you must convert the quoted APR to the APY.

internal rate of return (IRR)

the discount rate used in capital budgeting that makes the net present value of all cash flows from a particular investment equal to zero. This is the rate of return you expect to receive if you put your money into a project

__________ interest is the amount of interest that is earned on both the original principal and the interestearned, and reinvested, in prior periods. Compound interest includes both _____ interest and _____-on-_____.

Compound interest is the amount of interest that is earned on both the original principal and the interestearned, and reinvested, in prior periods. Compound interest includes both simple interest and interest-on-interest.

______ is the process of determining the present value of money to be received in the future -solving for PV.

Discounting is the process of determining the present value of money to be received in the future -solving for PV.

For interest rates, the _______ form is used to calculate TVM when using equations and spreadsheets. The ________ form is used to calculate TVM when using a financial calculator.

For interest rates, the decimal form is used to calculate TVM when using equations and spreadsheets. The percentage form is used to calculate TVM when using a financial calculator.

In the context of loans, the borrower is paying the lender the ________ rate. This rate protects the lender from _____ (h) and rewards the lender in real terms for the service of providing money (R).

In the context of loans, the borrower is paying the lender the nominal rate. This rate protects the lender from inflation (h) and rewards the lender in real terms for the service of providing money (R).

_____ ______ of _____ (IRR) is a formula used in the capital budgeting process to calculate the profitability of an investment. The IRR is the interest rate (r) at which your NPV becomes _____. A project with an IRR that is greater than that of the next best similar opportunity should be ______

Internal rate of return (IRR) is a formula used in the capital budgeting process to calculate the profitability of an investment. The IRR is the interest rate (r) at which your NPV becomes zero. A project with an IRR that is greater than that of the next best similar opportunity should be accepted

____ _______ ________ (NPV) is used in the capital budgeting process to determine whether a project is worth investing in. NPV compares the amount you have invested today with the _____ _____ (PV) of the _______ returns. A positive NPV suggests the present value of the expected returns is ________ than the initial investment, and therefore the investment should be __________.

Net present value (NPV) is used in the capital budgeting process to determine whether a project is worth investing in. NPV compares the amount you have invested today with the present value (PV) of the expected returns. A positive NPV suggests the present value of the expected returns is greater than the initial investment, and therefore the investment should be accepted.

Over time, simple interest grows ______ while interest-on-interest grows _______. Therefore as time increases the interest-on-interest component of compound interest becomes ______

Over time, simple interest grows linearly while interest-on-interest grows exponentially. Therefore as time increases the interest-on-interest component of compound interest becomes larger

_______ interest is the amount of interest that is earned on the original principal only

Simple interest is the amount of interest that is earned on the original principal only

The Fisher Equation, r ≈ _ + _, describes the relationship between inflation (h) and both real (R) and nominal (r) interest rates.

The Fisher Equation, r ≈ R + h, describes the relationship between inflation (h) and both real (R) and nominal (r) interest rates.

The difference between the annual percentage rate (APR) and the annual percentage yield (APY) is the ____ takes into account any compounding that takes place throughout the year, while the _____ does not.

The difference between the annual percentage rate (APR) and the annual percentage yield (APY) is the APY takes into account any compounding that takes place throughout the year, while the APR does not.

simple interest

the interest an investment earns on the original principal only

periodic rate (r)

the interest rate defined in a contract that specifically states how much interest is earned over an internal of time

interest on interest

the interest that is earned upon reinvestment of interest payments

The equation FV = ___ (1 + __)__ is the foundation of all finance. Each variable can be solved for algebraically given the other three variables. The FV equation illustrates the relationship between the future valueand the other three variables - a change in PV, r, or t will impact the future value of an investment.

The equation FV = PV (1 + r)t is the foundation of all finance. Each variable can be solved for algebraically given the other three variables. The FV equation illustrates the relationship between the future valueand the other three variables - a change in PV, r, or t will impact the future value of an investment.

The _______ interest rate reflects the percentage change in consumption, or purchasing power, for a given period. The _______ rate is the percentage change in actual dollars.

The real interest rate reflects the percentage change in consumption, or purchasing power, for a given period. The nominal rate is the percentage change in actual dollars.

Time value of money calculations are essentially comparisons between ________ _____ (PV), what a cash flow would be worth to you today, and ______ _____ (FV), what a cash flow will be worth to you inthe future. Calculating the time value of money allows financial managers to compare alternative investments that do not occur during the same ______ ______.

Time value of money calculations are essentially comparisons between present value (PV), what a cash flow would be worth to you today, and future value (FV), what a cash flow will be worth to you inthe future. Calculating the time value of money allows financial managers to compare alternative investments that do not occur during the same time periods.

annual percentage rate (APR)

a nominal simple interest rate that banks are required by law to state on all loans

certificate of deposit

a savings certificate issued by a bank entitling the holder to receive interest for a specified term

treasury bill

a short-term debt obligation backed by the U.S. government with a maturity of less than one year

basis point

a unit that is equal to 1/100th of 1%. A basis point is a unit of measure used in finance to describe the percentage change in the value or rate of a financial instrument

NPV rule

accept all investments that are positive NPV because they create value, reject all projects that are negative NPV because they destroy value

IRR rule

accept projects when the IRR is greater than the opportunity cost, reject if less

consistent

in TVM calculations, the periodic rate and the number of periods are both defined over the same unit of time

effective rate

the annual interest rate adjusted for intra-year compounding. It is used to compare the annual interest between loans with different compounding terms

real interest rate

the rate of interest an investor expects to receive after allowing for inflation. The real rate of interest is approximately the nominal interest rate minus the inflation rate. It reflects an investor's change in purchasing power.

nominal interest rate

the rate that the lender sates a borrower is paying. The nominal interest rate is approximately the desired real rate of return plus an adjustment for inflation. It reflects an investor's change in dollars

future value (FV)

the value of a cash flow at some specific future time