CH5 F

LG6 Describe the procedures involved in (1) determining deposits needed to accumulate a future sum, (2) loan amortization, (3) finding interest or growth rates, and (4) finding an unknown number of periods.

(1) The periodic deposit to accumulate a given future sum can be found by solving the equation for the future value of an annuity for the annual payment. (2) A loan can be amortized into equal periodic payments by solving the equation for the present value of an annuity for the periodic payment. (3) Interest or growth rates can be estimated by finding the unknown interest rate in the equation for the present value of a single amount or an annuity. (4) An unknown number of periods can be estimated by finding the unknown number of periods in the equation for the present value of a single amount or an annuity.

LG2 Understand the concepts of future value and present value, their calculation for single amounts, and the RELATIONSHIP between PV & FV

(FV) - compound interest to measure future amounts: The INITIAL principal or deposit in one period, along with the interest earned on it, becomes the beginning principal of the following period. (PV) of a FUTURE amount is the amount of money today that is equivalent to the given future amount, considering the return that can be earned. Present value is the inverse of future value.

1. inverse

1. PROTIVOPOLOZHNOE

LG4 Calculate both the future value and the present value of a mixed stream of cash flows.

A mixed stream of cash flows is a stream of unequal periodic cash flows that reflect no particular pattern. The future value of a mixed stream of cash flows is the sum of the future values of each individual cash flow. Similarly, the present value of a mixed stream of cash flows is the sum of the present values of the individual cash flows.

lump sum

A single payment made at a particular time, as opposed to a number of smaller payments or installments.

LG1 Discuss the ROLE of TIME VALUE in finance, the use of computational tools, and the basic patterns of cash flow.

Financial managers and investors use TIME VALUE OF MONEY techniques when assessing the value of EXPECTED cash flow streams. Alternatives can be assessed by either COMPOUNDING - (FV) DISCOUNTING PV Financial managers rely primarily on PV techniques. The cash flow of a firm can be described by its pattern—single amount, annuity, or mixed stream.

LG5 Understand the effect that compounding interest more frequently than annually has on future value and the effective annual rate of interest.

Interest can be compounded at intervals ranging from annually to daily, and even continuously. The more often interest is compounded, the larger the future amount that will be accumulated, and the higher the effective, or true, annual rate (EAR).

LG3 Find the FV and the PV of both an ORDINARY ANNUITY and an ANNUITY DUE, and find the present value of a PERPETUITY.

The future or present value of an ordinary annuity can be found by using algebraic equations, a financial calculator, or a spreadsheet program. The value of an annuity due is always r% greater than the value of an identical annuity. The present value of a perpetuity—an infinite-lived annuity—is found using 1 divided by the discount rate to represent the present value interest factor.

ANNUITY DUE

an annuity for which the cash flows occur at the beginning of the period

ORDINARY ANNUITY

an annuity with payments that occur at the end of each period

PERPETUITY

the state of going on forever; everlasting