Corporate Finance Chapters 4 & 5

Calculating the value of an annuity due involves two steps:

1. Calculate the present or future value as though it were an ordinary annuity. 2. Multiply your answer by 1 + r.

There are two ways to calculate future values for multiple cash flows:

1. Compound the accumulated balance forward one year at a time. 2. Calculate the future value of each cash flow first and then add these up. Both give the same answer.

Perpetuity

An annuity in which the cash flows continue forever.

As you increase the length of time involved, what happens to the future value of an annuity?

As you increase the time, there will be more annuity payments. The future value of an annuity will increase at an increasing rate due to both the greater number of payments and the greater compounded interest.

What happens to the future value of an annuity if you increase the rate, r? What happens to the present value?

Assuming positive cash flows and a positive interest rate, the present value will fall, and the future value will rise.

Why would a company be willing to accept such a small amount today in exchange for a promise to repay about four times that amount in the future?

It's a reflection of the time value of money.

Future Value FV

The amount of money an investment will grow to over some period of time at some given interest rate.

Present Value PV

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

What happens to a future value if you increase the rate, r?

The future value rises, assuming a positive rate of return.

Annual Percentage Rate APR

The interest rate charged per period multiplied by the number of periods per year.

Effective Annual Rate EAR

The interest rate expressed as if it were compounded once per year.

Stated Interest Rate

The interest rate expressed in terms of the interest payment made each period. Also, quoted interest rate.

What happens to a present value if you increase the rate, r?

The present value falls.

As you increase the length of time involved, what happens to the present value of an annuity?

The present value of an annuity will increase at a decreasing rate due to the greater number of payments further and further

Compounding

The process of accumulating interest in an investment over time to earn more interest.

Discount Rate

The rate used to calculate the present value of future cash flows.

Many loans are

annuities. The process of paying off a loan gradually is called amortizing the loan.

Interest rates can be quoted in a variety of ways. For financial decisions, it is important that

any rates being compared be first converted to effective rates.

The expression 1 + r is sometimes called the

future value interest factor or just future value factor.

For a given rate of return, the value at some point in the future of an investment made today can be determined by calculating the

future value of that investment.

With simple interest, the interest is not

reinvested, so interest is earned each period only on the original principle.

The current worth of a future cash flow can be determined for a given rate of return by calculating

the present value of the cash flow involved.

Annuity

A level stream of cash flows for a fixed period of time.

What is discounting?

Discounting is the process of determining the value today of an amount to be received in the future.

Compounding the interest means earning

interest on interest, so we call the result compound interest.

Consol

A type of perpetuity.

Annuity Due

An annuity for which the cash flows occur at the beginning of the period.

Discount

Calculate the present value of some future amount.

What is compounding?

Compounding refers to the growth of a dollar amount through time via reinvestment of interest earned. It is also the process of determining the future value of an investment.

Discounted Cash flow valuation DCF

Valuation calculating the present value of a future cash flow to determine its value today.

Present values and discount rates are

inversely related. Increasing the discount rate decreases the present value and vise versa.

For a given length of time, the higher the discount rate, the

lower the present value is.

A series of constant cash flows that arrive or are paid at the end of each period is called an

ordinary annuity.