FINANCE CHAPTER 6

Continuous Compounding

-Sometimes investments or loans are figured based on continuous compounding -EAR = eq - 1 --The e is a special function on the calculator normally denoted by ex -Example: What is the effective annual rate of 7% compounded continuously? --EAR = e.07 - 1 =

Annual Percentage Rate

-This is the annual rate that is quoted by law -By definition APR = period rate times the number of periods per year -Consequently, to get the period rate we rearrange the APR equation: -Period rate = APR / number of periods per year -You should NEVER divide the effective rate by the number of periods per year - it will NOT give you the period rate

Amorized Loans

-With a pure discount or interest-only loan, the principal is repaid all at once. An alternative is an amortized loan, with which the lender may require the borrower to repay parts of the loan amount over time. -The process of providing for a loan to be paid off by making regular principal reductions is called amortizing the loan.

Things to Remember

-You ALWAYS need to make sure that the interest rate and the time period match. --If you are looking at annual periods, you need an annual rate. --If you are looking at monthly periods, you need a monthly rate. -If you have an APR based on monthly compounding, you have to use monthly periods for lump sums, or adjust the interest rate appropriately if you have payments other than monthly

Annuities and Perpetuities Defined -Perpetuities

-infinite series of equal payments -Perpetuity: PV = C / r -Preferred Stock is an example of a perpetuity. The buyer is promised a fixed cash dividend every period forever. Must be paid before any dividend can be paid to stockholders.

Annuity Due

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

Consol

A type of perpetuity -perpetuity's called these particularly in Canada and the United Kingdom

[Annuity Period] As you increase the length of time involved, what happens to the present value of an annuity? What happens to the future value?

Assuming positive cash flows, both the present and the future values will rise.

[Interest Rates] 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, the present value will fall and the future value will rise.

Interest-only Loans

Calls for the borrower to pay interest each period and to repay the entire principal (the original loan amount) at some point in the future. -Notice that if there is just one period, a pure discount loan and an interest-only loan are the same thing -Most corporate bonds

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 known as the quoted interest rate

Pure Discount Loans

The principal amount is repaid at some future date, without any periodic interest payments. Treasury bills are excellent examples of pure discount loans.

[Perpetuity Values] What happens to the future value of a perpetuity if interest rates increase? What if interest rates decrease?

This is a trick question. The future value of a perpetuity is undefined since the payments are perpetual. Finding the future value at any particular point automatically ignores all cash flows beyond that point.

Effective Annual Rate (EAR)

This is the actual rate paid (or received) after accounting for compounding that occurs during the year If you want to compare two alternative investments with different compounding periods, you need to compute the EAR and use that for comparison.

Loans

Three types of loans Pure discount loan Interest-only loan Amortized loan

Annuities and Perpetuities Defined -Annunity

finite series of equal payments that occur at regular intervals -If the first payment occurs at the end of the period, it is called an ordinary annuity -If the first payment occurs at the beginning of the period, it is called an annuity due