Corp Finance Chapter 5

Semiannual compounding

compounding of interest over 2 periods within the year Ex: $100 at 8% compounded semiannually 6 months: $100 x (1 + .04) = $104 12 months: $104 x (1 + .04) = 108.16

Quarterly Compounding

compounding of interest over 4 periods within the year Ex: $100 at 8% compounded quarterly 3 months: $100 x (1 + .02) = $102 6 months: $102 x (1 + .02) = 104.04... continues

Continuous Compounding

compounding of interest, literally, all the time. Equivalent to compounding interest an infinite number of times per year

Nominal (stated) annual rate

contractual annual rate of interest charged by a lender or promised by a borrower

Basic Patterns of Cash Flow: Annuity

-A level of periodic stream of cash flow -Receiving or making a fixed payment each month/year for several years -Mortgage payment

Basic Patterns of Cash Flow: Mixed Stream

-A stream of cash flow that is not an annuity; a stream of unequal periodic cash flows that reflect no particular pattern -Business investment decisions

Lecture: Monthly Compounding

-Adjust N & I/Y Accordingly -N (years) * 12 (months) -I/Y (interest rate) / 12 (months)

Lecture: Quarterly Compounding (Discounting)

-Adjust N & I/Y Accordingly -N (years) * 4 (quarters) -I/Y (interest rate) / 4 (quarters)

Lecture: Payments into Perpetuity

-Payments that happen forever (no maturity date/end point) (Ex: Dividend payment on a stock) (Ex: Stocks are issued into perpetuity) -PV of future payments that has no end point Payment (PMT)/Discount Rate (I/Y) = PV of future cash into perpetuity

Lecture: Present Value & Future Value

-Present Value = Value in today's $ -Future Value = Value at a future date

Lecture: Annuity

-Series of payments that happen over a period of time -Equals $ amount paid (or received) at set intervals for a number of periods -PMT is key on calculator (Used for the annuity payment) -Example: mortgage payment is a set # amount due on the 1st day of every month

Basic Patterns of Cash Flow

-Single Amount -Annuity -Mixed Stream

Comparison of an Annuity Due with an Ordinary Annuity: FV

-The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity -Because the cash flow of the annuity due occurs at the beginning of the period rather than at the end, its future value is greater

Comparison of an Annuity Due with an Ordinary Annuity: PV

-The present value of an annuity due is always greater than the present value of an otherwise identical ordinary annuity -Because the cash flows of the annuity due occur at the beginning of each period rather than at the end, their present values are greater

Basic Patterns of Cash Flow: Single Amount

A lump sum amount either currently held or expected at some future date

Growing Perpetuity

An annuity with an infinite life, providing continual annual cash flow, with the cash flow growing at a constant annual rate

Lecture: When doing FV calculations

As I/Y increases, FV increases As N increases, FV increases

Lecture: When doing PV calculations

As I/Y increases, PV decreases As N increases, PV decreases INVERSE RELATIONSHIPS

Lecture: Compounding & Discounting

Compounding = Present Value to Future Value -Forward from PV to Future Value -Add interest every year to our calculation -Yr 1: 100 at 10% -Yr 2: 110 at 10% Discounting = Future Value to Present Value (Opportunity Cost) -Backwards from FV to PV

Lecture: PV or FV of a Mixed Stream of Payments

Either pay or receive payments at regular intervals, but dollar amount will not be the same (Different from annuities; payment amount changes) -Series of cash flows whose payment changes -Cash flow doesn't have to go in the same direction every time -Payments have to be either at beginning or end for every period (Either Ordinary Annuity or Annuity Due for every payment) Take PV of each amount and add them together

Types of Annuities

Ordinary Annuity: an annuity for which the cash flow occurs at the end of each period Annuity Due: an annuity for which the cash flow occurs at the beginning of each period

Lecture: Single Payment (Receipt)

PV = In today's $ FV = In future $ N = # of periods (years) I/Y = Annual Interest Rate -If you know 3 of the 4 factors, you can solve for the one you are missing -When you have PV and FV, one must be positive, one must be negative

Compounding & Future Value

The future value technique uses compounding to find the future value of each cash flow at the end of the investment's life and then sums these values to find the investment's future value

Discounting & Present Value

The present value technique uses discounting to find the present value of each cash flow at time zero and then sums these values to find the investment's value today

Lecture: Annuity Due

assumes payment happens @ beginning of period -First day of period (Jan 1) -Take Ordinary Annuity Amount x 1.(insert interest rate)***

Lecture: Ordinary Annuity

assumes payment happens @ end of period -Timing of payment, when money is actual paid -Last day of period (Jan 31) -PROBLEM DOESN'T SAY, ASSUME ORDINARY ANNUITY

Time value of money concept

better to receive money sooner rather than later

Mixed Stream & Future Value

To determine the future value of a mixed stream of cash flows, compute the future value of each cash flow at the specified future date and then add all the individual future values to find the total future value

Mixed Stream & Present Value

To determine the present value of a mixed stream of cash flows, compute the present value of each cash flow and then add all the individual present values to find the total present value

Timeline

a horizontal line on which time zero appears at the leftmost end and future periods are marked from left to right; can be used to depict investment cash flows -Negative value - cash outflows (what we spend/invest) -Positive value - cash inflows (what we earn)

Annuity: Definition

a stream of equal periodic cash flows over a specified time period. These cash flows can be inflows or outflows of funds

Mixed Stream: Definition

a stream of unequal periodic cash flows that reflect no particular pattern

Perpetuity: Definition

an annuity with an infinite life, providing continual annual cash flow

Compound Interest

interest that is earned on a given deposit and has become part of the principal at the end of a specified period

Simple Interest

interest that is earned only on an investment's original principal and not on interest that accumulates over time

Compounding

process of adding interest to an investment's principal and paying interest on the new, higher balance

Principal

the amount of money on which interest is paid

Effective (true) annual rate (EAR)

the annual rate of interest actually paid or earned

Discounting Cash Flows

the process of finding present values; the inverse of compounding interest

Present value

the value in today's dollars of some future cash flow

Future Value

the value on some future date of money that you invest today