The time value of money. (Lecture 2)

THE TIME VALUE OF MONEY (TVM)

Money (a dollar or a yen,

COMPOUNDING VS. DISCOUNTING

Compounding
The process of going from today’s value, or

SIMPLE INTEREST

With Simple Interest, the interest rate each year
is applied

COMPOUNDING INTEREST

With Compounding Interest, the interest rate each year is applied

COMPOUNDING INTEREST

1776 1800 1865 1929 1996

To see how much $2

THE TIMELINE

A timeline is a linear representation of the timing of

THE TIMELINE: EXAMPLE

Problem
Suppose you have a choice between receiving $5,000 today

THE TIMELINE: EXAMPLE

Solution
The time line looks like this:
In five years,

COMPOUNDING INTEREST

FV=PV×(1+r)n

FIN 3121 Principles of Finance

FREQUENCY OF COMPOUNDING

There are 12 compounding events in Bank B
compared

DISCOUNTING

Discounting is a process of converting values to be received or

DISCOUNTING

If you can earn 5% interest compounded annually what do you

UNKNOWN VARIABLES

Any time value problem involving lump sums -- i.e.,

EXAMPLE: UNKNOWN RATE

Problem
Bank A offers to pay you a lump sum

EXAMPLE: UNKNOWN RATE

Solution
To answer this question, you have to

EXAMPLE: UNKNOWN № OF PERIODS

You have decided that you will sell

RULE OF 72

The number of years it takes for a sum

STREAM OF CASH FLOWS

FIN 3121 Principles of Finance

ONLY VALUES AT THE SAME POINT IN TIME
CAN BE COMPARED

Valuing a Stream of Cash Flows

General formula for valuing a stream

where
PV = the Present Value of the Cash Flow Stream,

Find the Present Value of the following cash flow stream given

Future value
of a stream of cash flows

where
FVt =

Find the Future Value at the end of year 4 of

PERPETUITIES

When a constant cash flow will occur at regular intervals forever

PERPETUITIES

The value of a perpetuity is simply the cash flow divided

PERPETUITIES: EXAMPLE

Problem
You want to donate to your University to endow an

PERPETUITIES: EXAMPLE

FIN 3121 Principles of Finance

When a constant cash flow will occur at regular intervals for

ANNUITIES

FIN 3121 Principles of Finance

FUTURE VALUE INTEREST FACTOR OF AN ANNUITY (FVIFA)

FVIFA =

FVIFA –

FUTURE VALUE OF AN ORDINARY ANNUITY STREAM

Problem
Jill has been faithfully depositing

FUTURE VALUE OF AN ORDINARY ANNUITY STREAM

Solution
Future Value of Payment One

FUTURE VALUE OF AN ORDINARY ANNUITY STREAM

FIN 3121 Principles of Finance

PRESENT VALUE OF AN ANNUITY

To calculate the value of a series

TIME LINE OF PRESENT VALUE OF ANNUITY STREAM

FIN 3121 Principles of

ANNUITY DUE VS ORDINARY ANNUITY

A cash flow stream such as rent,

PV annuity due = PV ordinary annuity x (1+r)
FV annuity due

ANNUITY DUE VS ORDINARY ANNUITY

Problem:
Let’s say that you are saving up

ANNUITY DUE VS ORDINARY ANNUITY

Given information: PMT = $3,000; n=20; i=

TYPES OF LOAN REPAYMENTS

There are 3 basic ways to repay a

LOAN REPAYMENTS: EXAMPLE

Problem:
The Corner Bar & Grill is in the

LOAN REPAYMENTS: EXAMPLE

Solution:
Under Option 1: Principal and Interest Due at the

LOAN REPAYMENTS: EXAMPLE

Solution:
Under Option 2: Interest-only Loan
Annual Interest Payment (Years 1-4)

LOAN REPAYMENTS: EXAMPLE

Solution:
Under Option 3: Amortized Loan
To calculate the

LOAN REPAYMENTS: EXAMPLE

Comparison of total payments and interest paid under each

AMORTIZATION SCHEDULES

Amortization schedule contains the following information:
Beginning principal;
Total periodic payments;

AMORTIZATION SCHEDULES

Problem
$ 25,000 loan being paid off at 8%

AMORTIZATION SCHEDULES

Solution
For all consequent periods:
1. Apply step 3 to the

AMORTIZATION SCHEDULES

FIN 3121 Principles of Finance