FINANCIAL_MGT_-_REPORTING_GRP_11.pptx

Lesson 3:
Why do
Interest
Rates Exist?
Lesson 1
:
Finding the
Present and
Future Cash
Flows
Lesson 2:
Financial
Decision-
Making
Criteria
Table of Contents
Topics Covered

Financial managers and investors are always confronted
with opportunities to generate positive returns on their
funds, whether through investments in attractive projects or
in interest-bearing securities or deposits. Therefore, the
timing of cash inflows and outflows has important economic
consequences that financial managers explicitly recognize
as the time value of money. Time value is based on the
assumption that a dollar today is worth more than a dollar
received at a later date. We begin our study of fair value in
finance by looking at the two viewpoints of fair value: future
value and present value, the computational tools used to
optimize fair value calculations, and basic cash flow pattern.
Introduction

LESSON 1
:FINDING
THE PRESENT AND
FUTURE CASH FLOWS
Go Back to Agenda Page

In financial management, the concept of time value of
money is crucial. It can be used to asses investment options an
solve difficulties concerning loans, mortgages, leases, savings,
and annuities, among other things.
The concept of Time Value of Money states that the current
value of your money is worth more than the same amount of
money that you will have in the future because you may invest
it now and collect interest. To put it another way, the money
you have today is worth more than the same amount of
money you will have in the future because you may invest it
now and collect interest. After all, you should be compensated
for the money you saved.

For example, if you invest Php 1
.0 for a
year at 7%annual interest, you will end up
with Php 1
.07 at the end of the year.Given a
7%interest rate and a one-year period, the
peso's future value can be calculated as Php
1
.07.As a result, the Php 1
.07 you expect to
get in a year has a present value of only
Php 1
.0.

FORMULA:
Future Value
FV =PV (1
+
r)
n
Present Value
PV = FV
(1+r)n

Example: What is the future value of Php 10,000
twenty years from now given an annual interest of
6%?
FV =PV (1
+
r)
=1
0,000 (1
+
0.06)
n
20
=1
0,000 (1
.06)20
FV =32, 071
.35

PV
1
0,000
20,000
6 %
FV
32,071
.35

What is the present value of Php 100,000 ten years from now given the
same annual interest rate of 6%
?
PV =FV
(1+r)
=1
00,000
(1+0.06)
=1
00,000
(1.06)
PV =55,839.48

PV
55,839.48
1
0 years
6 %
FV
1
00,000

LESSON 2:FINANCIAL
DECISION-MAKING
CRITERIA

1
.A peso invested today will generate interest
and be worth more than a peso by the end of
the year. Similarly, a cash flow of Php. 5,000
received in two years is worth more than a
cash flow of Php. 5,000 received in three
years because, while the magnitude of the
cash flow is the same, they occur at different
times, and the potential to earn interest on
the earlier cash flow influences its relative
value.

2. 1
. Mabuhay!!! You’ve earned a monetary award!
There are two payment choices available to you:
A.Received Php.1
0, 000 now
B.Received a total of Php. 10, 000 over the course of
three years.

Which option
do you think
you’d go with?

If you’re like most people, you’d like to get the Php 10,000 right now.
Three years is a long time to wait, after all. Why would a sensible
person postpone payment when he or she could receive the same
money right now? Taking money in the moment is instinctual for the
majority of us. At its most basic level, the time value of money shows
that, all other things being equal, it is preferable to have money now
rather than later.

Back to our example, by getting Php. 10,000 today, you
will be able to improve the value of your money in the
future by investing and earning interest over time. You
don’t have time on your time on your side with Option B,
therefore the sum you receive in three years will be future
value. Weve included a timeline as an example:

If you choose Option A and invest the entire sum at a
simple annual rate 4.5% the future value of your
investment at the end of the first year will be Php.
10,450, which is calculated by multiplying the principal
amount of Php. 10,000 by the 4.5% interest rate and
then adding interest to the principal amount:
If you choose Option A and invest the entire sum at a
simple annual rate and then adding the interest
earned to the principal amount:
Future value of investment at end of first year:
=(Php. 10,000) +Php. 10,450

A simple adjustment of the preceding calculation can also
be used to calculate the total amount of a one-year
investment:
·Original equation: (Php. 10,000 x 0.045) +Php. 10,000 =
Php. 450
·Manipulation: Php. 10,000 x [(1 x 0.0450) +1] =Php. 10,450
·Final equation: Php. 10,000 x (0.045 +1) =Php. 10,450

The altered equation above is merely a division of the entire
original equation by Php. 10,000 to remove the like-variable Php.
10,450 left in your investment account at the end o the first year
was left untouched and invested at 4.5 percent for another year?
To compute this, multiply the Php. 10,450 by 1.045 (0.045 +1).
You’d have Php. 10,920 at the end of two years: Future value of
investment at the end of second year:
=Php. 10,450 x (1+0.045)
=Php. 10,920.25
The above calculation, then, is equivalent to the following
equation:
Future Value =php. 10,000 x (1+0.045)

Remember the rule of exponents from math class? It states that
multiplying like term is equivalent to adding their exponents. The
two similar terms in the above equation are (1+0.045), and the
exponent on each is 1.As a result, the equation can be written as
follows:

Illustrative
Examples:
Finding Future Value (Single-Sum
Problem)

1
.If you invest Php 10,000 today at 8%and expect to
use it 20 years from now for your child’s education,
how much will have at that time?
Future Value =Present Value (Future Value Factor)
Future Value =Php 1
0,000 (4.661
0) =Php,61
0

2. Assume a deposit of Php 100 is made today into a savings account
with a 12percent annual interest rate. What will the account be worth
at the end of the first year-that is, how much will this single sum be
worth in the future?
Future Value =Php 1
00 +(Php 1
00 x 0.1
2)
=
Php 1
00 +1
2 =Php 1
1
2
What is the Future Value of Php 100 at the end of year 2?
Php 1
1
2 +(Php 1
1
2 x 0.1
2)
Php 1
1
2 +Php 1
3.44 =Php 1
25.44

LESSON 3:WHY
DO INTEREST
RATES EXIST?

The time value of money exists because of interest
rates.It is commonly said that the interest rate is the
price of money, but this explanation, though
convenient, is not entirely correct.

Why are current goods
considered more valuable
than future goods?

First, almost all people have a positive time preference. This is a
behavioral characteristic that, for whatever reason, people prefer
current consumption to future consumption. Whatever the intensity
of the preference for now as opposed to later, it is almost always
positive, although it may vary from one person to another from one
society to another. This time preference alone suggests why positive
interest rates exist.

Simple interest is calculated solely on the basis of the
original principal. Interest from previous periods is not
factored into the computations. For a single term of a less
than a year, such as 30 or 60 days, simple interest is usually
utilized.

Formula:
Simple Interest =p*
i*
n
Where:
p=principal
i=interest rate for one period
n=number of periods

Examples:
1. You borrow Php 10,000 for three years at a simple yearly interest rate
of 5%.
Interest =p*
i*
n =10,000 *
.05 *3 =1,500
2. You take out a $10,000 loan for 60 days at a simple interest rate of 5%
per year.
(Assume a 365 day year)
Interest =p*i*n =10,000 *.05 *(60/365) =82.191

3. A 2-year loan of $500 is made with 4% simple interest. Find the interest
earned.
Time is 2 years: t=2
Initial amount is $500: P=500
The rate is 4%. Write this as a decimal: r=0.04
Now apply the formula:
I=Prt
=500(0.04)(2)=40

4. Ariel takes a loan of $8,000 to buy a used truck at the rate of 9 %simple
Interest.Calculate the annual interest to be paid for the loan amount.
I =P x T x R
=8,000 x 1x 0.09
=720.00
Annual Interest to be paid =$720

Each period, compound interest is calculated on the
initial principle plus all interest accrued in previous periods. The
compounding periods can be yearly, semi-annually, quarterly,
or even constantly, even if the interest is expressed as a yearly
rate.
Compound interest can be thought of as a succession
of back-to-back simple interest contracts. The interest earned
in each period is added to the previous period’s principal to
form the next period’s principal.

ILLUSTRATIVEEXAMPLE
Example 1:
Jayjay borrowed Php 20,000 with an interest rate of 10% compounded
monthly which he borrowed from cooperative. Compute how much he will pay in:
A. 85 months
B. 1year
Formula:
A =P (1+r)
t
Where:
P =Principal Amount
r =Rate
t =time

ILLUSTRATIVEEXAMPLE
P =20,000
r =10%=0.1
t =5
A =P (1+r)t
=20,000 (1+0.1)5
=20,000 (1.1)
5
=32,210.2
A =P (1+r)t
=20,000 (1+0.1)
12
=20,000 (1.1)
12
=62,768.57

ILLUSTRATIVEEXAMPLE
Example 2:
Gadon deposited Php 50,000.00 with an interest rate of 6% compounded
yearly. What is the amount of money after 5 years.
A =P (1+r)t
P =50,000
r =6%=0.06
t =5
A =50,000 (1+0.06)
5
=50,000 (1.06)5
=66,911.27

THANK YOU
FOR LISTENING!
Prepared by:
Group 1

FINANCIAL_MGT_-_REPORTING_GRP_11.pptx

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