BUSFIN1
(Business Finance)
4th QUARTER
(Second Sem, SY 2020-2021)
Be reminded of our class
preliminaries!
VIRTUAL CLASSROOM RULES/REMINDERS!!!
CHAPTER 4.
Basic Long-Term Financial Concepts
LESSON. Time Value of Money
OBJECTIVES:
At the end of the lesson, you should be able to:
 explain the concept on time value money;
 compute problems concerning the time value of
money; and
 apply the concepts in real-life scenarios
Recap of previous lesson
To be able to acquire assets, our funds must have
come somewhere.
If
it
is
acquired
using
cash
from
our
pockets/stockholders, it is financed by ____________.
On the other hand, if we used money from our
borrowings, the asset bought is financed by
___________.
Recap of previous lesson
 Debt which is scheduled to mature in
more than one year but in less than
years.
 Debt which is scheduled to mature in
more than ten years.
 Debt scheduled to be paid within a year.
Introduction
Time Value of Money
 The idea that the MONEY available NOW is worth
MORE THAN the same amount that will be
available at some FUTURE date.
“The connecting piece or
link between present
(today) and future is the
Interest Rate.”
Interest
 The rate which is charged or paid for the use of
money.
 Excess of resources (usually cash) received or
paid over the amount of resources loaned or
borrowed which is called the principal.
SIMPLE INTEREST vs COMPOUNDED INTEREST
2 Types of Interest
(1) Simple Interest – occurs when there is no interest
earned on top of interest that was earned in the
previous periods.
SIMPLE INTEREST
I = P x r x T
EXERCISE 1
I = P x r x T
You invested Php10,000 for 3 years at 9% and the
proceeds from the investment will be collected at the
end of 3 years. Calculate the simple interest.
2 Types of Interest
(2) Compound Interest – occurs when interest is earned
on the interest that was earned from the previous
periods.
*m is the compounding frequency
Compounding Frequency - the number of times
interest is computed on a certain principal in
one year.
COMPOUND INTEREST
Compound Interest
Year
Principal
Interest (P x r)
Cumulative Interest
Total
1
Php 500,000.00
Php 40,000.00
Php 40,000.00
Php 540,000.00
2
540,000.00
43,200.00
83,200.00
583,200.00
3
583,200.00
46,656.00
129,856.00
629,856.00
4
629,856.00
50,388.48
180,244.48
680,244.48
5
680,244.48
54,419.56
Php 234,664.04
Php 734,664.04
EXERCISE 1
You invested P 10,000 for 3 years at 9% and the
proceeds from the investment will be collected at the
end of 3 years. Calculate the compound interest.
TIME LINES
 is a graphical representation of the timing of cash
flows.
period
PRESENT VALUE (PV) vs FUTURE VALUE (FV)
• also known as discounting
where, (𝟏 + 𝒊) −𝒏 = Present value
interest factor (PVIF)* or discount
factor
• value of the present value after n
time periods
FUTURE VALUE (FV)
Using the formula, find the future values of P 1,000 compounded at a
10% annual interest at the end of one year? two years? and five
years?
OTHER COMPOUNDING
PERIODS
If compounded annually: Apply the given formula to
get the future value of money worth Php 1,000.00
that was deposited in an interest bearing account. The
annual interest rate is 6% and the money will stay in
the account for 5 years.
FV = Php 1,338.23
OTHER COMPOUNDING
PERIODS
Apply the given formula to get the future value of money worth Php 1,000.00
that was deposited in an interest bearing account. The annual interest rate is
6% and the money will stay in the account for 5 years.
What if the 6% interest rate is compounded semi-annually? What will be the
future value?
a. Divide the interest rate by 2 (semi-annual), making it 3%.
b. Multiply the number of periods by 2, making it 10
FV = Php 1,343.92
Exercise
Determine the compound amount on an investment at the end of 2
years if Php 20,000 is deposited at 4% compounded (a) semi-annually
and (b) quarterly.
PRESENT VALUE (PV) vs FUTURE VALUE (FV)
• also known as discounting
where, (𝟏 + 𝒊) −𝒏 = Present value
interest factor (PVIF)* or discount
factor
• value of the present value after n
time periods
PRESENT VALUE (PV)
Jack would like to buy a car two years from now using the
proceeds of a 20% investment that is compounded semiannually. If the projected price of the car is P 1,400,000.00 how
much money must be invested today to earn the price of the car?
EXERCISE:
You need PHP25,000 to buy a laptop when you enter college 2
years from now. How much must you invest now if the interest rate
is at 6% per annum.
PV = 25,000/(1.1236) = PHP22,249.91
You need to invest PHP22,249.91 to have PHP25,000
by the end of 2 years.
REAL LIFE APPLICATION
c/o Group 3
ANNUITIES
 A series of equal payments at fixed intervals for a
specified number of periods (normally in years).
ORDINARY ANNUITY
 The type of annuity wherein payments occur at the end of the
period.
Period
1
0
2
3
Php 300
Php 300
5%
Payments
Php 300
ANNUITY DUE
 The type of annuity wherein payments occur at the beginning
of each period.
Period
1
0
2
3
5%
Payments
Php 300
Php 300
Php 300
Php 0
FUTURE VALUE OF ORDINARY ANNUITY
Given:
t = 3 ; r = 5%
R/PMT/Cash Flow (annuity payment) = Php 300
FVA
=
ordinary
Php 945.75
FUTURE VALUE OF ORDINARY ANNUITY
EXAMPLE (Ordinary
Annuity):
Mr. Mendoza wishes to determine how much will be the value of
his savings in 5 years if he will put PHP1,000 per year in a bank that
provides 7% interest per annum.
FV = 1,000 x (FVA factor: 5.7507 t=5, r=7%)
FVA
=
ordinary
Php 5,750.70
FUTURE VALUE OF ANNUITY DUE
Given:
t=3
r = 5%
R/PMT/Cash Flow
(annuity payment)
= Php 300
FVAdue= FVA
(1
+
r)
ordinary
FVA due =
Php 945.75 (1+0.05)
FVAdue= Php 993.04
PRESENT VALUE OF ORDINARY ANNUITY
Given:
t = 3 ; r = 5%
PMT/Cash Flow (annuity payment) = Php 300
PVA =
Php 817.20
PRESENT VALUE OF ORDINARY ANNUITY
Mr. Yusoph wants to buy a pair of shoes worth P10,500. He has the
option of paying it today for PHP10,500 or buying in installment where he
has to pay a down payment of PHP4,000 today, and the balance will be
paid in two equal payments of PHP4,000 each for the next two years.
Given an interest rate of 10%, which is the better option?
PV = 4,000 + 4000 x (PVA factor: 1.7355 t=2, r=10%)
PV = PHP10,932.00 for buying on installment vs.
PV PHP10,500 for buying today.
PRESENT VALUE OF ANNUITY DUE
If a supplier would allow you to pay P 50 000 annually at
10% for 3 years with the first payment due immediately, how
much would be the present value?
PVA
=
Php 136,776.00
i = i/m
n = mt
EFFECTIVE ANNUAL RATE
 The annual rate of interest actually
being earned.
 Equivalent Annual Rate (EAR)
 EFF%
1 + r
m
m
-1
Nominal Rate – the rate stated or quoted in a contract.
m – number of compounding periods per year
EFFECTIVE ANNUAL RATE
What is the effective annual rate of a 10% nominal
interest rate compounded semi-annually? annually?
1 + r
m
2
m
-1
= (1 + .1) – 1
2
= (1 + .05) – 1
= 0.1025
= 0.05
EFF% = 10.25%
EFF% = 5%
LOAN AMORTIZATION
• The payment of a loan in installments over a
specified period of time.
AMORTIZED LOAN
• A loan that is to be repaid in equal payments over a
specified period of time.
Example:
A home improvement loan in the amount of Php
100,000 has an interest rate of 6%. The term of the loan
is for 5 years. Equal payments at the end of every year
should be made until the loan (including the interest) is
paid off.
AMORTIZATION SCHEDULE
A home improvement loan in the amount of Php
100,000 has an interest rate of 6%. The term of the loan
is for 5 years. Equal payments at the end of every year
should be made until the loan (including the interest) is
paid off. PMT IS Php 23,739.64.
AMORTIZATION SCHEDULE
Amount Borrowed: Php 100,000
Years: 5
Interest Rate: 6%
PMT: Php 23,739.64
Year Beginning
Payment
Amount
Interest
Repayment of
Principal
Ending Balance
1
Php100,000
Php23,739.64
Php6,000.00
Php17,739.64
Php82,260.36
2
82,260.36
Php23,739.64
4,935.62
18,804.02
63,456.34
3
63,456.34
Php23,739.64
3,807.38
19,932.26
43,524.08
4
43,524.08
Php23,739.64
2,611.44
21,128.20
22,395.89
5
22,395.89
Php23,739.64
1,343.75
22,395.89
0.00
EXERCISE 1