Time Value Analysis
• Among the financial concepts, the time
value of money is the single most important
concept.
• The application of the time value of analysis
includes planning for retirement, valuing
stocks and bonds, setting up loan payment
schedules And making decisions regarding
investing in new plant and equipment.
Time Value Analysis
The first step in time value analysis is to
set up a timeline, which will help in the
visualization of what will happen with a
particular problem.
Example
P10,000 (present value) that is on hand
today, if invested to yield at 5% interest,
will have a value (future value) after 4
years that is more than what is on hand
today.
Diagram
Future Values
• A peso in hand today is worth more than
a peso to be received in the future
because if invested, it will earn interest
and yield more than a peso in the future.
• The process of conversion to future
values (FVs) from present values (PVs)
is called compounding.
Example
Assume that P5,000 will be deposited in a
bank which pays a guaranteed 3% interest
each year. How much would it be at the
end of year 5?
Illustration
Calculation of Future Value
using a Formula
FVN = PV(1 + i)
N
FV5 = P5,000 (1.03)
= P5,796.37
5
Present Values
• The term discounting is simply the
opposite of compounding.
• The applicable formula for the
computation of the present value is as
follows:
Present Value Formula
Present Values
• The calculation of the present value is
simply the reverse of computing for a
future value.
• The process of computing the present
value of a cash flow or a series of cash
flow is called discounting.
Illustration
A bank offers to sell a treasury bond that will pay
P5,788.12 three years from now. Banks are currently
offering a guaranteed 5% interest 3-year time deposit
certificate. Given this scenario, there is a need to
decide whether to invest the money in a treasury bond
or just invest it on a 3-year time deposit certificate.
Computing the Present Value
Effective Interest Rate
• The rate being charged by the credit card
companies, auto dealers, and so forth is called
nominal interest rate or quoted or stated rate.
• The stated rate of 8% for loans offered by two
banks is not the same if one requires monthly
payments and the other quarterly payments.
Illustration
A nominal rate of 10% with semi-annual
compounding is equivalent to a rate of
10.25%, with annual compounding
because both rates will cause P10,000 to
grow to the same amount after 2 year.
Formula to find the effective
annual rate
Loan Amortization
An important application of compound
interest involves loans that are paid off in
instalments over time. Included are car
loans, housing loans, SSS/GSIS loans and
many business loans.
Loan Amortization
These loans that require payment in
equal amounts either on a monthly,
quarterly, or annual basis are called an
amortized loan.
Illustration of Amortization
process
A homeowner borrows P1,000,000 from a
bank and the loan is to be repaid in five
equal payments at the end of the next 5
years. The bank charges 8% on the
balance at the beginning of each year.
Determine the payment, the homeowner
must make each year.
Illustration of Amortization
process
PV = P1,000,000
I = 8%
N = 5 years
PMT = P250,456.45
Illustration of Amortization
process
Therefore, the homeowner must pay the
bank, P250, 456.45 per year for the next 5
years. Each payment consists of two parts
– interest and repayment of principal.
This breakdown is shown on an
amortization schedule as follows:
Illustration of Amortization
process