Time Value of Money (TVM), also known as present discounted value, refers to the notion that money available now is worth more than the same amount in the future, because of its ability to grow. The term is similar to the concept of ‘time is money’, in the sense of the money itself, rather than one’s own time that is invested. As long as money can earn interest (which it can), it is worth more the sooner you get it.

1. TIME VALUE OF MONEY
PRESENTERS:
GERALD DIADID
ARNULFO GUTIERREZ
JOHN MICHAEL EUBRA

3. Time Value of Money (TVM), also known as present
discounted value, refers to the notion that money available now is
worth more than the same amount in the future, because of its
ability to grow.
The term is similar to the concept of ‘time is money’, in the
sense of the money itself, rather than one’s own time that is
invested. As long as money can earn interest (which it can), it is
worth more the sooner you get it.
TIME VALUE OF MONEY

4. TIME VALUE OF MONEY

5. Example of Time Value of Money
Imagine you lent a friend $1,000 and he paid you back today. You
immediately deposit that money into an account that earns 7% annually. It will be
worth $1,070 in exactly one year’s time.
If, on the other hand, you received the $1,000 in one year’s time, it would only be
worth $934.58 ($1,000 ÷ 1.07), assuming a 7% annual interest rate.
If you asked people whether they would prefer to receive $1,000 now or that
amount in one year’s time, they would probably all say they wanted it now, for
several reasons:
1. They want to be sure they get the money. Waiting a year increases the risk of
not getting the money.
2. They may want to go out shopping or go on vacation soon, and that money
would be useful.
3. If they invested that money today in a deposit account, the $1,000 would be
worth more in one year’s time. They are aware of the Time Value of Money.
TIME VALUE OF MONEY

6. TIME VALUE OF MONEY

7. It can be defined as today’s value of a single payment or
series of payments to be received at a later date, given at a
specified discount rate. The process of determining the present
value of a future payment or a series of payments or receipts is
known as discounting.
In absolute terms, discounting is the opposite of
compounding. It is a process for calculating the value of money
specified at a future date in today’s terms. The interest rate for
converting the value of money specified at a future date in today’s
terms is known as the discount rate.
TIME VALUE OF MONEY
PRESENT VALUE OF MONEY

8. It can be defined as the rising value of today’s sum
at a specified future date given at a specified interest
rate. The compounding technique calculates it.
Compounding of money is the value addition in the
initial principal amount after defined intervals at a
given interest rate.
TIME VALUE OF MONEY
FUTURE VALUE OF MONEY

9. TIME VALUE OF MONEY

10. TIME VALUE OF MONEY
A specific formula can be used for calculating the future value of money so
that it can be compared to the present value:
Where:
FV = the future value of money
PV = the present value
i = the interest rate or other return that can be earned on the money
t = the number of years to take into consideration
n = the number of compounding periods of interest per year
Using the formula above, let’s look at an example where you have $5,000 and
can expect to earn 5% interest on that sum each year for the next two years.
Assuming the interest is only compounded annually, the future value of your
$5,000 today can be calculated as follows:
FV = $5,000 x (1 + (5% / 1) ^ (1 x 2) = $5,512.50

11. The formula can also be used to calculate the present value of money to be received in the future.
You simply divide the future value rather than multiplying the present value. This can be helpful in considering
two varying present and future amounts.
PV = FV / (1+r)n Or PV = FV * 1/(1+r)n
Where,
PV=Present value or the principal amount
FV= FV of the initial principal n years hence
r= Rate of Interest per annum
n= number of years for which the amount has been invested.
In this equation, ‘1/(1+r)n‘ is the discounting factor which is called the “Present
Value Interest Factor.”
TIME VALUE OF MONEY

12. In our original example, we considered the options of someone paying your
$1,000 today versus $1,100 a year from now. If you could earn 5% on investing the money
now, and wanted to know what present value would equal the future value of $1,100 – or
how much money you would need in hand now in order to have $1,100 a year from now –
the formula would be as follows:
PV = $1,100 / (1 + (5% / 1) ^ (1 x 1) = $1,047
The calculation above shows you that, with an available return of 5% annually,
you would need to receive $1,047 in the present to equal the future value of $1,100 to be
received a year from now.
TIME VALUE OF MONEY

13. Rule of 72 Trick
There are a general question in an investor’s mind How many years will it take
to double my money? ‘Rule of 72‘ is a user-friendly mathematical rule used to
quickly estimate the ‘rate of interest’ required to double your money given the
‘number of years of investment and vice versa. It is specifically called the rule
of 72 because the number 72 is used in its formula.
TIME VALUE OF MONEY

14. Present Value vs. Future Value: Interest
Factors (PVIF) and (FVIF) Tables
TIME VALUE OF MONEY
FVIF Rate of Interest (r)
Period
(n)
1% 2% 3% 4% 5% 6% 7%
1 1.010 1.020 1.030 1.040 1.050 1.060 1.070
2 1.020 1.040 1.061 1.082 1.103 1.124 1.145
3 1.030 1.061 1.093 1.125 1.158 1.191 1.225
4 1.041 1.082 1.126 1.170 1.216 1.262 1.311
5 1.051 1.104 1.159 1.217 1.276 1.338 1.403
6 1.062 1.126 1.194 1.265 1.340 1.419 1.501
7 1.072 1.149 1.230 1.316 1.407 1.504 1.606
PVIF Rate of Interest (r)
Period (n) 1% 2% 3% 4% 5% 6% 7%
1 0.99 0.98 0.971 0.962 0.952 0.943 0.935
2 0.98 0.961 0.943 0.925 0.907 0.89 0.873
3 0.971 0.942 0.915 0.889 0.864 0.84 0.816
4 0.961 0.924 0.888 0.855 0.823 0.792 0.763
5 0.951 0.906 0.863 0.822 0.784 0.747 0.713
6 0.942 0.888 0.837 0.79 0.746 0.705 0.666
7 0.933 0.871 0.813 0.76 0.711 0.665 0.623
TIME VALUE OF MONEY

15. LONG-TERM FINANCIAL
CONCEPTS:
TIME VALUE OF MONEY
TIME VALUE OF MONEY

16. TVM (Time Value of Money)
“ A peso today is worth more than a peso tomorrow.”
• Where to put money
• Real assets
• Financial assets
• Where to get money
• Investors
• Financial institutions
The time value of money must be considered in making the appropriate
investment decision.
• determine their future value at a future date
• compute their present value today
TIME VALUE OF MONEY

17. Present Value Vs. Future value
• Future value:
What amount of money in the future is equivalent to ₱15,000 today? In other
words, what is the future value of ₱15,000?
• Present Value:
What amount today is equivalent to ₱17,000 paid out over the next 5 years as
outlined above? In other words, what is the present value of the stream of cash
flows coming in the next 5 years?
Time line:
TIME VALUE OF MONEY

18. Present Value Vs. Future value
• Future value: Uses compounding
• Present Value: Uses discounting
Cash Flow:
• Single Amount
• Annuity
• Mixed Stream
TIME VALUE OF MONEY

19. Cash Flow: Future Value of a Single Amount
Future value is the amount to which an amount of money will grow in a defined period of time at a specified investment rate. A business may
face questions such as:
■ Question 1
If we borrow ₱380,000 today to replace outdated equipment and the terms are 8 percent for 5 years compounded quarterly, what is the total
cost of the purchase?
To determine the total cost of the equipment purchase, the calculation is
FV = PV (1 + r)n
FV = future value of the investment or loan
P= principal
r = interest rate per period of compounding
n = number of compounding periods in the length of the loan
Where:
PV = 380,000
r= 8% / 4 (quarterly) = 2% or .02 = quarterly interest
n = 4 (quarterly) x 5 (years) = 20 = compounding periods
FV = ₱380,000 (1 + 0.02)20
FV = ₱380,000 (1.4859)
FV = ₱564,642
TIME VALUE OF MONEY

20. Cash Flow: Present Value of a Single Amount
Borrowing money: the lender will charge interest for the time the company uses the money. A typical procedure is for the
lender to discount the loan.
A discount is the amount of money subtracted from a loan at the time of lending equal to the interest charged by the lender.
PV = FV ÷ (1 + r)n
■ Example 1
If a business borrows ₱10,000 for one year from a bank at an interest (discount) rate of 8 percent, how much is the actual
amount of money received?
Where:
FV = 10,000
r =8%
n = 1
PV = 10,000 ÷ (1 + .08)1
PV = 10,000 ÷ (1 + .08)1
PV = 9,260.00
TIME VALUE OF MONEY

21. Annuity
A stream of equal periodic cash flows over a specified time period.
These cash flows can be inflows of returns earned on investments
or outflows of funds invested to earn future returns.
Types of Annuities:
• Ordinary Annuity
• Annuity Due
TIME VALUE OF MONEY

22. FUTURE VALUE OF AN ORDINARY ANNUITY
FVn = CF [(1 + r)n – 1] ÷r
FV = Future value
CF = Cash Flow / annual payment
r = interest rate per period of compounding
n = number of compounding periods in the length of the loan
Example:
Ms. Dela Cruz wishes to determine how much money she will have at the end of 5 years if she chooses ordinary annuity. She will deposit
₱1,000 annually, at the end of each of the next 5 years, into a savings account paying 7% annual interest.
Where:
CF = 1,000
r = 7%
n = 5 years
FV5 = ₱1,000 [(1 + .07)5 – 1] ÷.07
FV5 = ₱1,000 [1.40255 – 1] ÷.07
FV5 = ₱402.5517÷ 0.07
FV5 = ₱5,751.00
TIME VALUE OF MONEY

23. FUTURE VALUE OF AN ANNUITY DUE
FVn = CF [((1 + r)n – 1)÷r] (1+r)
Where:
CF = 1,000
r = 7%
n = 5 year
FV5 = ₱1,000 [((1 + .07)5 – 1) ÷.07] x (1.07)
FV5 = ₱1,000 [1.40255 – 1) ÷.07] (1.07)
FV5 = ₱402.5517÷ 0.07 (1.07)
FV5 = ₱5,750.74 (1.07)
FV5 = ₱6,153.00
**Ordinary annuity ₱5,750.74 versus Annuity due ₱6,153.29
TIME VALUE OF MONEY

24. PRESENT VALUE OF AN ORDINARY ANNUITY
Formula: PVn = (CF÷r) [1 – (1÷(1+r)n )]
Example:
Braden Company, a small producer of plastic toys, wants to determine the most it should pay to purchase
a particular ordinary annuity. The annuity consists of cash flows of ₱700 at the end of each year for 5
years. The firm requires the annuity to provide a minimum return of 8%.
Where:
CF = 700
r = 8%
n = 5 years
PV5 = (700÷.08) [1 – (1÷(1+.08)5 )]
PV5 = (8,750) [1 – (1÷(1+.08)5 )]
PV5 = (8,750) [1 – (1÷(1.4693)]
PV5 = (8,750) [1 – .680596]
PV5 = (8,750) [.31940]
PV5 = 2,795.00
TIME VALUE OF MONEY

25. 1. Solve Annuity Payments, Periods, and Interest Rates
2. Solve Perpetuities
3. Solve Uneven Cash Flows
Learning Objectives
TIME VALUE OF MONEY

26. Finding Annuity Payments
Suppose we need to accumulate Php10,000 and have it available five years
from now. Suppose further that we can earn a return of 6% on our savings,
which are currently zero. Find the Annuity Payment.
GIVEN
N = 5 years
I/YR = 6% = 0.06
PV = 0
PMT = ?
FV = 10,000
TIME VALUE OF MONEY

27. Finding Annuity Payments
Suppose we need to accumulate Php10,000 and have it available five years
from now. Suppose further that we can earn a return of 6% on our savings,
which are currently zero. Find the Annuity Payment.
TIME VALUE OF MONEY

28. TIME VALUE OF MONEY
PMT = FV
( 1 + i)n -1
i
PMT = 10,000
( 1 + 0.06)5 -1
0.06
Finding Annuity Payments
Suppose we need to accumulate Php10,000 and have it available five
years from now. Suppose further that we can earn a return of 6% on our
savings, which are currently zero. Find the Annuity Payment

29. TIME VALUE OF MONEY
PMT = 10,000
( 1.06)5 -1
0.06
PMT = 10,000
1.338225578 -1
0.06
Finding Annuity Payments
Suppose we need to accumulate Php10,000 and have it available five years
from now. Suppose further that we can earn a return of 6% on our savings,
which are currently zero. Find the Annuity Payment

30. TIME VALUE OF MONEY
PMT = 10,000
0.338225577
0.06
PMT = 10,000
5.63709296
PMT (Ordinary Annuity) = Php1,773.96
Finding Annuity Payments
Suppose we need to accumulate Php10,000 and have it available five years
from now. Suppose further that we can earn a return of 6% on our savings,
which are currently zero. Find the Annuity Payment

31. TIME VALUE OF MONEY
PMT (Annuity Due) = Ordinary Annuity Payment
1 + i
PMT (Annuity Due) = Php1,773.96
1.06
PMT (Annuity Due) = Php1,673.55
Finding Annuity Payments
Suppose we need to accumulate Php10,000 and have it available five years
from now. Suppose further that we can earn a return of 6% on our savings,
which are currently zero. Find the Annuity Payment

32. TIME VALUE OF MONEY
Finding the Number of Periods, N
Suppose you decide to make end-of-year deposits, but you can only save
$1,200per year. Again assuming that you would earn 6%, how long would it
take you toreach your $10,000 goal?

33. TIME VALUE OF MONEY
Finding the Number of Periods, N
Suppose you decide to make end-of-year deposits, but you can only save
$1,200per year. Again assuming that you would earn 6%, how long would
it take you toreach your $10,000 goal?

34. TIME VALUE OF MONEY
Finding the Interest Rate, I
Now suppose you can only save $1,200 annually, but you still want to have
the $10,000 in five years. What rate of return would enable you to achieve
your goal?

35. TIME VALUE OF MONEY
Finding the Interest Rate, I
Now suppose you can only save $1,200 annually, but you still want to have
the $10,000 in five years. What rate of return would enable you to achieve
your goal?

36. TIME VALUE OF MONEY
Perpetuities
A perpetuity is simply an annuity with an extended life. Since the
payments go on forever, you can’t apply the step-by-step approach.
However, it’s easy to find the PV of a perpetuity with the following formula:
PV of a perpetuity= PMT
I

37. TIME VALUE OF MONEY
Perpetuities
Find the value of a British consol with a face valueof $1,000 that
pays $25 per year in perpetuity. The answer depends on the interest rate.
In 1888, the “going rate” as established in the financial marketplace was
2.5%
PV of a perpetuity= PMT
I
Consol value1888 = $25 / 0.025 = $1,000

38. TIME VALUE OF MONEY
Perpetuities
Find the value of a British consol with a face valueof $1,000 that pays
$25 per year in perpetuity. The answer depends on the interest rate.
In 2006, 118 years later, the annual payment was still $25, but the going
interest rate had risen to 5.2%.
PV of a perpetuity= PMT
I
Consol value2006 = $25 / 0.052 = $480.77

39. Perpetuities
TIME VALUE OF MONEY
Find the value of a British consol with a face valueof $1,000 that
pays $25 per year in perpetuity. The answer depends on the interest rate.
Note, though, that if interest rates decline in the future, say to 2%, the
value of the consol will rise:
PV of a perpetuity= PMT
I
Consol value2006 = $25 / 0.02 = $1,250

40. TIME VALUE OF MONEY
Uneven Cash Flows
The definition of an annuity includes the term
constant payment—in other words, annuities involve
payments that are equal in every period. Although many
financial decisions do involve constant payments, many
others involve nonconstant, or uneven, cash flows. For
example, the dividends on common stocks typically increase
over time, and investments in capital equipment almost
always generate uneven cash flows.

41. Uneven Cash Flows
There are two important classes of uneven
cash flows: (1) a stream that consists of a series of
annuity payments plus an additional final lump sum
and (2) all other uneven streams. Bonds represent
the best example of the first type, while stocks and
capital investments illustrate the other type.
TIME VALUE OF MONEY