TIME VALUE OF MONEY
PREPARED BY
LEC. KASHFIA MAISHA
WHAT IS TIME VALUE OF MONEY
Time value of money is the concept that money today is worth more than
money tomorrow. That is because money today can be used, invested, or
grown. Therefore, $1 earned today is not the same as $1 earned one year
from now because the money earned today can generate interest,
unrealized gains, or unrealized losses.
For example, money deposited into a savings account earns interest.
Over time, the interest is added to the principal, earning more interest.
That's the power of compounding interest.
WHAT IS TIME VALUE OF MONEY (CONT.)
If it is not invested, the value of the money erodes over time. If you hide
$1,000 in a mattress for three years, you will lose the additional money it
could have earned over that time if invested. It will have even less
buying power when you retrieve it because inflation reduces its value.
Question: Suppose I offer you the choice of taking Rs. 1,00,000 from me
today or taking this same sum from me after a year. What decision will you
make?
WHAT IS TIME VALUE OF MONEY (CONT.)
If you chose to take the sum today, you’ve made the right choice. There are 2 reasons why taking up the
first option is better –
High purchasing power – Because of inflation, it’s safe to consider that an amount of money can get us
more services and goods than it can in the future. You have chosen the first option in the previous
example because you understand that Rs. 1,00,000 can get you more things today than it will get you a
year later.
Risks involved– What if, in the previous example, you chose to receive the money a year later, but when
you approach me then, I don’t have any money to give to you? This could also happen to you if you lend
money to someone, but they go bankrupt before they can repay you. This shows that there is a certain
level of risk involved if you choose to get your money later.
WHY IS TIME VALUE OF MONEY IMPORTANT?
Time value of money is important because it helps investors and people saving for
retirement determine how to get the most out of their dollars. This concept is
fundamental to financial literacy and applies to your savings, investments and
purchasing power.
1. Savings: If the basic idea of the TVM is that money is worth more today than
it is tomorrow, you’d think it’d be wiser to spend it now rather than save it for
later - but we know that isn’t always the case. While inflation works against
you, meaning it makes your dollar worth less tomorrow than today, compound
interest can work for you to elevate the value of your present dollar tomorrow.
WHY IS TIME VALUE OF MONEY IMPORTANT?
(CONT.)
II. Investment: If it is not invested, the value of the money erodes over
time. If you hide $1,000 in a mattress for three years, you will lose the
additional money it could have earned over that time if invested. It will have
even less buying power when you retrieve it because inflation reduces its
value. The time value of money has a negative relationship with
inflation.
III. Purchasing Power: Inflation is the loss of purchasing power over time,
so purchasing power often decreases as time progresses.
WHY IS TIME VALUE OF MONEY IMPORTANT?
(CONT.)
For instance, if a milk gallon had been priced at $2.50 in the 1990s and you
needed $50 worth of milk, you could have bought 20 gallons. Fast forward
30 years later, and you still wish to buy $50 worth of milk — but inflation
has caused the price per gallon to increase to $3.50. Now, you can only
purchase 14 gallons. In simpler terms, your money can buy you more today
compared with 30 years from now.
COMPONENTS OF TIME VALUE OF
MONEY
Interest/Discount Rate (i)
Time Periods (n)
Present value (PV)
Future value (FV)
COMPONENTS OF TIME VALUE OF MONEY
(CONT.)
• Future Value (FV): The future value (FV) is the projected cash flow expected to
be received in the future, i.e. the cash flow amount we are discounting to the
present date.
Future value (FV) is a financial concept that assigns a value to an asset based on
estimated variables such as future interest rates or cashflows. It may be useful for
an investor to know how much their investment may be in five years given an
expected rate of return. This concept of taking the investment value today,
applying expected growth, and calculating what the investment will be in the
future is future value.
COMPONENTS OF TIME VALUE OF MONEY
(CONT.)
The Present Value (PV) is an estimation of how much a future cash flow (or
stream of cash flows) is worth right now. All future cash flows must be
discounted to the present using an appropriate rate that reflects the expected
rate of return (and risk profile) because of the “time value of money.” The
present value (PV) concept is fundamental to corporate finance and valuation.
The premise of the present value theory is based on the “time value of money”,
which states that a dollar today is worth more than a dollar received in the
future. Therefore, receiving cash today is preferable (and more valuable) than
receiving the same amount at some point in the future.
•There are two primary reasons that support this theory:
•Opportunity Cost of Capital: If the cash is currently in
your possession, those funds could be invested into other
projects to earn a higher return over time.
COMPONENTS •Inflation: Another risk to consider is the effects of
OF TIME VALUE inflation, which can erode the actual return on an
OF MONEY investment (and thereby future cash flows lose value due
(CONT.) to uncertainty).
PRESENT VALUE VS. FUTURE VALUE: WHAT IS THE DIFFERENCE?
The present value (PV) calculates how much a future cash flow is worth
today, whereas the future value is how much a current cash flow will be
worth on a future date based on a growth rate assumption.
While the present value is used to determine how much interest (i.e. the
rate of return) is needed to earn a sufficient return in the future, the future
value is usually used to project the value of an investment in the future.
Present Value (PV) → How much is the future cash flow worth today?
Future Value (PV) → How will this current cash flow be worth in the future?
COMPONENTS OF TIME VALUE OF MONEY
(CONT.)
Discount Rate (r): The “r” is the discount rate – the expected rate of return
(interest) – which is a function of the riskiness of the cash flow (i.e. greater
risk → higher discount rate).
Number of Periods (n): The final input is the number of periods (“n”),
which is the duration between the date the cash flow occurs and the present
date – and is equal to the number of years multiplied by the compounding
frequency.
TUTORIAL
https://www.investopedia.com/terms/t/timevalueofmoney.asp
BASIC
FORMULA
• Calculating
present value
• Calculating
future value
TUTORIAL
https://www.youtube.com/watch?v=cy4PiY5ERTI
WHEN CALCULATING FUTURE VALUE
WITH INTEREST
WHEN CALCULATING PRESENT VALUE WITH
INTEREST
WHEN CALCULATING FUTURE VALUE WITH
INTEREST
PROBLEM EXAMPLE
Example: Alex promises you $900 in 3 years at 10%, what is the
Present Value?
• Future Value (FV): $900
• n: 3 years
• r: 10%
PV = FV / (1+r)n
PV = $900 / (1 + 0.10)3 = $900 / 1.103
= $676.18 (to nearest cent).
PROBLEMS
2. What is $570 next year worth now, at an interest rate of
10% ?
3. What is $570 in 3 years time worth now, at an interest
rate of 10% ?
SOLUTION
2. PV = $570 / (1+0.10)1 = $570 / 1.10
= $518.18 (to nearest cent)
3. PV = $570 / (1+0.10)3 = $570 / 1.331
= $428.25 (to nearest cent)
PROBLEM EXAMPLE 4.
PROBLEM EXERCISE 5.
SOLUTION 5.
PROBLEM EXAMPLE
Example 6: Jonathan borrowed some amount from a bank at a rate of
7% per annum compounded annually. If he finished paying his loan by
paying $6,500 at the end of 4 years, then what is the amount of loan that
he had taken? Round your answer to the nearest thousands.
SOLUTION 6.
• The future value is, FV = $6500.
• The time is t = 4 years.
• n = 1 (as the amount is compounded annually).
• The rate of interest is, r = 7% =0.07.
Substitute all these values in the present value formula:
PV = FV / (1 + r / n)nt
PV = 6500 / (1 + 0.07/1)1(4) = 6500 / (1.07)4 = 5,000 (The answer is rounded to the nearest
thousands).
Therefore, the borrowed amount = $5,000
PROBLEM EXAMPLE
Example 7: Mia invested some amount in a bank where her amount gets
compounded daily at 5% annual interest. What is the amount invested
by Mia if the amount she got after 10 years is $1,650? Round your
answer to the nearest thousands.
Example 8: Josie borrowed some amount from a bank at a rate of 5%
per annum compounded annually. If she finished paying her loan by
paying $4,500 at the end of 4 years, then what is the amount of loan that
she had taken? Round your answer to the nearest thousands.
SOLUTION 7.
• The future value is, FV = $1650.
• The time, t = 10 years.
• n = 365 (as the amount is compounded daily).
• The rate of interest is, r = 5% =0.05.
Substitute all these values in the present value formula:
PV = FV / (1 + r / n)n t
PV = 1650 / (1 + 0.05/365)365(10) = 1000 (The answer is rounded to the nearest thousands).
Therefore, the invested amount = $1,000
SOLUTION 8.
• The future value is, FV = $4500.
• The time is t = 4 years.
• n = 1 (as the amount is compounded annually).
• The rate of interest is, r = 5% =0.05.
Substitute all these values in the the present value formula:
PV = FV / (1 + r / n)nt
PV = 4500 / (1 + 0.05/1)1(4) = 4500 / (1.05)4 = 3,800 (The answer is rounded to the
nearest thousands).
Therefore, the borrowed amount = $3,800
PROBLEM
Example 9: David borrowed $5000 from a bank at a rate of 7%
per annum compounded annually. How much he has to pay
back at the end of 4 years?
Example 10: You have invested $1000 in a bank where your
amount gets compounded daily at 5% annual interest. Then what
is the future value of the amount you have invested for 10 years?
SOLUTION
9. To find: The future value of the borrowed amount after 4 years.
• The present value (investment) , PV = $5000.
• The rate of interest, r = 7% =7/100 = 0.07.
• The time in years, t = 4.
• Since the amount is compounded annually, n = 1.
Using the future value formula of compound interest:
FV = PV (1 + r / n)n t
A = $6,553.98
Answer: The future value = $6,553.98.
SOLUTION
10. To find: Future value for an investment after 10 years.
• The present value (investment), PV = $1000.
• The rate of interest, r = 5% =5/100 = 0.05.
• The time in years, t = 10.
• Since the amount is compounded daily, n = 365.
• Using the future value formula of compound interest:
• FV = PV (1 + r / n)n t
• FV = $1648.66
• Answer: The future value = $1648.66.
EXERCISE
1. What is $570 next year worth now, at an interest rate of 15% ?
2. You are promised $800 in 10 years time. What is its Present Value at
an interest rate of 6% ?
3. An investor deposited $10,000 in a savings account paying 5% converted quarterly. At
the end of 5 years what is the value of the account?
4. If your friend has promised to repay the entire borrowed amount in five years, how much
is the $10,000 at 5% worth on the date the borrowed funds are returned?
5. You are scheduled to receive Rs. 13,000 in two years. When you receive it, you will
invest it for six more years at 8 percent per year. How much will you have in eight years?
EXERCISE
6. You have Rs. 9,000 to deposit. ABC Bank offers 12 percent per year compounded
monthly, while King Bank offers 12 percent but will only compound annually. How
much will your investment be worth in 10 years at each bank?
7. What is the present value of a certificate of deposit with a maturity value of $1,000
due in 3 years, if money is worth 6% compounded semi-annually?
8. Find the value of $1,000 invested at 8% for 10 years with interest compounded
annually?
9. Find the present value of $5,000 due in 4 years if money is worth 4% compounded
semi-annually?
THANK YOU!
