Time Value of Money
What is time value of Money?
•The time value of money (TVM) is the concept
that money you have now is worth more than the
identical sum in the future due to its potential earning
capacity. This core principle of finance holds that
provided money can earn interest, any amount
of money is worth more the sooner it is received.
Time Line
• Line depicting an investment’s cash flow
• Time Zero appears on the leftmost end and future periods are marked
from left to right
• Negative values represent cash outflows and positive values
represent cash inflows
Time Line
2000 3000 4000 5000 4500 3500
(10000)
Techniques of Time value of Money
• Compounding
• Discounting
Present Value or Discounting
Present Value or Discounting
• Present value (PV) is the current value of a future sum of money or
stream of cash flows given a specified rate of return. Future cash
flows are discounted at the discount rate, and the higher the discount
rate, the lower the present value of the future cash flows.
• If an investor wants to earn INR 500000 after 5 years, how much he
needs to invest today if interest rate is 7%?
Future Value or Compounding
Future Value or Compounding
•Future value is the value of an asset at a specific date.
It measures the nominal future sum of money that a
given sum of money is "worth" at a specified time in
the future assuming a certain interest rate, or more
generally, rate of return; it is the present value
multiplied by the accumulation function.
•An investor invested INR 65000 for 6 years at 8% and
9% p.a. What is its FV?
Types of Cash flows
• Single cash flow
• Multiple Even Cash flow-Annuity
• Multiple uneven cash flows
• An investor invests INR 5000 each for the next 5 years at 9% pa. What
is its value at the end of 5 years.
• An investor invests INR 5000, 6000, 4000, 7000 and Inr 5000 for the
next 5 years. What is its value at the end of 5 years.
Future Value
• Single Sum
• Annuity
• Mixed stream
Future Value – Single sum
If a person invests Rs 10000 into a bank at 10% rate of interest. How
much his money will grow at the end of 5 years and 10 years.
tables.pdf
Future Value - Annuity
If a person invests Rs 5000 every year for 5 years. How much his money
will grow at the end of 5 years
Future value – Mixed stream
Find the future value of the following CF at the end of 5 years if interest
rate is 8%:
Year CF
1 10000
2 12000
3 14000
4 22000
5 24000
Solve:
• If an investor is investing the following cash flows in the next 4 years,
find out its future value, assume discount rate to be 10%.
Year 1 INR 50000
2 INR 100000
3 INR 75000
4 INR 80000
Present value
• Single sum
• Annuity
• Mixed stream
• Perpetuity
Present Value
• Find the present value of 10000 to be received after 1 year and 5
years ( interest 12%).
Present Value - Annuity
What is the present value of Rs10000 to be received every year for the
next 4 years.
Present Value – Mixed stream
• If a business is receiving the following cash flows in the next 5 years,
find out its present value, assume discount rate to be 9%
Year 1 INR 67000
2 INR 100000
3 INR 90000
4 INR 80000
Present Value - Perpetuity
Find the present value of Rs 10000 to be received for ever, if interest
rate is 10%
Review
• If an investor invests INR 4000 each for 5 years, what’s its value at the
end of 5 years at 10% interest?
• If an investor receives INR 10000 each for the next 5 years, what is its
present value at 9% discount rate?
Effective Rate of Interest:
The Effective Rate of interest is the rate of interest actually earned on an investment or paid on a loan as a result
of compounding the interest over a given period of time. It is usually higher than the nominal rate and is used to
compare different financial products that calculate annual interest with different compounding periods – weekly,
monthly, quarterly, semi annually, and yearly. Increasing the number of compounding periods makes the
effective interest rate increase as time goes by.
• Find the effective rate of interest
a) 6% compounded semi-annually.
b) 6% compounded quarterly.
c) 6% compounded monthly
Loan Amortisation
• You borrow $10,000 today and will repay the loan in equal
installments at the end of the next 4 years. How much is your annual
payment if the interest rate is 9%?
Step 1 : Calculation of instalment
Annual instalment = loan amount/ Annuity factor ( r%, n years)
10000/ 3.240( 9%, 4 years) = 3087
Step 2- Loan Amortisation Table
Review questions
Determine the future value for each of the following situations.
A. You are saving for a car and you put away $5,000 in a savings account.
You want to know how much your initial savings will be worth in 7
years if you have an anticipated annual interest rate of 5%.
B. You are saving for retirement and make contributions of $11,500 per
year for the next 14 years to your retirement plan. The interest rate
yield is 8%.
A. Use FV of $1 table. Future value factor where n = 7 and i = 5 is 1.407.
1.407 × 5,000 = $7,035. B. Use FV of an ordinary annuity table. Future
value factor where n = 14 and i = 8 is 24.215. 24.215 × 11,500 =
$278,472.50.
