- The time value of money concept holds that money today is worth more than the same amount in the future due to its potential for growth through interest. - Formulas for future value, present value, future value interest factors, and present value interest factors are provided to calculate the value of money over time at different interest rates and compounding periods. - Examples demonstrate calculating future and present values using these time value of money formulas in different scenarios like annual, semi-annual, and daily compounding.

1. Portfolio Management

2. Time Value of Money (TVM)
• The time value of money draws from the idea that
rational investors prefer to receive money today
rather than the same amount of money in the
future because of money's potential to grow in
value over a given period of time.
– For example, money deposited into a savings account earns
a certain interest rate and is therefore said to be
compounding in value.

3. Time Value of Money Formula
• FV = PV x [ 1 + (i / n) ] (n x t)
FV = Future value of money
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years

4. Example Problems
1. Assume a sum of Rs.10,000 is invested for one
year at 10% interest. Calculate the future value of that
money.
FV = ?
PV = 10,000
i = 10%
n = 1
t = 1
FV = PV x [ 1 + (i / n) ] (n x t)
FV = 10,000 x [1 + (10% / 1)] ^ (1 x 1)
= Rs. 11,000

5. 2. Taking the same problem, Rs.10,000 is invested at 10% interest,
if the number of compounding periods is increased to quarterly,
monthly, or daily, the ending future value calculations are:
• Quarterly Compounding:
FV = PV x [ 1 + (i / n) ] (n x t)
FV = 10,000 x [1 + (10% / 4)] ^ (4 x 1)
= Rs.11,038
• Monthly Compounding:
FV = 10,000 x [1 + (10% / 12)] ^ (12 x 1)
= 11,047
• Daily Compounding:
FV = 10,000 x [1 + (10% / 365)] ^ (365 x 1)
= 11,052
This shows TVM depends not only on interest rate and time
horizon, but also on how many times the compounding
calculations are computed each year.

6. Future Value Interest Factor (FVIF)
• Future value interest factor (FVIF), also known as a
future value factor, is a component that helps to
calculate the future value of a cash flow that will be
paid at a certain point in the future.
• The future cash flow could be a single cash flow or a
series of cash flows (that occur at regular time
intervals)

7. Formula
Formula for Future Value Interest factor:
FVIF = (1+r)n
• r = interest rate per period
• n = number of time periods
Formula for Future Value factor:
FV=C0×(1+r)n
• C0 = Cash flow at the initial point (present value)
• r = rate of return
• n = number of periods

8. Example Problems
1. Paul deposits Rs.1,000 in a bank for 2 years at 6% per year compounded
annually. What will be the value of the money at the end of 2 years?
FVIF = (1+r)n
• r = 6% = 0.06
• n = 2
FVIF = (1 + 0.06)²
FVIF = 1.1236
FV=C0​×(1+r)n
• C0 = Rs. 1000
• r = 6% = 0.06
• n = 2
FV = 1000 * 1.1236
FV = Rs. 1,123.60

9. 2. Paul deposits Rs. 1,000 in a bank for 2 years at 6% per year,
but this time it is compounded semi-annually. What will be the
value of the money at the end of 2 years?
Hint: The number of periods, in this case, would be 4 (2 years * 2 periods
per year) and the rate will be 3% (6% divided by 2 periods).
FVIF = (1+r)n
r = .% = 0.03; n = 4
FVIF = (1 + 0.03)4
FVIF = 1.1255
FV=C0​×(1+r)n
C0 = Rs. 1000; r = 3% = 0.03; n = 4
FV = 1000 * 1.1255
FV = Rs. 1,125.50

10. Present Value Interest Factor (PVIF)
• The present value interest factor (PVIF) is a formula
used to estimate the current worth of a sum of
money that is to be received at some future date.
PVIFs are often presented in the form of a table with
values for different time periods and interest rate
combinations.

11. Formula
PVIF = 1 / (1 + r)n
where:
a = The future sum to be received
r = The discount interest rate
n = The number of years or other time period​

12. Understanding the PVIF
• The present value interest factor is based on the key
financial concept of the time value of money. That is, a
sum of money today is worth more than the same
sum will be in the future, because money has the
potential to grow in value over a given period of time.
Provided money can earn interest, any amount of
money is worth more the sooner it is received.
• Present value impact factors are often used in
analyzing annuities. The present value interest factor
of an annuity (PVIFA) is useful when deciding
whether to take a lump-sum payment now or accept an
annuity payment in future periods.

13. • Using estimated rates of return, you can compare the value of
the annuity payments to the lump sum.
• The present value interest factor may only be calculated if the
annuity payments are for a predetermined amount spanning a
predetermined range of time.

14. Example
Assume an individual is going to receive Rs. 10,000 five years
from now, and that the current discount interest rate is 5%.
PVIF = a / (1 + r)n
where:
a = 10,000
r = 5% or 0.05
n = 5 years​
PVIF = 10,000 / (1 + .05) ^ 5
= 7835.26

15. The present value of the future sum is then
determined by subtracting the PVIF figure from the
total future sum to be received. Thus, the present
value of the
Rs.10,000 to be received five years in the future
would be
PV = Rs.10,000 – Rs. 7,835.26
PV = Rs. 2,164.74.