Convert present cash flows to future period through Compounding techniques

1. Dr Raju Indukoori 1
Compounding
(Future Value of Money)
S S N Raju Indukoori

2. Dr Raju Indukoori 2
Future Value of Money (FVM)
COMPOUNDING

3. Dr Raju Indukoori 3
Future Value of Money
It is the Process of
Compounding
PV of money
for a
Future Period of Time

4. Dr Raju Indukoori 4
Purpose of compounding
1) To Know Future value of single CF
• Bank Deposits
• Retirement plan
2) To Know Future value of multiple CF
1) Irregular
» Portfolio Investments
» Business Participation
2) Regular
a) Even CF
» Recurring Deposits
» Future redemption (Sinking fund)
b) Uneven CF
» Chit funds

5. Compounding – Time Line

6. Dr Raju Indukoori 6
Single Cash Flow or Lump sum
0 1 2 3 54
1st Jan 19
CIF2 CIF3 CIF4CIF1 CIF5COF0
Rs 1,000
1st Jan 20 1st Jan 221st Jan 21 1st Jan 23 1st Jan 24
PV FV ?

7. Dr Raju Indukoori 7
Multiple Uneven Cash Flow
0 1 2 3 54
1st Jan 19
CIF2 CIF3 CIF4CIF1 CIF5COF0
Rs 1,000
1st Jan 20 1st Jan 221st Jan 21 1st Jan 23 1st Jan 24
PV FV ?
Rs 2,000 Rs 3,000 Rs 2,000 Rs 4,000

8. Dr Raju Indukoori 8
Multiple Uneven Cash Flow
or
Annuity Cash Flow
0 1 2 3 54
1st Jan 19
CIF2 CIF3 CIF4CIF1 CIF5COF0
Rs 1,000
1st Jan 20 1st Jan 221st Jan 21 1st Jan 23 1st Jan 24
PV FV ?
Rs 1,000 Rs 1,000 Rs 1,000 Rs 1,000

9. Compounding Tools

10. Dr Raju Indukoori 10
Compounding Tools
1) Future value of a Single CF
2) Future value of Multiple CF
a) Regular Cash Flows
• Even Cash Flows (Annuities)
• Uneven Cash Flows
b) Irregular Cash Flows
3) Sinking fund factor

11. Dr Raju Indukoori 11
Future Value of a Single Cash Flow
FV = PV(1+r)n
= PV (FVIFnR)

12. Dr Raju Indukoori 12
FUTURE VALUE OF SINGLE CASH FLOW
An Example
• Deposit with a Bank : Rs 1,00,000
• Rate of Interest (k) : 9%
• Period (n) : 5 Years
FV = 1,00,000(1+0.09)5 = Rs 1,53,862
Or using Time value compounding table
FV = 1,00,000 (1.5386) = Rs 1,53,860

13. Dr Raju Indukoori 13
FUTURE VALUE OF ANNUITIES
FV = A (FVIFA)







 

r
1-r)(1
A
n
FVn

14. Dr Raju Indukoori 14
FUTURE VALUE OF ANNUITIES
- An Example
• Annual Insurance Premium : Rs 50,000
• Rate of Interest (k) : 9%
• Period (n) : 20 Years
FV = = 25,58,000
Or
FV = 50000 (51.1601) = 25,58,005







 
0.09
1-200.09)(1
50000

15. Dr Raju Indukoori 15
Sinking Fund Factor
Equated Annual Installment to meet future redemption
A = FVA (Sinking Fund Factor)










1r)(1
r
FVn
n







FVIFA
1
FVn

16. Dr Raju Indukoori 16
Sinking Fund Factor
An Example
• Future Payment : Rs 1,00,000
• Rate of Interest (k) : 10%
• Period (n) : 5 Years
A = 16,380
Or
= 16,380










15.10)0(1
0.10
1,00,000







6.105
1
1,00,000

17. Dr Raju Indukoori 17
Yearly Compoundingm = 1
Role of Multiple Compounding
m=Frequency of Compounding
m = 2
m = 3
m = 4
m = 8
m = 12
m = 52
m = 365
m = ∞
Semi Annual Compounding
Once in 4 months
Quarterly Compounding
Once in 45 days
Monthly Compounding
Weekly Compounding
Daily Compounding
Continuous Compounding

18. Dr Raju Indukoori 18
Role of Multiple Compounding
‘m’ and TVM
• As ‘m’ increases, compounded value
increases, vice versa
• As ‘m’ increases, discounted value decreases,
vice versa

19. Dr Raju Indukoori 19
Role of Multiple Compounding
• Minimum value of ‘m’ is 1
If m = 1, then ERR = R
• As ‘m’ increases r also
increases, Vice versa
If m > 1, then R > ERR
• Maximum value of ‘ERR’ is
there when ‘m’ is at
continuous compounding
100*)1m
r
1(ERR
365m1








m
 
7183.2
1ERR e
gCompoundinContinous


e
r
‘m’ and Effective Rate of Return (ERR)

20. Dr Raju Indukoori 20
ERR = 10.00m = 1
EXAMPLE
Multiple Compounding
PV: 1,00,000, Rate of Interest (R): 10%, Period (n) : 5 Years
m = 2
m = 3
m = 4
m = 8
m = 12
m = 52
m = 365
m = ∞
FV = 110,000
FV = 110,337
FV = 110,381
FV = 110,449
FV = 110,471
FV = 110,506
FV = 110,515
FV = 110,517
FV = 110,250
ERR = 10.51
ERR = 10.52
ERR = 10.52
ERR = 10.38
ERR = 10.45
ERR = 10.47
ERR = 10.25
ERR = 10.34

21. Dr Raju Indukoori 21
Any Questions

22. Dr Raju Indukoori 22
Thank You
Dr Raju Indukoori