Time Value of money

1. Dr Raju Indukoori 1
Time Value of Money

2. Dr Raju Indukoori 2
Value of Money
• Face Value of Money
• Physical Value of Money
• Internal Value of Money
• External Value of Money
• Time Value of Money

3. Dr Raju Indukoori 3
What is Time Value of Money
(TVM)
It is the value of money
which changes in accordance with
the given direction and length of time.

4. Dr Raju Indukoori 4
k and TVM
k represents discounting or compounding rate
1. Real Risk Free Return (R)
2. Inflation (I)
3. Risk Premium (P)
Hence k = R + I + P

5. Dr Raju Indukoori 5
What Changes TVM
1) Length of the time (n)
2) Direction of time (PV / FV)
3) Rate of discount or compound (k)

6. Dr Raju Indukoori 6
1) Present Value of Money
2) Future Value of Money
Forms of Time Value
1) Present Value of Money
2) Future Value of Money

7. Dr Raju Indukoori 7
Direction of Time Value of Money
(TVM)
Compounding
Discounting
0 1 2 3 54
FVPV

8. Dr Raju Indukoori 8
Compounding
0 1 2 3 54
FVPV Converting
Present Value (PV) to Future Value (FV)

9. Dr Raju Indukoori 9
Discounting
0 1 2 3 54
FVPV
Converting
Future Value (FV) to Present Value (PV)

10. Dr Raju Indukoori 10
MBA, PGDM, MCom, MS Fin, MFM, MIB
CA, ICWA, CFA, CPA, CIMA
Retail
Institutional
Savings & Expenditure
Retirement Plans
Public Finance
Project financing
Investors
Companies
Government
Employees
Students
Need for Understanding TVM
Business Valuation, M&A
Capital Expenditure
Borrowers
Home Loans
Personal Loans

11. Dr Raju Indukoori 11
Application of TVM
Compounding
• Maturity value of bank deposit
• Redemption value of RD
• Realization of chit fund
• Payment of future redemption (Sinking
Fund)
• Retirement benefits
Discounting
• Capital budgeting
• Bond Valuation
• Equity Valuation
• Loan payments on borrowing (EMIs)
• Lease Analysis

12. Dr Raju Indukoori 12
Represented by ‘r’
k = . R .
100
Number of Years, ‘n’
Period with in a year
TVM Tables
Formulas + Normal Calculator
Spread Sheet
Financial Calculator
Represented by ‘m’
m = 1 or m > 1
Period
Cash-flows
Frequency of
Compounding
Method or
Approach
Rate
Requirements to compute TVM
PV or FV
PMT

13. Dr Raju Indukoori 13
Process of computing TVM
1) Verbal description of the problem
PV/FV, r, n, m
2) Diagram description on a time line
Represent direction and timing of the cash flows
3) Rational choice of approach
Based on the cash flows
4) Interpret the results
Help to make a decision

14. Dr Raju Indukoori 14
Forms of Cash Flow
BASED ON DIRECTION OF THE FLOW
1) Cash Inflow (CIF)
• Interest
• Dividend
• Earnings
2) Cash Outflow (COF)
• Principal
• Investment
• Capital Expenditure

15. Dr Raju Indukoori 15
Forms of Cash Flow
BASED ON TIMING OF CASH FLOWS
1)Single Cash flow
2)Multiple Cash flow
a)Irregular
b)Regular
i) Uneven Cash flows
ii)Annuity Cash flows
• Deferred Annuity: At the end of period
• Annuity Due: At the beginning period

16. Dr Raju Indukoori 16
Single Cash Flow in Present
Ex : Rs 10,000 Deposited in a Bank in 2019
0 1 2 3 54
1st Jan 19
CIF2 CIF3 CIF4CIF1 CIF5COF0
10,000
1st Jan 20 1st Jan 221st Jan 21 1st Jan 23 1st Jan 24

17. Dr Raju Indukoori 17
Single Cash Flow in Future
Ex : Rs 1,00,000 will be received as bonus in 2024
0 1 2 3 54
1st Jan 19
CIF2 CIF3 CIF4CIF1 CIF5COF0
1,00,000
1st Jan 20 1st Jan 221st Jan 21 1st Jan 23 1st Jan 24

18. Dr Raju Indukoori 18
Annuity Cash Flows – Due
Ex : Deposited Rs 1,000 yearly in a Bank
0 1 2 3 54
1st Jan 14
CIF2 CIF3 CIF4CIF1 CIF5
1,000 1,000 1,000 1,000
COF0
1,000
1st Jan 15 1st Jan 171st Jan 16 1st Jan 18 1st Jan 19

19. Dr Raju Indukoori 19
Annuity Cash Flow – Deferred
Ex : Received Rs 1,000 monthly from a Bank
0 1 2 3 54
1st Jan 09
CIF2 CIF3 CIF4CIF1 CIF5
100 100 100 100
COF0
1st Jan 10 1st Jan 121st Jan 11 1st Jan 13 1st Jan 14
100

20. Dr Raju Indukoori 20
Uneven Cash Flows – Due
Ex : Will receive dividends from a company
0 1 2 3 54
1st Jan 19
CIF2 CIF3 CIF4CIF1 CIF5
100 200 200 300
COF0
1st Jan 20 1st Jan 221st Jan 21 1st Jan 23 1st Jan 24
300

21. Dr Raju Indukoori 21
Uneven Cash Flows – Deferred
Ex : Will receive dividends from a company
0 1 2 3 54
1st Jan 19
CIF2 CIF3 CIF4CIF1 CIF5
100 200 200 300
COF0
1st Jan 20 1st Jan 221st Jan 21 1st Jan 23 1st Jan 24
50

22. Dr Raju Indukoori 22
Approaches to find TVM
2) Spread sheet: More and Irregular CF
a) Use time value functions
b) Apply formula
3) Financial Calculator : Complex CF
a) Enter requirements to compute TVM
b) Old value remain same till you change
1) Numerical: Single CF and Annuities
a) Formulas
b) Time value tables
c) Normal Calculator

23. Dr Raju Indukoori 23
Types of TVM Tables
A.1
Future Value Interest Factor (FVIF k,n)
A.2
Future Value Interest Factor Annuity (FVIFA k,n)
A.3
Present Value Interest Factor (PVIFk,n)
A.4
Present Value Interest Factor Annuity (PVIFAk,n)

24. Dr Raju Indukoori 24
Types of Spread Sheets
1) MS Excel
2) Lotus 1-2-3

25. Dr Raju Indukoori 25
Types of Financial Calculators

26. Dr Raju Indukoori 26
Any Questions

27. Dr Raju Indukoori 27
Thank You
Dr Raju Indukoori