This document discusses the concept of discounting or present value of money. It explains that discounting is the process of calculating the present value of future cash flows. It then outlines some of the key tools and methods used in discounting, including calculating the present value of a single cash flow, present value of annuities for regular cash flows, and using the capital recovery factor to calculate loan payments. Examples are provided to illustrate how to use these discounting formulas and tables to determine the present value of various cash flows given a discount rate.

1. Dr Raju Indukoori 1
Discounting
(Present value of money)
S S N Raju Indukoori

2. Dr Raju Indukoori 2
Present Value of Money (FVM)
DISCOUNTING

3. Dr Raju Indukoori 3
Present Value of Money
It is Process of
Discounting
FV of money
from a
future period of time

4. Dr Raju Indukoori 4
Purpose of Discounting
1) Present value of single CF
a) Discounted bond
b) Equity valuation
2) Present value of multiple CF
1) Irregular
2) Regular
a) Even CF
a) Constant Dividends
b) Interest payments on bonds and debentures or band deposits
c) EMI calculation (Capital Recovery)
b) Uneven CF
a) Capital Expenditure

5. Discounting Time Line

6. Dr Raju Indukoori 6
Single CF or Lump Sum
CF5
0 1 2 3 54
PV ? FV
1st Jan 241st Jan 231st Jan 221st Jan 211st Jan 201st Jan 19
Rs 100

7. Dr Raju Indukoori 7
Multiple Uneven CF
CF5
0 1 2 3 54
PV ?
1st Jan 241st Jan 231st Jan 221st Jan 211st Jan 201st Jan 19
CF4CF3CF2CF1
Rs 50Rs 90Rs 110 Rs 150 Rs 100

8. Dr Raju Indukoori 8
Multiple Uneven Cash Flow
or
Annuity Cash Flow
CF5
0 1 2 3 54
PV ?
1st Jan 241st Jan 231st Jan 221st Jan 211st Jan 201st Jan 19
CF4CF3CF2CF1
Rs 100Rs 100Rs 100 Rs 100 Rs 100

9. Discounting Tools

10. Dr Raju Indukoori 10
Discounting Tools
1) Present value of a Single CF
2) Present value of Multiple CF
a) Regular Cash Flows
• Even Cash Flows (Annuities)
• Uneven Cash Flows
b) Irregular Cash Flows
3) Capital Recovery factor

11. Dr Raju Indukoori 11
Present Value of a Single CF
 k+1
FV
PV n
n

FV(PVIF)PV 

12. Dr Raju Indukoori 12
PRESENT VALUE OF SINGLE CASH FLOW
An Example
• Receive bonus : Rs 1,00,000
• Period (n) : After 5 Years
• Discount Rate (k) : 9%
Or using time value discounting factor table
PV = 1,00,000 (0.6499) = Rs 64,990
 
64,990Rs
0.09+1
1,00,000
PV 5


13. Dr Raju Indukoori 13
Present Value of Annuities











n
n
k)k(1
1-k)(1
APV
(PVIFA)APV 

14. Dr Raju Indukoori 14
PRESENT VALUE OF ANNUITIES
- An Example
• Annual Dividend to be received pershare : Rs 66
• Investors required rate of return (k) : 9%
• Number of dividend paying years (n) : 10 Years
Using annuity table of discounting
PV = 66 (6.4177) = Rs 423.57
57.423
100.09)0.09(1
1-100.09)(1
66PV Rs












15. Dr Raju Indukoori 15
Capital Recovery Factor
Equated Annual Installment on a loan is
A = PVA (Capital Recovery Factor)











1k)(1
k)k(1
PVA
n
n







PVIFA
1
PVA

16. Dr Raju Indukoori 16
Capital Recovery Factor
- An Example
• Home lone take : Rs 30,00,000
• Rate of Interest (k) : 12%per annum or 1% per month
• Period (n) : 55 months
Using Time value table of discounting











1550.01)(1
550.01)0.01(1
30,00,000EMI
 
90.71178
0237263.0000,00,30
42.1472
1
30,00,000EMI
RsEMI 








17. Dr Raju Indukoori 17
Rs
0 1 2 3
Interest
Principal Payments
n
Principal and Interest Composition of EMI

18. Dr Raju Indukoori 18
Any Questions

19. Dr Raju Indukoori 19
Thank You
Dr Raju Indukoori