Time value of money is an important concept in Finance. It is used in the Corporate finance, Financial management and Financial markets etc.

1. Time value of Money
Manohar Boda

2. Why Money has Time Value?
Because it involves;
Risks and uncertainties.
The purchasing power of the money varies over time because of
inflation.
Money can be employed productively to generate returns.
 Returns are in the form of Interest rate and the interest is
categorized into two types.

3. Interest
Rates
Real Interest
Rates
Nominal
Interest Rate

4. Real Interest Rate:
The compensation that is paid by the borrower for the
postponement of consumption in the Interest Rate is
Real Interest Rate.
Nominal Interest Rate:
The Interest Rate that includes inflation value to the
Real Interest Rate. Real Interest Rate + Expected Rate of
inflation + Risk premium to compensate uncertainty.

5. Time value can be done in two ways:
Compounding
 Discounting
Compounding:
It is the process of converting cash flows today or future into even
further future and the resulting value is future value.
Discounting:
The process of converting cash flows in the future into cash flows
today. And cash flows in the into cash flows today. And cash flows of
the future converted today eilds a value phenomenon is called as
discounting.

6. Basic types of compounding problem :
Future value of lump sum or a single flow.
The future value of uneven multiple flows.
The future value of Annuity or Series of identical payments.

7. Finding future value of lump sum or single flow:
If the Interest Rate of future value of a single flow is calculated per
annum:
FV n = PV0 (1+R)n
Ex: The Fixed Deposit scheme of Andhra Bank offers 11% interest per
annum. What will be the value of 10,000 rupees after three years?
Sol: n = 3years
PV0=10,000
Rate of Interest (R)= 0.11

8. Cont.…….
FV= PV0 (1+R)n
= 10,000 (1+0.11)3
= 10,000 (1.11)3
= 10,000 (1.368)
= 13,680.
Hence.,
The value of 10,000rupees after three years becomes 13,680rupees

9. Future value of money of a single flow with
payments made quarterly and half yearly:
 If the Rate of Interest is paid more than once in a year, it
means the Rate of Interest frequency has got increased.
The rate of interest can be paid on Quarterly basis and Semi
Annual basis.
FVn = PVO(1+R⁄m)m*n
If the Rate of Interest paid quarterly m = 4
If it is paid semi annually m = 2

10. Ex: Under the Vijay cash certificate scheme Interest Is paid
quarterly the ROI is 10% per annum. Calculate the value of
1000 rupees invested after two years?
sol: PV0=1000
ROI (R)=0.1
n= 2
m=4
FVn = PV0(1+R/m)m*n
= 1000 (1+0.1/4)4*2
= 1000(0.025)8
= 1000(1.218)
= 1218

11. Future value of multiple flows:
FVn = FV1+FV2+FV3+……. FVn
Here, we are finding the future value of uneven flows, some time
multiple flow value might be identical and it is said to be Annuity.
Ex: If 1000 rupees invested at the beginning of 1st year, 2000 rupees
at the beginning of 2nd year and 3000 rupees at third year at 12% Rate
of Interest per annum. What will be the value of investment after
3years?
Sol: (1) future value of 1st years flow:
FV1=1000 (1+0.12)3 =1000 (1.12)3 =1000 (1.404) =1404

12. Contd…….
(2) Future value of second years flow:
FV2 =2000 (1+0.12)2 =2000 (1.12)2 =2000 (1.254) =2508.8
(3) Future value of 3rd years flow
FV3 =3000 (1+0.12)1= 3000 (1.12)1= 3360
Hence, The future cash flow value of uneven multiple flow is
FVn =FV1 +FV2 +FV3
=1404 +2508.8 +3360 = 7272.8

13. Annuity:
It is the term used to describe a series of periodic flows of equal
amounts this flows can be either receipts or payments.
Regular/differed/ordinary Annuity:
A series of equal payments made at the end of each period over a fixed
amount of time.
Annuity Due:
When the cash flows occur at the beginning of each period.

14. Future value of an Annuity:
FVAn =A [ (1+R)t -1 /R]
Ex: Suppose 5000rupees is set aside at the end of each year for the next
10yers at 6% Rate of Interest. Calculate the future value of an Annuity?
sol: A=5000
R=0.06
T=10
FVA = A[ (1+r)t -1/r]
=5000 [ (1+0.06)10 -1/0.06]
=5000 [ (1.06)10 -1/0.06]

15. Contd……..
=5000 [FVIFA]
=5000*13.181
=65916
Hence, The future value of the Annuity is 65,916rupees.

16. Discounting:
The process of converting cash flows in the future into the cash flows
today. And the cash flows future converted today eilds a value
=>Present value of a single flow or lump sum:
PV =FVn /(1+R)n
Ex: Pragathi Cash Certificate Scheme of Syndicate Bank issued a cash
certificate of 1lakh rupees to be received after 10years at 12%per
annum. Find out present value?
FVn=100,000
R = 0.12

17. Contd……..
PV= 100,000/1+0.12
= 100,000/1.12
= 89285.714

18. Present value of Uneven multiple flows:
PVn =FV (PVIF)m,n
Ex: In the first year cash flow is 2lakh and 2nd year 4lakh and 3rd year 6lakhs
and cost of capital is 12%. Evaluate the present value of cash inflow?
Year cash flow PV
1 2 = FV(PVIF)12,1 = 200,000(0.893) = 178000
2 4 =FV(PVIF)12,2 = 400,000(0.797) = 316000
3 6 =FV(PVIF)12,3 = 6000000(0.712) = 410000
12lakh 920000
There is a higher difference between the future value and current value of
the scheme. It is advisable to the borrower not to opt for this scheme.

19. Present value of Annuity:
PVAn= A [1-1 / (1+R)n /R]
Ex: Calculate the Present Value of 20lakh rupees for 25years at 6
percent?
Sol: PVAn =20,00,000[1 -1/(1+0.06)25/0.06]
=20,00,000(12.783)
=2,55,66,000
The present value of Annuity is 2,55,66,000rupees.