- Time value of money is important for financial decisions like capital budgeting, capital structure, and dividends. - Money has time value because people prefer current consumption to future consumption, money can be reinvested, and inflation decreases future purchasing power. - Compounding allows money to earn interest on prior interest amounts over time, increasing the future value. Present value calculations discount future cash flows to determine their value today. - Tables provide compound interest factors to simplify calculations of future and present values for single amounts, series of cash flows, and annuities received or paid periodically.

1. Time Value of Money
• Three Major Decision for Financial Manager
– How Big should be the corporate
• How much fund do I need, How do I Generate these
funds
• Financing Decisions(Capital Structure Decisions)
– How to earn on the Funds ? Where to Invest
• Investing Decisions (Capital Budgeting Decisions)
– How to part with the profit
• Dividend Decisions

2. Time Value of Money
• TVM is important for all the above mentioned
three decisions
• Money has Time Value because of the
following reasons
– Individual prefer current consumption to future
consumption
– Money received today can be reinvested
– In an inflationary economy purchasing power of
money decrease in future

3. Time Value of Money
• So money received today is more “valuable” than
received tomorrow
• Corollary: Money received tomorrow is less
valuable than received today.
• Time Preference for money is central concept in
Finance.
• Businesses when faced with the cash receipts or
disbursement of the funds over several periods of
time take help of TVM to make decisions

4. Time Value of Money
• VALUATION CONCEPT
• Compounding
• Rs 1000 invested @ 10% compounded annually for 3
years
• The calculation become tedious as no of years increase
YEAR Amount
1 1000+100=1100
2 1100+110=1210
3 1210+121=1331

5. Time Value of Money
– Compounding using Formula
• A=P(1+k/100)n
• A= amount after n years
• k = interest rate used for compounding(%)
• P= Initial amount invested
–Recalculating
• A=1000(1.10)3
• A = Rs 1331

6. Time Value of Money
– Using the Compound value table
• What if in the previous problem the n= 25 years
• The calculation is tedious
• For convenience of calculation the factor
shown in the box is pre-calculated
• A=1000X (1.10)25
• This factor is called “CVIF” (Compound Value Interest
Factor) CVIF ( 10%, 25 years) =10.835.
• A = Rs1000X 10.835 =Rs 10835

7. Compound Value Interest Factor(CVIF) Table
(for 1 Rs)
Year 1% 2% 3% 4%
1 1.010 1.020 1.030 1.040
2 1.020 1.040 1.062 1.082
3 1.030 1.061 1.093 1.125
4 1.041 1.082 1.126 1.170
5 1.051 1.104 1.159 1.217

8. Time Value of Money
–Recalculating using Table
• P=1000
• K = 10%
• N= 10 years
• CVIF= 2.594
• A= P X CVIF(10 %,10 Years) => 1000 X 2.594=Rs 2594

9. Time Value of Money
–Future value of a series of cash flows
–An investor invests money as follows
• End of 1 year =Rs 500
• End of 2 year =Rs 1000
• End of 3 year =Rs 2000
• Calculate the total money in the account at the end of
3 years with k@ 10% pa

10. Time Value of Money
– 500 is invested for 2 years @10% -- CVIF=1.210
– 1000 is invested for 1 year @10 %--- CVIF =1.100
– 2000 is invested for 0 years @ 10% CVIF =1
– Investment after 3 year =Rs 3705
– What if the investment was done at the start of
the year ? Recalculate

11. Time Value of Money
–Future value of an Annuity
–An investor invests money as follows
• End of 1 year =Rs 1000
• End of 2 year =Rs 1000
• End of 3 year =Rs 1000
• Calculate the money at the end of 3 years with k@ 10%
pa

12. Time Value of Money
– 1000 is invested for 2 years @10% -- CVIF=1.210
– 1000 is invested for 1 year @10 %--- CVIF =1.100
– 1000 is invested for 0 years @ 10% CVIF =1
– Investment after 3 year
=1000X1.210+1000X1.110+1000X1
=1000(1.210+1.100+1)
=1000(3.310) =3310
Factor 3.3310 can be directly read from the table
and is called CVIFA (Compound Value Interest
Factor Annuity)

13. Time Value of Money
–Present value of Money
• PV= FV/ (1+k/100)n
• We can write PV= FV X 1/ (1+k/100)n
• The factor 1/ (1+k/100)n is called PVIF
• So PV= FVX PVIF
– A depositor will get Rs 1000 after 1 year. The
discount rate is 10%.What is the Present worth of
1000 Rs.
– From table PVIF =.909
– Thus PV = 1000X.909 =RS 909

14. Time Value of Money
–Present value of a single Cash inflow
– A depositor will get Rs 1000 after 1 year. The
discount rate is 10%.What is the Present worth of
1000 Rs.
– From table PVIF =.909
– Thus PV = 1000X.909 =RS 909
1 2 30
PV = FV1/(1+i)
FV1

15. Time Value of Money
–Present value of a series of cash inflows
–Mr. X may get money in future as follows
• End of 1 year =Rs 500
• End of 2 year =Rs 1000
• End of 3 year =Rs 2000
• Calculate the Present worth of the future cash flows
that are coming to the investor with k@ 10% pa

16. 16
Single Sum - Future & Present Value
1 2 30
PV = FV1/(1+k)
FV1
PV = FV2/(1+k)2
FV2
PV = FV3/(1+k)3
FV3

17. Time Value of Money
– 500 is coming after 1 years -- PVIF=.909
– 1000 is coming after 2 years --- PVIF =.826
– 2000 is coming after 3 years ---PVIF =.751
– Present Worth of future cash flows =Rs 2782.5
– Recalculate with k= 12%.Will the Present worth
will be more or less that 2782.5???

18. Time Value of Money
–Present value of an Annuity
–An investor will get money as follows
• After 1 year =Rs 1000
• After 2 year =Rs 1000
• After 3 year =Rs 1000
• Calculate the Present worth with k@ 10% pa

19. Time Value of Money
– Present value of an Annuity
– An investor will get money as as follows
• After 1 year =Rs 1000
• After 2 year =Rs 1000
• After 3 year =Rs 1000
• Calculate the Present worth with k@ 10% pa
– for 2 years @10% -- CVIF=1.210
– 1000 is investe1000 is invested d for 1 year @10 %--- CVIF
=1.100
– 1000 is invested for 0 years @ 10% CVIF =1
– Investment after 3 year =1000X1.210+1000X1.110+1000X1
=1000(1.210+1.100+1)
=1000(3.310) =3310
Factor 3.3310 can be directly read from the table and is called
CVIFA (Compound Value Interest Factor Annuity)

20. PV Table
(for 1 Rs received annually for n years)
Year 5% 6% 8% 10%
1 .952 .943 .926 .909
2 1.859 1.833 1.783 .736
3 2.773 2.676 2.577 2.847
4 3.546 3.456 3.312 3.170
5 4.330 4.212 3.393 3.791