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Time Value of Money- Money received today has greater value than money received tomorrow.
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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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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???
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
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)
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
