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# Time value of money- TVM ( Discouting and Compounding)

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Time Value of Money
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# Time value of money- TVM ( Discouting and Compounding)

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

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

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### Time value of money- TVM ( Discouting and Compounding)

1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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