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Time Value of Money

Time Value of Money. A) Introduction. Would you prefer to have $1 million now or $1 million 10 years from now?Of course, we would all prefer the money now! This illustrates that there is an inherent monetary value attached to time. What is The Time Value of Money?.

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Time Value of Money

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  1. Time Value of Money

  2. A) Introduction • Would you prefer to have $1 million now or $1 million 10 years from now?Of course, we would all prefer the money now! • This illustrates that there is an inherent monetary value attached to time.

  3. What is The Time Value of Money? • A Rupee received today is worth more than a Rupee received tomorrow • This is because a Rupee received today can be invested to earn interest • The amount of interest earned depends on the rate of return that can be earned on the investment • Time value of money quantifies the value of a Rupee through time

  4. The reason of time value of money • Productively employed to generate real returns I.e. product made in 100 Rs. Can be sold in 110 Rs. To generate return of 10%. • Purchasing Power Rs. Had high purchasing power in past than rs. Had today. Similarly rs. Has high purchasing power today than rs. Has in future. • Risk and uncertainty As future is uncertain, it is prefer to spend rs. Today than in future.

  5. Uses of Time Value of Money • Time Value of Money, or TVM, is a concept that is used in all aspects of finance including: • Bond valuation • Stock valuation • Accept/reject decisions for project management • Financial analysis of firms • And many others!

  6. B). Compounding Technique • Used to know future value of all cash flow at the end of some time period at particular rate of return. • Example 1 • Mr. X deposit 100 Rs. For 3 years in a bank with rate of interest 5% compounded yearly. • Answer is 115.77

  7. Equation for compounding • A = P(1 + r)n A = Amount in received in future P = Principle r = Interest rate n = no. of year amount is compounded • If Amount is compounded frequently I.e. more than one time in a year. Than A = P(1 + r/m)nm m = number of time it is compounded in year.

  8. Example 2 In previous example take that amount is compounded quarterly in a year. • So compounding factor m = 12/3 = 4 • A = 100 (1 + 0.05/4)3*4 = 100(1.0125)12 = 100 (1.161) = 116.10 • This shows that more frequent compounding in a year provides more return of money than compounding yearly. • After having knowledge of compounding technique now it is easy to find future value of money.

  9. (C) Future Value • Future value of money include following calculations like • Future value of lump sum Amount • Future value of Series of Cash flow with different amount • Future value of Series of Cash flow with the same amount. (annuity)

  10. (C-1) Future Value Equation • FV = PV* (1+i)n • It is the same as compounding technique. • Here (1+I) n is shows the future value of initial investment of Rs. At end of n year at interest rate I, referred to as Future Value Interest Factor (FVIF).

  11. Example 3 • Mr. P want to know FV of the investment in mutual fund of Rs. 1000 for 3 year at 10%. n=3, i =3, PV = 1000, FV = ? FV = 1000 (1+ 10/100) 3 = 1000 ( 1.1)3 = 1000 (1.331) = 1331

  12. (C-2) FV of series of Cash flow of different amount • The future value of a cash flow stream is equal to the sum of the future values of the individual cash flows. • The FV of a cash flow stream can also be found by taking the PV of that same stream and finding the FV of that lump sum using the appropriate rate of return for the appropriate number of periods.

  13. Example 4 • Assume Mr. A has the had invested $ 100 in first year, $ 300 in second year, $ 500 in third year and $ 1000 in 4th year, so what would be FV of his amount with the rate of interest is 10%.

  14. Time line • Draw a timeline: $100 $300 $500 $1000 0 1 2 3 4 $1000 i = 10% ? ? ?

  15. Table/ solution

  16. (C-3) Future value of Series of Cash flow with the same amount. (annuity) • Annuity refers to the periodic flows of equal amounts. • These flows can be either termed as receipts or payments. • I.e. Mr. A deposit Rs.1000 annually for 10 year in a bank than 1000 rs would be annuity.

  17. Equation • FVAn = A* [(1+i)n – 1]/ i • FVAn - FV of annuity amount at end of n years • N = no of years • A = amount deposited every year / annuity amount. • [(1+i)n – 1]/ i = Future Value Interest Factor for Annuity (FVIFA) (The value of FVIFA can be found from the appendix 4 of text book)

  18. Example 5 • Assume that Sally owns an investment that will pay her $100 each year for 20 years. The current interest rate is 10%. What is the FV of this annuity? • Draw a timeline $100 $100 $100 $100 $100 0 1 2 3 …………………………. 19 20 ? i = 10%

  19. Solution • FV = 100 FVIFA (10%, 20 Yrs.) • FV = 100 [(1+i)n – 1]/ I = 100 [ (1+ 0.10)20 – 1]/ 0.1 = 100 [(1.1) 20 – 1]/0.1 = 100 [ (6.72 –1)]/0.1 = 100 (5.72 / 0.1) = 100 (57.20) = 5720 OR Find value of FVIFA for 10 % and 20 yrs from appendix 4 of text book and do the calculation = 100 (57.274) = 5727.4

  20. Doubling Period • A doubling period can be determined by rule of 72 or 69. • Rule of 72 = 72/I, I = interest rate • While rule of 69 = 0.35+69/I

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