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Time value of money

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What is time value of money? Annuities, simple interest, compound interests, present value, future value, etc.

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Time value of money

  1. 1. Time Value of Money
  2. 2. Would you prefer to have 1 crore now or 1 crore 10 years from now? Would you prefer to have 1 crore now or 1 crore 10 years from now?
  3. 3. The Terminology of Time ValueThe Terminology of Time Value  Present Value - An amount of money today, or the current value of a future cash flow  Future Value - An amount of money at some future time period  Period - A length of time (often a year, but can be a month, week, day, hour, etc.)  Interest Rate - The compensation paid to a lender (or saver) for the use of funds expressed as a percentage for a period (normally expressed as an annual rate)  Present Value - An amount of money today, or the current value of a future cash flow  Future Value - An amount of money at some future time period  Period - A length of time (often a year, but can be a month, week, day, hour, etc.)  Interest Rate - The compensation paid to a lender (or saver) for the use of funds expressed as a percentage for a period (normally expressed as an annual rate)
  4. 4. Time Value of Money • The value of money changes with change in time. • A rupee received today is more valuable than a rupee received one year later. – Present Value concept (PV concept) – Future or Compounding Value concept (FV concept) • The value of money changes with change in time. • A rupee received today is more valuable than a rupee received one year later. – Present Value concept (PV concept) – Future or Compounding Value concept (FV concept)
  5. 5. Reasons for Time Preference of Money • Uncertain future • Risk involvement • Present needs • Return • Uncertain future • Risk involvement • Present needs • Return
  6. 6. Note: Annuity means series of constant cash flows starting from first year to nth year (say up to 5th year, 10 years etc.).
  7. 7. Future Value of a Single Amount Say that you put $1,000 into the bank today. How much will you have after a year? After two years? This kind of problem is called a future value / compounding problem. Say that you put $1,000 into the bank today. How much will you have after a year? After two years? This kind of problem is called a future value / compounding problem.
  8. 8. Compounding vs. Simple Interest • Compounding interest is defined as earning interest on interest. • Simple interest is interest earned on the principal investment. • Principal refers to the original amount of money invested or saved • Compounding interest is defined as earning interest on interest. • Simple interest is interest earned on the principal investment. • Principal refers to the original amount of money invested or saved
  9. 9. Future Value of a Single Amount You have Rs.1,000 today and you deposit it with a financial institution, which pays 10 per cent interest compounded annually, for a period of 3 years. What is the total amount after 3 years? You have Rs.1,000 today and you deposit it with a financial institution, which pays 10 per cent interest compounded annually, for a period of 3 years. What is the total amount after 3 years?
  10. 10. Formula FVn =PV×(1+k)n FVn = Future value n years PV = Present Value (cash today) k = Interest rate per annum n = Number of years for which compounding is done FVn =PV×(1+k)n FVn = Future value n years PV = Present Value (cash today) k = Interest rate per annum n = Number of years for which compounding is done
  11. 11. If you deposit Rs.10,000 today in a bank which pays 12% interest compounded annually, how much will the deposit grow to after 10 years and 12 years? Example If you deposit Rs.10,000 today in a bank which pays 12% interest compounded annually, how much will the deposit grow to after 10 years and 12 years?
  12. 12. Doubling period • How much time is required to double my investment? • The length of period which an amount is going to take o double at a certain given rate of interest. • How much time is required to double my investment? • The length of period which an amount is going to take o double at a certain given rate of interest.
  13. 13. Rule of 72 72 Doubling Period = --------------------- Rate of Interest 72 Doubling Period = --------------------- Rate of Interest
  14. 14. If you deposit Rs.10,000 today at 6 per cent rate of interest, in how many years will this amount double? Workout this with the rule of 72. Example If you deposit Rs.10,000 today at 6 per cent rate of interest, in how many years will this amount double? Workout this with the rule of 72.
  15. 15. Rule of 69 69 Doubling Period = 0.35 + --------------------- Rate of Interest 69 Doubling Period = 0.35 + --------------------- Rate of Interest
  16. 16. If you deposit Rs.20,000 today at 6 per cent rate of interest, in how many years will this amount double? Workout this with the rule of 69. Example If you deposit Rs.20,000 today at 6 per cent rate of interest, in how many years will this amount double? Workout this with the rule of 69.
  17. 17. Multiple Compounding Periods • Interest may have to be compounded more than once a year. • Example: Banks may allow interest on quarterly or half yearly basis; or a company may allow compounding of interest twice a year. • Interest may have to be compounded more than once a year. • Example: Banks may allow interest on quarterly or half yearly basis; or a company may allow compounding of interest twice a year.
  18. 18. Formula FVn =PV×(1+k/m)m x n FVn = Future value n years PV = Present Value (cash today) k = Interest rate per annum n = Number of years for which compounding is done m = Number of times compounding is done during a year FVn =PV×(1+k/m)m x n FVn = Future value n years PV = Present Value (cash today) k = Interest rate per annum n = Number of years for which compounding is done m = Number of times compounding is done during a year
  19. 19. Calculate the compound vale of Rs.10,000 at the end of 3 years at 12% rate of interest when interest is calculated on – Yearly basis – Half yearly basis – Quarterly basis Example Calculate the compound vale of Rs.10,000 at the end of 3 years at 12% rate of interest when interest is calculated on – Yearly basis – Half yearly basis – Quarterly basis
  20. 20. Effective Vs. Nominal Rate • Effective Interest rate: The percentage rate of return on an annual basis. It reflects the effect of intra-year compounding. (Ex. 12.36%) • Nominal Interest rate: Interest rate expresses in monitory terms. (Ex. 12%) • Effective Interest rate: The percentage rate of return on an annual basis. It reflects the effect of intra-year compounding. (Ex. 12.36%) • Nominal Interest rate: Interest rate expresses in monitory terms. (Ex. 12%)
  21. 21. Formula ERI = (1 + k/m)m – 1 ERI = Effective Rate of Interest k = Nominal Rate of Interest m = Frequency of compounding per year ERI = (1 + k/m)m – 1 ERI = Effective Rate of Interest k = Nominal Rate of Interest m = Frequency of compounding per year
  22. 22. Example A bank offers 8 per cent nominal rate of interest on deposits. What is the effective rate of interest if the compounding is done i) half yearly ii) quarterly & iii) monthly A bank offers 8 per cent nominal rate of interest on deposits. What is the effective rate of interest if the compounding is done i) half yearly ii) quarterly & iii) monthly
  23. 23. Future Value of an Annuity • Suppose you deposit Rs.1,000 annually in a bank for 5 years and your deposits earn a compound interest rate of 10 per cent. What will be the value of this series of deposits (an annuity) at the end of 5 years? • Suppose you deposit Rs.1,000 annually in a bank for 5 years and your deposits earn a compound interest rate of 10 per cent. What will be the value of this series of deposits (an annuity) at the end of 5 years?
  24. 24. • 1000 (1.1)4 + 1000 (1.1)3 + 1000 (1.1)2 + 1000 (1.1)1 + 1000 • 1000 (1.4641) + 1000 (1.331) + 1000 (1.21) + 1000 (1.1) + 1000 • 6,105 • 1000 (1.1)4 + 1000 (1.1)3 + 1000 (1.1)2 + 1000 (1.1)1 + 1000 • 1000 (1.4641) + 1000 (1.331) + 1000 (1.21) + 1000 (1.1) + 1000 • 6,105
  25. 25. Formula (1 + K)n – 1 FVAn = A ----------- K FVAn = Future value of an Annuity n years A = Constant periodic flow k = Interest rate per period n = duration of the annuity (1 + K)n – 1 FVAn = A ----------- K FVAn = Future value of an Annuity n years A = Constant periodic flow k = Interest rate per period n = duration of the annuity
  26. 26. (1 +.1)5 – 1 • FVA = 1000 -------------------- .1 (1 +.1)5 – 1 • FVA = 1000 -------------------- .1
  27. 27. Present Value of a Single Amount • Suppose someone promises to give you Rs.1,000 three years hence. What is the present value of this amount if the interest rate is 10 per cent? • Suppose someone promises to give you Rs.1,000 three years hence. What is the present value of this amount if the interest rate is 10 per cent?
  28. 28. Formula n PV = FVn
  29. 29. Present Value of An Annuity Suppose you expect to receive Rs.1,000 annually for 3 years, each receipt occurring at the end of the year. What is the present value of this stream of benefits I the discount rate is 10 per cent? Suppose you expect to receive Rs.1,000 annually for 3 years, each receipt occurring at the end of the year. What is the present value of this stream of benefits I the discount rate is 10 per cent?
  30. 30. • 1000 (1/1.1) + 1000 (1/1.1)2 + 1000 (1/1.1)3 • 1000x.909 + 1000x.826 + 1000x.751 • 2486 • 1000 (1/1.1) + 1000 (1/1.1)2 + 1000 (1/1.1)3 • 1000x.909 + 1000x.826 + 1000x.751 • 2486

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