00:00

Understanding the Time Value of Money in Finance

Explore the concept of Time Value of Money (TVM) which states that a rupee today is worth more than a rupee tomorrow due to factors like inflation and earning potential. Delve into compounding, discounting, and adjusting cash flows for TVM, learning how to calculate present and future values using interest rates and time periods. Discover the significance of annuities, different forms of cash flows, and applying TVM in financial decision-making.

pedrajo
Télécharger la présentation

Understanding the Time Value of Money in Finance

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. TIME VALUE OF MONEY

  2. In this session we shall cover • Meaning of Time value of money • What is Compounding and Discounting? • Different patterns of Cash flows and adjusting them for TVM • Multi period compounding/discounting • Use of TVM in finance

  3. Time Value of Money • The basic principle in finance is that “ A rupee today is worth more than a rupee tomorrow” Why?

  4. Time Value of Money • Because of inflation the rupee would lose its purchasing power with time, so an early receipt would be preferred • Because of uncertainty future, an earlier receipt would be preferred associated with

  5. “ A rupee today is worth more than a rupee tomorrow” because “ the former can be invested to start earning interest immediately ”

  6. Example • If I have a Re1 today with me and I can invest it at an interest rate = 10% p.a. for 5 years, then this Re1 shall grow to

  7. Example Rs 1.611 after 5 years. How?

  8. Example • Using the formula P(1+r)n where ‘P’ is the principal amount today, ‘r’ is the rate of interest per annum and ‘n’ are the number of years =

  9. Example

  10. COMPOUNDING Present Value

  11. COMPOUNDING Future Value = Present Value (1+r)

  12. COMPOUNDING Future Value = Present Value (1+r)

  13. DISCOUNTING Future value

  14. DISCOUNTING • Present value = Future value (1+r)

  15. DISCOUNTING • Present value = Future value (1+r)

  16. Example • Rs 50,000 is to be received after 15 years from now. What would be its present value if the interest rate is 9% p.a.?

  17. Rs 50,000 is to be received after 15 years from now. What would be its present value if the interest rate is 9% p.a.? • PV = FV / (1+r)n = 50,000 / (1+0.09)15 = Rs 13,750 • This means that Rs 13,750 received today or Rs 50,000 received after 15 years shall have the same value if the opportunity to earn interest is 9% p.a.

  18. CVF and PVF Tables (Single amounts) • CVF Table: provides the FV of Re 1 today for various combinations of ‘r’ and ‘n’ FV = PV * CVF (r%, n) • PVF Table: provides the PV of Re 1 in future for various combinations of ‘r’ and ‘n’ PV = FV * PVF (r%, n)

  19. CVF and PVF Tables (Single amounts) Insert tables here

  20. CVF and PVF Tables (Single amounts) • Insert tables here

  21. Rs 50,000 is to be received after 15 years from now. What would be its present value if the interest rate is 9% p.a.? • PV= FV * PVF (9%, 15) = 50,000 * 0.275 = Rs 13,750

  22. Eg of FV of a Single amount • Rs 10,000 is being deposited in a bank today for 5 years. What shall it grow to after 5 years if interest rate is 10% p.a.?

  23. Rs 10,000 is being deposited in a bank today for 5 years. What shall it grow to after 5 years if interest rate is 10% p.a.? • FV = PV * CVF (r%, n) = 10,000 * CVF (10%, 5) = 10,000 * 1.464 = Rs 14,640 • It means that Rs 10,000 of today and Rs 14,640 after 5 years from now carry the same value if the interest rate is 10% p.a.

  24. Different other forms of amounts • Multiple cash flows • Annuity • Perpetuity • Annuity due • Growing annuity • Growing perpetuity

  25. Multiple cash flows • This refers to more than one amount occurring (cash inflow) or having to pay (cash outflow) at different points of time in future

  26. Eg of Multiple cash flows • An investment will pay Rs 100 after one year, Rs 300 in the second year, Rs 500 in the third year and Rs 1000 in the fourth year. If the interest rate is 10%, what is the present value of these multiple cash flows together?

  27. Eg of Multiple cash flows PV = 100/(1+0.1)1+ 300/(1+0.1)2+ 500/(1+0.1)3+ 1000/(1+0.1)4 OR = 100*PVF(10%,1) + 300*PVF(10%,2) + 500*PVF(10%,3) + 1000*PVF(10%,4) = Rs 1397.91

  28. Annuity • It refers to the same amount of cash flow at regular intervals of time for a specified period • This cash flow occurs at the end of each year • If it occurs at the beginning of each year, we call it ‘Annuity due’

  29. Calculating PV of an Annuity • The PVs of Re1 annuities for different combinations of ‘n’ and ‘r’ can be had from PVAF Table • PV (any annuity amount) = Annuity amount * PVAF (r%, n)

  30. Example of Annuity • What would be the PV of Rs 900 to be paid at the end of each year for 3 years from now at interest rate of 10%?

  31. Example of Annuity • What would be the PV of Rs 900 to be paid at the end of each year for 3 years from now at interest rate of 10%? • PV of Rs 900 of annuity is to be calculated

  32. Example of Annuity • What would be the PV of Rs 900 to be paid at the end of each year for 3 years from now at interest rate of 10%? • PV of Rs 900 of annuity is to be calculated • PV (any annuity amount) = Annuity amount * PVAF (r%, n)

  33. Example of Annuity • What would be the PV of Rs 900 to be paid at the end of each year for 3 years from now at interest rate of 10%? • PV of Rs 900 of annuity is to be calculated • PV (any annuity amount) = Annuity amount * PVAF (r%, n) • PV (Rs 900 annuity) = 900 * PVAF (10%, 3)

  34. Example of Annuity • What would be the PV of Rs 900 to be paid at the end of each year for 3 years from now at interest rate of 10%? • PV of Rs 900 of annuity is to be calculated • PV (any annuity amount) = Annuity amount * PVAF (r%, n) • PV (Rs 900 annuity) = 900 * PVAF (10%, 3) = 900 * 2.487 = Rs 2,238

  35. Example of Annuity • What would be the PV of Rs 900 to be paid at the end of each year for 3 years from now at interest rate of 10%? • PV (Rs 900 annuity) = 900 * PVAF (10%, 3) = 900 * 2.487 = Rs 2,238

  36. Perpetuity • It is the same amount of cash flow occurring at regular intervals of time for an infinite time in future • This also occurs at the end of each year

  37. Calculating present value of Perpetuity • PV (Perpetuity) = Annual amount / r

  38. Example of Perpetuity • Find out the PV of an investment which is expected to give a return of Rs 2500 p.a. infinitely and the rate of interest is 12% p.a.

  39. Example of Perpetuity • Find out the PV of an investment which is expected to give a return of Rs 2500 p.a. infinitely and the rate of interest is 12% p.a. • PV of (perpetuity=2500) = 2500/0.12 = Rs 20,833.33

  40. Growing Annuity • It refers to a finite series of periodic cash flows growing at a constant rate every period

  41. Calculating PV of a Growing Annuity (growth rate = g% p.a.) • When r > g, PV of a growing annuity = Amount value at the end of year ‘1’ * (1 + g)n (r – g) (1 + r)n

  42. Calculating PV of a Growing Annuity (growth rate = g% p.a.) • When r = g, PV of a growing annuity = (Amount value at end of year 1) * n ( 1 + r )

  43. Growing Perpetuity • These are the infinite series of periodic cash flows that grow at a constant rate per period

  44. Calculating PV of a Growing Perpetuity • PV of Growing Perpetuity = Annual amount value at the end of year ‘1’ ( r – g )

  45. Calculating PV of a Growing Perpetuity • PV of Growing Perpetuity = Annual amount value at the end of year ‘1’ ( r – g ) • The above formula can be used only when r > g

  46. Multi period Compounding / Discounting • The compounding / discounting may take place more than once a year i.e. monthly, quarterly, semi annually, etc.

  47. Multi period Compounding / Discounting • The compounding / discounting may take place more than once a year i.e. monthly, quarterly, semi annually, etc. • In that case an adjustment would be required in ‘r’ and ‘n’ in the formula of PV and FV, all else remaining the same

  48. Multi period Compounding / Discounting • The compounding / discounting may take place more than once a year i.e. monthly, quarterly, semi annually, etc. • In that case an adjustment would be required in ‘r’ and ‘n’ in the formula of PV and FV, all else remaining the same • r% p.a. : (r/x) % per period of compounding / discounting

  49. Multi period Compounding / Discounting • The compounding / discounting may take place more than once a year i.e. monthly, quarterly, semi annually, etc. • in that case an adjustment would be required in ‘r’ and ‘n’ in the formula of PV and FV, all else remaining the same • r% p.a. : (r/x) % per period of compounding / discounting • n : n x periods of compounding / discounting

  50. Multi period Compounding / Discounting • The compounding / discounting may take place more than once a year i.e. monthly, quarterly, semi annually, etc. • in that case an adjustment would be required in ‘r’ and ‘n’ in the formula of PV and FV, all else remaining the same • r% p.a. : (r/x) % per period of compounding / discounting • n : n x periods of compounding / discounting • Here ‘x’ are the number of times compounding / discounting takes place in a year

More Related