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- 1. CHAPTER 4 CHAPTER 41TIME VALUE OF MONEY
- 2. CONTENTS Time Value of Money- An introduction Compounding Discounting Annuity Future Value of Annuity Present Value of Annuity Continuous Compounding & Discounting Effective rate of Interest Equated Monthly Instalments TIME VALUE OF MONEY 2 CHAPTER 4
- 3. TIME VALUE OF MONEY (TVM)-AN INTRODUCTION Value of money varies with time. Not only is the amount of money important, equally important is the time when is it received or paid. One of the most important concepts used in financial decision- making. Applications include: o Personal finance o Capital budgeting o Valuation o Derivatives and risk management. TIME VALUE OF MONEY 3 CHAPTER 4
- 4. TIME VALUE OF MONEY AN INTRODUCTION Value of money varies with time due to: • Presence of inflation • Preference for current consumption • Investment opportunities available Does not account for the investment risks. Present cash flows are compounded to find their Future value. Future Cash flows are discounted to arrive at their Present value. TIME VALUE OF MONEY 4 CHAPTER 4
- 5. COMPOUNDING Application of interest over interest is known as compounding. Present cash flows, P are compounded to their future values, F for an estimated time period, n at an expected rate of interest, r. Future value interest factor (FVIFr,n) TIME VALUE OF MONEY 5 r)P x (F n += 1 n r)( += 1 CHAPTER 4
- 6. COMPOUNDING AND RATE Effect of compounding increases with the increase in interest rates. TIME VALUE OF MONEY 6 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 1 2 3 4 5 6 7 8 9 Time (yrs) FutureValue at 5% at 10% at 15% at 20% at 25% CHAPTER 4
- 7. COMPOUNDING AND TIME Effect of compounding increases as the time lengthens. TIME VALUE OF MONEY 7 (Rs. 1 at 12%) 1.120 1.254 1.405 1.574 1.762 1.974 2.211 2.476 2.773 3.106 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 2 3 4 5 6 7 8 9 Time (yrs) FutureValue CHAPTER 4
- 8. DISCOUNTING Value of the money received or paid later is lesser than what it is today. The process of reduction in value eliminating the interest that could have accrued is known as discounting. Future cash flows (F) are discounted to their present values (P) for an estimated time period (n) at an expected rate of interest (r). TIME VALUE OF MONEY 8 n r)( FP + ×= 1 1 CHAPTER 4
- 9. DISCOUNTING Present value interest factor (PVIFr,n) TIME VALUE OF MONEY 9 n r)( + = 1 1 CHAPTER 4
- 10. DISCOUNTING AND RATE Severity of discounting increases with the increase in the rate of discounting. TIME VALUE OF MONEY 10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1 2 3 4 5 6 7 8 9 Time (yrs) PresentValue at 5% at 10% at 15% at 20% at 25% CHAPTER 4
- 11. DISCOUNTING AND TIME Effect of discounting increases as the time lengthens. TIME VALUE OF MONEY 11 (Rs. 1 at 12%) 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1 2 3 4 5 6 7 8 9 Time (yrs) PresentValue CHAPTER 4
- 12. ANNUITY Equal amounts of cash flows spaced uniformly over time, normally a year. Examples include: • Premium of insurance policy • EMI of a loan • Deposits to a recurring deposit account. TIME VALUE OF MONEY 12 CHAPTER 4
- 13. FUTURE VALUE OF ANNUITY Future value of annuity (FVAr,n) depends upon: • Amount of cash flow (i.e. annuity) • Rate of interest per period • Number of periods. Future value interest factor for annuity TIME VALUE OF MONEY 13 r r)( AnnuityFVA n r,n 11 −+ ×= r r)( FVIFA n r,n 11 −+ = CHAPTER 4
- 14. PRESENT VALUE OF ANNUITY Present value of annuity (PVA r,n) like its future value depends upon: • Amount of cash flow (i.e. annuity) • Rate of interest per period • Number of periods. Present value interest factor for annuity TIME VALUE OF MONEY 14 n n nr rr r AnnuityPVA )1( 1)1( , + −+ ×= n n nr rr r PVIFA )1( 1)1( , + −+ = CHAPTER 4
- 15. CONTINUOUS COMPOUNDING Value of compounding or discounting depends upon its frequency. The value rises/falls exponentially in case of continuous compounding. TIME VALUE OF MONEY 15 -rt rt rt = F x e e =F xe, Pesent Valu eue, F=P xFuture Val 1 Pr CHAPTER 4
- 16. EFFECTIVE RATE OF INTEREST The effective rate may be found for a given annual rate (r)and frequency of compounding (m) in a year. TIME VALUE OF MONEY 16 11= − + m m r ateInterest REffective CHAPTER 4
- 17. EQUATED MONTHLY INSTALMENTS Loans are repayable normally in Equated Monthly Installments (EMIs). EMIs are a form of annuity. Each EMI can be bifurcated into interest and principal repayment components. The interest component of EMIs declines while the principal component increases with successive EMIs. TIME VALUE OF MONEY 17 CHAPTER 4
- 18. FINDING EMI IN ADVANCE TIME VALUE OF MONEY 18 CHAPTER 4
- 19. SEGREGATING EMIS TIME VALUE OF MONEY 19 CHAPTER 4

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