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# Chapter 4

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### Chapter 4

1. 1. CHAPTER 4 CHAPTER 41TIME VALUE OF MONEY
2. 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. 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. 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. 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. 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. 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. 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. 9. DISCOUNTING  Present value interest factor (PVIFr,n) TIME VALUE OF MONEY 9 n r)( + = 1 1 CHAPTER 4
10. 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. 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. 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. 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. 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. 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. 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. 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. 18. FINDING EMI IN ADVANCE TIME VALUE OF MONEY 18 CHAPTER 4
19. 19. SEGREGATING EMIS TIME VALUE OF MONEY 19 CHAPTER 4