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# 4dfcf copy of time value of money (1)

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• Annuities are very common:
Rent
Mortgage payments
Car payment
Pension income
• ### 4dfcf copy of time value of money (1)

1. 1. Amity School of Business Amity School of Business BBA,3rd Semester Financial Management I 1
2. 2. Amity School of Business Time Value of money The concept. Process of Compounding and Discounting.  Future Value of a Single amount.  Future Value of an Annuity.  Present Value of a Single Amount. Present Value of an Annuity. 2
3. 3. Amity School of Business Reasons for preference of current money • Future uncertainty : • Preference for present consumption: • Reinvestment opportunities: Time value for the money is the rate of return which the firm can earn by reinvesting its present money. This rate of return can be expressed in terms of the required rate of return to make equal the worth of money of two different time period. 3
4. 4. Amity School of Business Compounding period Definition -- is the frequency that interest is applied to the investment. Examples -- daily, monthly, or annually 4
5. 5. Amity School of Business Discounting • The compound interest rate used for discounting the cash flows is also called the discount rate. 5
6. 6. Amity School of Business EFFECTIVE AND NOMINAL RATE OF INTEREST • Effective interest rate > Nominal Interest rate • Relationship between effective and nominal interest rate ( ) k m r = 1+ −1 m • where, r is the effective rate of interest k is the nominal rate of interest m is the frequency of compounding per year. 6
7. 7. Future value Amity School of Business r • The term (1 + ) is the compound value factor (CVF) of a lump sum of Re 1, and it always has a value greater than 1 for n positive i, indicating that CVF increases as i and n increase. Fn =P × CVFn,i 7
8. 8. Amity School of Business Future Value of Multiple Flows • The future value of multiple flows can be computed as • FVn = A1 (1+r)n + A2 (1+r)n-1 +A3(1+r)n-2 • where A1 , A2 and A3 are the investments at the beginning of the • year 1, 2 …..and 3 respectively. • FVn : Future value of the investment at the end of n years 0 A1 1 n 2 A2 A3 FV(A3)+ FV(A2)+ FV(A1) 8
9. 9. Amity School of Business Future value of an annuity • Annuity is a pattern of cash flows that are equal in each year. • Future value of an annuity: FVAn= A (1+r)n + A (1+r)n-1 +…....+A = A where FVIFA = [(1+r)n- 1]/r 0 1 A A n 2 A FV(A)+ FV(A) + FV(A) 9
10. 10. Sinking Fund Factor Amity School of Business  It is the inverse of the FVIFA.  Sinking fund factor = r n (1 +r) −1 10
11. 11. Present Value Amity School of Business • The present value of an amount expected at some time in future is calculated as: 1 A • PV= ; where PVIF = n (1 + r) n • (1 + r) n 0 A PV(A) 11
12. 12. Present Value of Multiple Period Amity School of Business • If A1, A2, An are the cash flows occurring at the end of the time period 1,2 and n respectively then their present value can be computed as: • PV = A1/(1+r) + A2/(1+r)2 +........+An/(1+r)n 1 0 A1 2 A2 n An PV(A1) + PV(A2)+ PV(A3) 12
13. 13. Amity School of Business Present value of an Annuity • The present value of an annuity can be computed as: PV= A/(1+r) + A/(1+r)2 +……+ A/(1+r)n n (1 + r) −1 (1 + r) −1 PV = A x n ; where PVIFA= n (1 + r) r (1 + r) r n 1 1 0 A PV(A)+ PV(A)+ 2 A n A PV(A) 13
14. 14. Capital Recovery Factor School of Business Amity Capital Recovery Factor helps in computing:  Loan installment to liquidate a loan.  Amount that can be withdrawn periodically when a particular amount is invested now. The Capital Recovery Factor is the inverse of PVIFA • Capital Recovery Factor = r(1 +r) n (1 +r) −1 n 14
15. 15. Amity School of Business Present Value of Perpetuity • Perpetuity: An annuity with an infinite duration. • Present value of a perpetuity= 1 P∞ =A × r where A is the constant annual payment. Immediate Perpetuity Perpetuity (Payment made at the end of each period) Perpetuity Due (Payment made at the beginning of each period) 15
16. 16. Annuity Due Amity School of Business Definition: If the cash flow occurs at the beginning of the each year (nth). Such a situation is called Annuity due. 16
17. 17. FV of an Annuity Due School of Business Amity • The FV of an annuity due is given by: FV = AnnuityAmount × CVAF (r , n) × (1 + r ) 17
18. 18. Amity School of Business Present Value of an Annuity Due • The present value of an annuity is given by : PV = AnnuityAmount × PVAF (r , n) × (1 + r ) 18
19. 19. Deferred Annuities Amity School of Business • Definition: A deferred annuity is the same as any other annuity, except that its payments do not begin until some later period. • The timeline shows a five-period deferred annuity. 100 0 1 2 100 100 100 100 3 4 5 6 7 19
20. 20. Amity School of Business PV of a Deferred Annuity  We can find the present value of a deferred annuity in the same way as any other annuity, with an extra step required.  Before we can do this howe ver, there is an important rule to understand: When using the PVA equation, the resulting PV is always one period before the first payment occurs
21. 21. Amity School of Business FV of a Deferred Annuity • The future value of a deferred annuity is calculated in exactly the same way as any other annuity • There are no extra steps at all.