The document discusses concepts related to time value of money including compounding, discounting, future value, and present value. It defines key terms like effective interest rate, nominal interest rate, compounding period, and sinking fund factor. Methods are presented for calculating future value and present value of single amounts, annuities, perpetuities, annuities due, and deferred annuities. Reasons for preference of current money like future uncertainty and reinvestment opportunities are also mentioned.

1. Amity School of Business
Amity School of Business
BBA,3rd Semester
Financial Management I
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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.
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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.
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4. Amity School of Business
Compounding period
Definition -- is the frequency that interest is applied to the
investment.
Examples -- daily, monthly, or annually
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5. Amity School of Business
Discounting
• The compound interest rate used for discounting the
cash flows is also called the discount rate.
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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.
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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
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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)
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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)
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10. Sinking Fund Factor
Amity School of Business
 It is the inverse of the FVIFA.
 Sinking fund factor =
r
n
(1 +r) −1
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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)
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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)
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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)
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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
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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)
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16. Annuity Due
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Definition: If the cash flow occurs at the beginning of the each
year (nth). Such a situation is called Annuity due.
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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 )
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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 )
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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
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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. 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.