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Amity School of BusinessBBA,3rd Semester

Financial Management I

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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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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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Compounding periodDefinition -- is the frequency that interest is applied to the investment. Examples -- daily, monthly, or annually

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Discounting• The compound interest rate used for

discounting the cash flows is also called the discount rate.

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EFFECTIVE AND NOMINAL RATE OF INTEREST

• Effective interest rate > Nominal Interest rate

• Relationship between effective and nominal interest rate

• where, r is the effective rate of interestk is the nominal rate of interestm is the frequency of compounding per year.

1m

m

k1r

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Future value

• The term is the compound value factor (CVF) of a lump sum of Re 1, and it always has a value greater than 1 for positive i, indicating that

CVF increases as i and n increase.

= CVFn n,iF P

nr)1(

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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 1 2 n

A1 A2 A3FV(A3)+FV(A2)+FV(A1)

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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 2 n

FV(A)+

FV(A) +

FV(A)

A A A

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Sinking Fund Factor

It is the inverse of the FVIFA.

Sinking fund factor =

1r)(1

rn

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Present Value

• The present value of an amount expected at some time in future is calculated as:

• PV= ; where PVIF =

•

nr)(1

A

nr)(1

1

A

n0

PV(A)

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Present Value of Multiple Period

• 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

PV(A1) +

PV(A2)+

PV(A3)

0 1 2 n

A1 A2 An

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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

PV = A x ; where PVIFA=

rn

n

r)(1

1r)(1

rn

n

r)(1

1r)(1

A A A

0

PV(A)+PV(A)+

PV(A)

11 2 n

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Capital Recovery Factor

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 =

1r)(1

r)r(1n

n

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Present Value of Perpetuity• Perpetuity: An annuity with an infinite duration.

• Present value of a perpetuity=

where A is the constant annual payment.

Perpetuity

r

1AP

(Payment made at the end of each

period)

Immediate Perpetuity

Perpetuity Due

(Payment made at the beginning of

each period)

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Annuity Due

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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FV of an Annuity Due

• The FV of an annuity due is given by:

)1(),( rnrCVAFuntAnnuityAmoFV

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Present Value of an Annuity Due• The present value of an annuity is given by :

)1(),( rnrPVAFuntAnnuityAmoPV

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Deferred Annuities

• 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.

0 1 2 3 4 5

100 100 100 100 100

6 7

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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

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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.