Time Value of Money

Time Value of Money (TVM) 1. Value of Money a function of Time Money received today has different value at future point of time. Similarly money proposed to be received at a future time has different value at present time. The rate of Compound Interest' is used to express the Time Value of money.

2. Two basic concepts involved in TVM : 2.1 Future Value (FV) : Future value is the value at some future time of a present single amount of money or a series of amounts (cash flow) determined based on a given interest rate (Principle of Compounding) 2.2 Present Value (PV): Present value is the current value of a future single amount of money or a series of amounts

PRESENT VALUE INTEREST FACTOR(PVIFin)

FUTURE VALUE INTEREST FACTOR(FVIFin)

(cash flow) determined based on a given interest rate (Principle of discounting).

CONCEPT OF FUTURE VALUE(COMPOUNDING)

4.00

i = 15% 3.50

Compounding for future value at 15% per year

3.00 2.50 i = 10% 2.00 i = 5%

1.50 0 1

2

3

4

5

0.90

6

7

8

9

10 11 12 13 14 15

PERIOD(n)(Years)

0.80 0.70

i = 5%

0.60 0.50 i = 10%

0.40 0.30 0.20

Discounting for present value at 15% per year

i = 15%

0.10 0.00

CONCEPT OF PRESENT VALUE(DISCOUNTING)

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Years

3. Applications of Time Value of Money a) All Financial decisions of firms are based on TVM. b) Individual investment decisions (e.g. Retirement Plans) c) Lending decisions (e.g. Housing loans repayments spread over years) d) Selection of alternatives between projects whose initial investment and period of yield differ where common basis are to be arrived e) Life cycle cost calculations (V.E. applications) (Machineries, Systems etc.)

4.1 Future Value (Compound Value) of a single present amount FVn = PV(1+i)n …………………..equation (1) FVn = PV(FVIFin) FVn

= Future Value after n years

PV

= Present Value

FVIFin = Future Value factor at i% for n periods It is assumed that compounding done once in a year i = 12%

7 i = 10% 6 5 4 FVIFin

i = 6% 3 2 i = 0%

1 0 2

4

6

8

10

12

14

16

18

20

Years

Approximate doubling period in years = 72 i Refer Standard Tables for F V I F for various combinations of period ( n ) and interest rate (i).

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4.2 Future Value of a Single Present Amount

if compounding done more number of

times in a year If m is number of times compounding done in a year, FVn= PV(1+i/m)m x n e.g. If compounding done semi-annually FVn = PV(1+i/2)2n

Effective Rate of Interest (i) Effective rate of interest is the annually compounded rate of interest which is equivalent to an annual interest rate compounded more than once in a year i 0 = (1+i/m)m – 1 e.g. If 8% is the nominal annual interest rate and compounding done quarterly (m=4) i 0 = (1+0.08/4)4 – 1 = 0.0824 = 8.24% >8%

i 0 = 12.68%(monthly compounded) i 0 = 12.63%(half yearly) i 0 = 12.74%(daily compounded) To compare alternate investments having different compounding periods it is necessary to calculate the effective annual interest rates.

5. Present Value(discounted value) of a single future amount From equation(1) FVn = PV(1+i)n PV = FVn[1/(1+i)n] PV = FVn(PVFin) PV

= Present Value

FVn

= Future amount after n years

PVIFin = Present Value interest factor with interest rate i for n periods

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PVIFin

1.25 1.00

i = 0%

0.75

i = 6%

0.50

i = 10%

0.25

i = 14%

0.00 2

4

6

8

10

Period

Present Value of Rs. 1 proposed to be received after 5 years at a discounting rate of 10% is about 50 paise.

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