Time Value of FM

8/3/2019 Time Value of FM

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TimeTime

Value ValueOf Of

MoneyMoney

TimeTime

Value ValueOf Of

MoneyMoney



The value of money received today is

different from the value of money received

after some time in future The reasons for this are

1. Inflation

2. Risk

3. Personal consumption preference

4. Investment opportunities

The value of money received today is

different from the value of money received

after some time in future The reasons for this are

1. Inflation

2. Risk

3. Personal consumption preference

4. Investment opportunities



PresentPresent Value Value is the current value of a future amount of money, or aseries of payments, evaluated at a given interest rate.

Future Value is the value at some future time of a present amount of money.

Compounding is the process of finding the future value of the presentstream of cash flows

Discounting is the process of finding out the present value of thefuture stream of cash flows.

The principal is the amount borrowed.

Interest is the compensation for the opportunity cost of funds and theuncertainty of repayment of the amount borrowed; that is, itrepresents both the price of time and the price of risk. The price of time is compensation for the opportunity cost of funds and the price of risk is compensation for bearing risk.



Compound InterestCompound Interest

Interest paid (earned) on any previous interest

earned, as well as on the principal borrowed(lent).

Simple InterestSimple Interest

Interest paid (earned) on only the original

amount, or principal, borrowed (lent).



If interest for one period is added to the principal

for the next period, it is called compound interest

The time period for compounding the interest may

be annual, semiannual or any other regularperiod of time.

A= P(1+i)n

A = amount at the end of ¶n· period

i= rate of interest per payment period

n = no. of payment periods



We will use the ´́RuleRule--of of--7272µ.µ.

Quick! How long does it take to double Rs

5,000 at a compound rate of 12% peryear (approx.)?



Approx. Years to Double = 7272 / i%

7272 / 12% = 6 Years6 Years

[Actual Time is 6.12 Years]

Quick! How long does it take to double Rs

5,000 at a compound rate of 12% per

year (approx.)?



General Formula:

FVn = PVPV00(1 + [i/m])mn

n: Number of Years

m: Compounding Periods per Year

i: Annual Interest Rate

FVn,m: FV at the end of Year nPVPV00: PV of the Cash Flow today



Sinking fund is a fund, which is created out of fixed payments

each period to accumulate to a future sum after a specified

period.

Companies generally create sinking fund to retire bonds on

maturity.

Fn = A * CVIFA n,i

A = Fn * 1/CVIFAn,i

A = Fn * SFFn,i

SFF n,i = sinking fund factor



Translating a value to the present is referred to as discounting.

Present value = PV = FV / (1 + i) n

Where:

PV = present value (today's value),

FV = future value (a value or cash flow sometime in the future),

i = interest rate per period, and

n = number of compounding periods

And [(1 + i) n] is the compound factor.



An An Annuity Annuity represents a series of equal payments (or

receipts) occurring over a specified number of

equidistant periods.

The word annuity in a broader sense includes payment

which can be annual, semiannual, quarterly or any

other fixed length of time.

It does not necessarily mean payment taken to be one

year.



Ordinary AnnuityOrdinary Annuity: Payments or receipts occurat the end of each period.

Annuity Due Annuity Due: Payments or receipts occur at

the beginning of each period.



Student Loan Payments

Car Loan Payments Insurance Premiums

Mortgage Payments

Retirement Savings



0 1 2 3

Rs100 Rs100 Rs 100

(Ordinary Annuity)

EndEnd of

Period 1

EndEnd of

Period 2

Today

EndEnd of

Period 3



0 1 2 3

Rs100 Rs100 Rs100

(Annuity Due)

BeginningBeginning of

Period 1


Period 2


Period 3



Effective Annual Interest Rate

The actual rate of interest earned (paid) after

adjusting the nominal rate for factors suchas the number of compounding periods per

year.

(1 + [ i / m ] )m

- 1



Perpetuity is a cash flow without a fixed time horizon.

For example if someone were promised that they would receive a cash

flow of Rs400 per year until they died, that would be perpetuity.

PV of Perpetuity Formula

PV = C

R

C = cash payment

R = interest rate

Example

If someone were promised a cash flow of Rs 400 per year until they died

and they could earn 6% on other investments of similar quality, in

present value terms the perpetuity would be worth Rs 6,666.67. (Rs 400 /

.06 = Rs 6,666.67)

Time Value of FM

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