time value of money (module 2)

7/31/2019 Time Value of Money (Module 2)

1/17

Time Value of Money


2/17

A rupee today is more valuable than a

rupee a year hence. Why? Individuals prefer current consumption to future

consumption.

Capital can be employed productively to generatepositive returns.

In an inflationary period, a rupee today represents a

greater real purchasing power than a rupee a yearhence.


3/17

Time lines and NotationA time line shows the timing and the amount of each cash flow in a

cash stream. Period of time Point of timeCash flow can be positive (cash inflow) or negative (cash outflow)

Notations used:PV : Present ValueFVn: Future value n years henceCt : Cash flow occurring at the end of year t

A : A stream of constant periodic cash flow over a giventimer : Interest rate or discount rateg : Expected growth rate in cash flowsn : Number of periods over which the cash flows occur.


4/17

Future value of a Single amount

The process of investing money as well as reinvesting the interest

earned thereon is calledCompounding. Thefuture value or compounded value of an investment after n years

when the interest rate is rpercent :

FVn= PV(1+r)n

In case of Simple Interest, the investment grows as follows:FV = PV [ 1+ Number of years * Interest rate ]

Doubling Period:

Rule of 72

Rule of 69

Finding the growth rate


5/17

Present value of a Single amount

The process of discounting , used for calculating the present value

, is the inverse of compounding.PV = FVn[ 1 / (1+r)n]

Present Value of an uneven cash flow stream:

PVn= [At/ (1+r)t ]

Where, PVn = Present value of a cash flow stream

At = Cash flow occuring at the end of year t

r= Discount rate

n = Duration of the cash flow stream

n

t=1


6/17

Annuity

An annuity is a stream of constant cash flows occurring at regular

intervals of time. Regular/Deferred annuity (end of the period)

Annuity due (beginning of the period)

Future value of an annuity

The future value of an annuity :

FVAn= A [ (1+r)^n 1] / rWhere, FVAn = FV of an annuity which has a duration ofn periods

A = Constant periodic flow

r= interest rate per period

n = duration of the annuity


7/17

Present value of an annuity

The present value of an annuity:

PVAn = A [ {1- (1/1+r)^n} / r ]

Annuities Due

The cash flows of an annuity due occur one period earlier incomparison to the cash flows on an ordinary annuity.

Annuity due value = Ordinary annuity value* (1+r)


8/17


9/17

Risk and Return

Risk is the chance that the actual return differ from its expectedreturn.

The riskiness of a financial asset is measured in terms of the

riskiness of its cash flows. Diversification is the key to effective risk management.


10/17

Risk and Return of a Single Asset

Rate of return:

Annual income + Ending price - Beginning price

Beginning price

Probability distributions: The probability for a particular outcome is simply the chance thatthe specified outcome will occur.

The result of considering these outcomes and their probabilitiestogether is a probability distribution.


11/17

Expected rate of return

It is the weighted average of all possible returns multiplied by their

respective probabilities.

Variance of returns

It is the difference between an expected and actual result.

It is a measure of dispersion of a set of data points around theirmean value.

= pi(Ri- E(R))

Where, = Variance

Ri = Return for the ith possible outcome

pi= The probability associated with the ith possible outcome

E (R)= Expected return


12/17

Standard deviation of returns It is a statistic used as a measure of dispersion or variation in adistribution

It is equal to the square root of the arithmetic mean of the squares

of the deviations from the arithmetic mean. =()^1/2

Where, = Standard deviation


13/17

Risk and Return of a Portfolio

Portfolio:

A collection of investments all owned by the same individual ororganization.

These investments often include:

Stocks (which are investments in individual businesses) Bonds (which are investments in debt that are designed to earn

interest)

Mutual funds (which are essentially pools of money from many

investors that are invested by professionals or according toindices)


14/17

Expected return on a portfolio

Where, E(Rp) = The expected return on portfolio

wi= The proportion of portfolio invested in security i

E(Ri)= The expected return on security i

n

1iiip )R(Ew)R(E


15/17

Measurement of Market risk

The market risk of a security reflects its sensitivity to marketmovements.

Total risk= Unique risk + Market risk

Unique risk/Unsystematic risk/Diversifiable risk Market risk/Systematic risk/Non-diversifiable risk


16/17

The sensitivity of a security to market movements is calledbeta().

Calculation of BetaRjt= j + jRMt +ej

Where, Rjt = The return of security j in period t

j = The intercept term alpha

j = The regression coefficient , betaRMt = The retun on market portfolio in period t

ej = The random error term

j= Cov(Rj,RM) / 2M

Beta for market portfolio = 1


17/17

Thank you

time value of money (module 2)

Documents