### MEANING OF TIME VALUE OF MONEY:

A rupee available today is worth more than a rupee available at a future date. This is because a rupee today can be invested to earn a return. There is an old saying “A bird in the hand is worth two in the bush “, in a way this expression refers to the time value of birds i.e. having a single bird in the hand is worth more than the chance of catching two birds in the future.

Also, this expression reflects two central concepts in finance the investors require to be compensated for both risk bearing and the time value of money. These two principles lie at the heart of the financial decision concepts. Knowledge of time value of money is essential for the managers to take many vital decisions on investments, financing and dividends involving cash flows at different points of time and even in capital budgeting. The preference of money now, as compared to future money is known as “Time preference of money”.

There is an old saying “A bird in the hand is worth two in the bush “, in a way this expression refers to the time value of birds i.e. having a single bird in the hand is worth more than the chance of catching two birds in the future. Also, this expression reflects two central concepts in finance the investors require to be compensated for both risk bearing and the time value of money. These two principles lie at the heart of the financial decision concepts. Knowledge of time value of money is essential for the managers to take many vital decisions on investments, financing and dividends involving cash flows at different points of time and even in capital budgeting. The preference of money now, as compared to future money is known as “Time preference of money”.

Money loses its value over time which makes it more desirable to have it now rather than later, There are four important reasons for time preference of money today over tomorrow:

Also, this expression reflects two central concepts in finance the investors require to be compensated for both risk bearing and the time value of money. These two principles lie at the heart of the financial decision concepts. Knowledge of time value of money is essential for the managers to take many vital decisions on investments, financing and dividends involving cash flows at different points of time and even in capital budgeting. The preference of money now, as compared to future money is known as “Time preference of money”.

There is an old saying “A bird in the hand is worth two in the bush “, in a way this expression refers to the time value of birds i.e. having a single bird in the hand is worth more than the chance of catching two birds in the future. Also, this expression reflects two central concepts in finance the investors require to be compensated for both risk bearing and the time value of money. These two principles lie at the heart of the financial decision concepts. Knowledge of time value of money is essential for the managers to take many vital decisions on investments, financing and dividends involving cash flows at different points of time and even in capital budgeting. The preference of money now, as compared to future money is known as “Time preference of money”.

### REASONS FOR TIME PREFERENCE OF MONEY NOW OVER FUTURE:

**Inflation erodes the time value of money, a rupee today has more purchasing power than a rupee one year later. Suppose present petrol price is Rs.40 per litre today, 25 litres of petrol can be purchased with Rs.1000 in hand now, if the price of the petrol increases to Rs.50 per litre in a year’s time, only 20 litres can be purchased with Rs.1000 in hand at that time. So inflation acts as an important component in time value.**

__a) Inflation –__**there are both financial and non-financial risk involved over time. Further, there is uncertainty, about the receipt of money in future. The longer the period of returns, the greater is the risk.**

__b).Risk premium:__**It is the annual income from an investment expressed as a proportion (usually a percentage) of the original investment, these acts as the important part in decision making.**

__c).The rate of return:__**Most of the persons and the companies have a preference for present money because of availabilities of opportunities of investment for additional cash flows. Example: An individual offered Rs. 1000 now or Rs. 1000 one year later, would prefer Rs.1000 now as he can invest it now and earn interest on it.**

__d).Investment opportunities:__## METHODS OF ANALYSIS OF TIME VALUE OF MONEY:

The concept of time value of money helps in arriving at the comparable value of the different rupee amounts arising at different points of time into equivalent values at a particular point of time (present or future) this can be done by either

__I) Compounding (or)__

__II) Discounting__

###
➢**COMPOUNDING:**

The compounding concept refers to the ascertainment of future value of money. It’s the process of determining the future value of an investment made today and/or the future value of a series of equal payments made over time (periodic payments). It is sImilar to the concept of compound interest, wherein the interest earned in the preceding year is reinvested at the prevailing rate of interest for the remaining period. The compounding interest technique to find out FV (future value) of a present money under the following heads:#### A).Compounding of Interest Over ‘n” Years:

The interest on investments generally spread over a number of years compounded annually to calculate the FV/ maturity value of the investment.

→Future value= P (1+R)n

→Where P = principal (the amount invested in the beginning)

→R = Rate of interest

→N = No. of years

Compounding with this formula can be very time consuming if the number of years becomes large say 10 or 15 years or more, then “compound value table’ can be used the table gives the compound value of Rs. 1 after ‘n’ years’ for a wide range of combination of R and n.

**FORMULA:**→Future value= P (1+R)n

→Where P = principal (the amount invested in the beginning)

→R = Rate of interest

→N = No. of years

Compounding with this formula can be very time consuming if the number of years becomes large say 10 or 15 years or more, then “compound value table’ can be used the table gives the compound value of Rs. 1 after ‘n’ years’ for a wide range of combination of R and n.

#### B).Multiple Compounding Periods:

In the above case, compounding was done on yearly basis but not necessary that compounding period stays same, it can be every half yearly or quarterly .the interest rate and time period has to be adjusted accordingly. Suppose if every half yearly interest compounded then the interest rate remains same but the interest rate amount of any 6 months will be compounded in next 6 months and so on and the period of interest increases to 2 for a year. Further, more frequently the interest is compounded, it in turns earns further higher interest.

→FV=P(1+R/m)nm

→P = Principal amount

→R = rate of interest

→n=no. of years

→m=frequency of compounding

**FORMULA:**→FV=P(1+R/m)nm

→P = Principal amount

→R = rate of interest

→n=no. of years

→m=frequency of compounding

#### C).Effective Rate of Interest:

The effective rate of interest is the annually compounded rate of interest that is equivalent to an annual interest rate compounded more than once per year. This is very much useful in financial decision making. For example, if ain an investment A gets 10%, compounded monthly, and an investment B pays 10.1% compounded semi-annually, the effective annual interest rate can be used to determine which investment will actually pay more over the course of the year.

→ERI= (1+R/m)n-1

→Where ERI stands for effective rate of interest

→R=rate of interest

→m=frequency of compounding

**FORMULA:**→ERI= (1+R/m)n-1

→Where ERI stands for effective rate of interest

→R=rate of interest

→m=frequency of compounding

__In the above example:__Effective annual interest rate = (1 + (nominal rate / number of compounding periods)) ^ (number of compounding periods) - 1

For investment A, this would be: 10.47% = (1 + (10% / 12)) ^ 12 - 1

And for investment B, it would be: 10.36% = (1 + (10.1% / 2)) ^ 2 - 1

Here B have high nominal rate still gets lower interest compared to A , the main reason being frequency is more in A.

#### D).Doubling Period:

it becomes necessary sometimes to know when the initial investment could double when interest rates ruled high in the nineties, the investment made in Indira Vikas Patra doubled in 5 years. The rule of thumb methods known as RULE72 and RULE OF 69 are used to know the doubling period.

→RULE OF 72:

→Doubling period= 72/rate of interest

→RULE OF 69: rule of 89 is a refinement over rule 72, and provides a more accurate result.

→Doubling period= 0.35+69/rate of interest

**FORMULA:**→RULE OF 72:

→Doubling period= 72/rate of interest

→RULE OF 69: rule of 89 is a refinement over rule 72, and provides a more accurate result.

→Doubling period= 0.35+69/rate of interest

#### E).Compound Value of An Annuity:

An annuity is a series of equal payments at regular intervals. Examples of annuities are regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments and pension payments. Annuities are classified by the frequency of payment dates. For example a deposit of Rs.5000 each year is to be made at the end of each of the next 3 years from today. This may be referred to as an annuity of deposit of Rs.5000 for 3years. In the case of an annuity, each cash flow is to be compounded to ascertain FV.

is an annuity where the regular payment is made at the end of the successive time periods. Suppose Mr X makes invests Rs.10000 every month end in his RD(recurring deposit) account for 2 years is an example of an ordinary annuity. It can be weekly, monthly, quarterly, semi-annually or annually basis. Here Mr.X will make payments, for example, January month in ending or the next month beginning.

ii).An ANNUITY DUE is an annuity where the regular payment Is made at the beginning of the month, say rent of any place has to be paid at beginning of the month.

generally speaking, ordinary annuities are appropriate for making payments and annuities due for receipts.

#### Annuities are two types

__I) An Ordinary annuity:__is an annuity where the regular payment is made at the end of the successive time periods. Suppose Mr X makes invests Rs.10000 every month end in his RD(recurring deposit) account for 2 years is an example of an ordinary annuity. It can be weekly, monthly, quarterly, semi-annually or annually basis. Here Mr.X will make payments, for example, January month in ending or the next month beginning.

ii).An ANNUITY DUE is an annuity where the regular payment Is made at the beginning of the month, say rent of any place has to be paid at beginning of the month.

generally speaking, ordinary annuities are appropriate for making payments and annuities due for receipts.

**FORMULAS FOR ANNUITIES:**Or FV=PV(1+R)n

→PV =present value of annuity

→P=principal

→R=rate of interest

→n=number of interest.

That’s all under the compounding topic friends, in the next two parts we will provide you the method of discounting followed by some examples and exercise questions till then keep updated with formulas (don’t mug up just understand).

*JAIIB Classes by Ramandeep Singh - Get details here*