THE TIME VALUE OF MONEY

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WHAT IS THE TIME VALUE OF MONEY.?

A dollar received today is worth more than a dollar received tomorrow

This is because a dollar received today can be invested to earn interest

The amount of interest earned depends on the rate of return that can be earned on the investment

Time value of money quantifies the value of a dollar through time

INTRODUCTION Understanding of Future Value and Present Value

of money is important for effective Financial Decision Making.

Every Organization tries to invest in New Ideas, New Projects, New Product or some Expansion and Modernization Activities.

It can be used to compare Investment alternatives and to solve problems involving Loans, Mortgages, Leases, Savings and Annuities.

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USES OF TIME VALUE OF MONEY

Time Value of Money or TVM is a

concept that is used in all aspects of

finance including:

Bond valuation

Stock valuation

Accept/ Reject decisions for project

management

Financial analysis of firms

And many others

SIMPLE INTEREST AND COMPOUND INTEREST

What is the difference between simple

interest and compound interest.?

Simple interest: Interest is earned only on the

principal amount.

Compound interest: Interest is earned on both the

principal and accumulated interest of prior periods.5

EXAMPLE

Suppose that you deposit Rs. 500 in

your savings account that earns 5%

annual interest, How much will you have

in your account after two years using

(a) simple interest and (b) compound

interest?

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Simple Interest

Interest earned = 5% of Rs. 500 = 500×.05 = Rs. 25 per year

Total interest earned = Rs. 25×2 = Rs.50

Balance in your savings account: = Principal + accumulated interest

= Rs. 500 + Rs. 50 = Rs. 550

Compound interest (assuming compounding once a year)

Interest earned in Year 1 = 5% of Rs. 500 = Rs. 25

Interest earned in Year 2 = 5% of (Rs. 500 + accumulated interest) = 5% of (Rs. 500 + 25) = 525 ×.05 = Rs. 26.25

Balance in your savings account: = Principal + interest earned = Rs. 500 + Rs. 25 + Rs.26.25 = Rs. 551.25 7

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TYPES OF TVM CALCULATIONS

There are many types of TVM

calculations

The basic types will be covered in this

review module and include:

Present Value of Single Amount

Future Value of Single Amount

Present and Future Value of Annuities

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BASIC RULES

The following are simple rules that you should always use no matter what type of TVM problem you are trying to solve:

1. Stop and think: Make sure you understand what the problem is asking. You will get the wrong answer if you are answering the wrong question.

2. Draw a representative timeline and label the cash flows and time periods appropriately.

3. Write out the complete formula using symbols first and then substitute the actual numbers to solve.

4. Check your answers using a calculator.

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FORMULAS

Common formulas that are used in TVM calculations:

Present Value Of Single Amount: PVIF= FV* 1 / (1+r)n Future Value Of Single Amount : FVIF = PV * (1+r)n

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FORMULAS (CONTINUED)

Present value of an annuity:

1PVIFA =FV * 1- (1+r)n

r

Future value of an annuity:

FVIFA = PV * (1+r)n -1 r

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VARIABLES

Where,

PV = Present Value

PVIFA = Present Value of an Annuity

FV = Future Value

FVIFA = Future Value of an Annuity

r = Rate of Return

n = Number of Time Periods

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PRESENT VALUE OF SINGLE AMOUNT

Present value calculations determine what the value of a cash flow received in the future would be worth today (time 0)

The process of finding a present value is called “Discounting”

The interest rate used to discount cash flows is generally called the Discount Rate

PRESENT VALUES

Present Value

Value today of a future cash

flow.

Discount Rate

Interest rate used to compute

present values of future cash flows.

Discount Factor

Present value of a Rs.1 future

payment.

PRESENT VALUES

nr)+(1

periodsn after Value Future=PV

PV=ValuePresent

PRESENT VALUE

What will be the present value of Rs. 500 to be received 10 years from today if the discount rate is 6%.?

PV = Rs. 500 {1/(1+.06)10} = Rs. 500 (1/1.791) = Rs. 500 (.558)

= Rs. 279

FUTURE VALUE OF SINGLE AMOUNT

- Future Value is the value at some future

time of a present amount of money, or a

series of payments, evaluated at a given

interest rate.

Future Value can be increased by:

• Increasing number of years of compounding

• Increasing the interest or discount rate

FUTURE VALUES

Example - FV

What is the future value of Rs. 100 if interest is compounded annually at a rate of 6% for 3 years.?

10.119.)06.1(100. 3 RsRsFV

FV = Rs. 100 *(1+r)

PRESENT VALUE V/S FUTURE VALUE

Present value factors are reciprocals of future value factors

Interest rates and future value are positively related

Interest rates and present value are negatively related

Time period and future value are positively related

Time period and present value are negatively related

TIME LINES

Show the timing of cash flows. Tick marks occur at the end of periods,

so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.

CF0 CF1 CF3CF2

0 1 2 3

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TYPES OF ANNUITIESTYPES OF ANNUITIES

Ordinary Annuity: Payments or receipts occur at the end of each period.

Annuity Due: Payments or receipts occur at the beginning of each period.

An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods.

PRESENT VALUE OF AN ANNUITY

Example: Mr. Alpesh deposit Rs. 2000 annually for 7

years and this deposit compounded at 10%. Find the Future Value Of Annuity.

FVIFA = PV x [(1+r)n -1/r] = 2000 [(1+0.10)7 -1 / 0.10] = 2000 [(1.1)7 – 1/ 0.10] = 2000 x 9.4872 = 18, 974

FUTURE VALUE OF AN ANNUITY

Example: Mr. Anil wants to purchase an apartment

costing Rs. 30 Lakes. His employer is willing to give loan at 10% for 5 years. Calculate amount of installment paid every year. PVIFA = A x [1- 1/(1+r)n/r]

30,00,000 = A x [1- 1/(1+0.10)5/0.10] 30,00,000 = A x [1- 1/(1.1)5/0.10]

30,00,000 = A x [3.791]A = 30,00,000/ 3.791

= 7,91,348

THANK YOU