Chapter+2_Time+Value+of+Money (1).pptx

Financial
Management
TIME VALUE OF MONEY
1
Copyright © 2013 by McGraw Hill Education ( India ) Pvt. Ltd.

• Money is the life line of all businesses.
• Theoretically, the value of money can increase or decrease with
time
• In real life it is found that the value of money invariably diminishes
with time.
Rationale (Basis of Time Value of Money)

Important concepts to solve time value of money problems are the
required rate of return and time line
Required Rate of Return:
– The required rate of return or the interest to be earned is the percentage
return which the firm must get on all its investments.
Time Line:
– A graphical depiction of the cash flows while solving a “time value of
money problem” is known as time line.
Important Basic Concepts to Solve Time Value
of Money Problems

• When the present value of money is to be converted to some future
time, it is called compounding.
• The value that is obtained in future is known as Future Value.
• Future value of a single cash flow can be found using the formula:
F = P X (1 + r)n
Where,
F = Future Value, P = Present Value, r = Rate of interest, n = Time
period
Future Value: Compounding

• Considering Re1 as Principal future values for different
combinations of ‘r’ and ‘n’ are known as future value interest factor,
FVIF(r, n).
FVIF can be found by referring to the Table given in book. Sample of
values is shown below. From Table FVIF (8%, 5), will be1.469.
•
Future Value Interest Factor (FVIF)

• A series of fixed cash flows at equal intervals is called an annuity.
• The lump sum amount at the end of the period is future value of an
annuity.
• Future value of annuity can be calculated using the formula or
through the use of future value interest factor annuity (FVIFA) table.
Future Value of an Annuity

The FVIFA are given in Table at the end of the book. Sample of values is
shown below. From Table FVIF (8%, 5), will be 5.867.
Sinking Fund:
• Sinking fund is an amount which the firm is required to pay on some
future date.
• Sinking fund factor (SFF) is the reciprocal of future value interest factor
of annuity. This factor when multiplied by future value gives the sinking
fund annuity.
Future Value Interest Factor of an Annuity and
Sinking Fund

• Let us take an example to understand the concept:
Future Value of a Series of Uneven Payments
(Cash Flows)

• Present value refers to the amount of money which is equivalent of a
certain amount on a future date.
• Discounting is the current equivalent of some future amount of money.
• The rate applicable for discounting is commonly known as ‘discounting
rate’, ‘cost of capital’ or ‘opportunity cost’.
• Present value of a single cash flow can be found using the formula:
Where,
F = Future Value, P = Present Value, r = Rate of interest, n = Time period
Present Value: Discounting

• Considering Re1 as Future Value, n as time period and r as rate of
interest, present values for different combinations of ‘r’ and ‘n’ using
are known as present value interest factor, PVIF(r, n).
Present Value Interest Factor (PVIF)

• The term, is present value interest factor of annuity
of 1, which we call PVIFA
• The annuity of an investment made today at a given rate of interest and
for a specified period is known as capital recovery.
•
Few Other examples of annuity include:
– Equated Monthly Instalments (EMIs)
– Pension Annuity
– Present Value of Future Perpetuities (Perpetual Annuities)
Present Value Interest Factor of an Annuity and
Capital Recovery

• Let us consider an example to illustrate the concept:
• XYZ company is undertaking 2 projects with some initial investment.
It expects to receive the following cash flows from the 2 projects:
a) Project 1: Rs 2,00,000 each year for the next 15 years
b) Project 2: Rs 6,00,000 for the first year, Rs 4,00,000 for the second
year, Rs 2,00,000 for the third year and Rs 1,50,000 each year for
the rest of 12 years
• Assuming 10% rate of interest, calculate the present value of the
cash inflows in 2 projects?
Present Value of Series of Uneven Cash Flows

Present Value of Series of Uneven Cash Flows

Present Value of Growing Annuity can be calculated using the formula
given below:
Present Value of Growing Perpetuity can be calculated using the
formula given below:
Where,
PV = Present Value, A = Annuity, g = Growth rate, r = Discount rate
Present Value of Growing Annuity and Growing
Perpetuity

• Annuity due refers to a series of payments for a given duration,
occurring at the beginning of each period.
• When the cash flows take place at the beginning of each period, we
work out the future value of such annuity due.
• When payments are made on the first day of each period the sum of
present value of all such values is called present value of annuity
due.
Value of Annuity Due

• Suppose you want to save for your child’s college expenses at
`1000 per year. Interest rate applicable is 5 per cent and time period
is18 years. Calculate the future value of annuity due.
Value of Annuity Due

• In continuous compounding, very short periods of time are
considered and compounding takes place regularly.
• Continuous Compounding:
Future value (F) = P * er * n
• In continuous discounting also very short periods of time are taken
into consideration and discounting is happening every elemental
time.
• Continuous Discounting:
Present value =
Continuous Compounding and Discounting

• For determining the time to double your money, you can use the
Rule of “72”
• According to this Rule, simply divide 72 by the interest rate (in per
cent form) and you can calculate the time.
• i.e., Doubling Period =
Rule of 72

Thank You

Chapter+2_Time+Value+of+Money (1).pptx

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