Time value of money final

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 Concept of Time value of Money
 What is Time Line
 Concept of Future Value
 What is Simple interest and Compound Interest
 Using Financial Calculator or Excel functions
 What is Present value and Discounting
 Finding the discount rate
 Finding number of period
 Rule of 72
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 Dollar in hand today is worth more than a dollar promised
at sometime in the future.
 One earns interest on the dollar value at a later stage.
 Refer: http://www.transtutors.com/finance-
homework-help/time-value-of-money/ for more
details

 Present Value - An amount of money today, or the current
value of a future cash flow
 Future Value - An amount of money at some future time
period
 Period - A length of time (often a year, but can be a month,
week, day, hour, etc.)
 Interest Rate - The compensation paid to a lender (or
saver) for the use of funds expressed as a percentage for a
period (normally expressed as an annual rate)

 Time lines are used to help visualize what is happening in time value of
money problems.
 It is a graphical device used to clarify the timing of the cash flows for an
investment
 Cash flows are placed directly below the tick marks, and interest rates
are shown directly above the time line; unknown cash flows are
indicated by a symbol for the particular item that is missing.
 Each tick mark represents single period.
0 1 2 3 4 5

 Which of the following is incorrect?
o Each tick mark in time line represents single period.
o An amount of money at some future time period is Future value
o The compensation paid to a lender (or saver) for the use of funds
expressed as a percentage for a period (normally expressed as an
annual rate) is Interest.
o Cash flows are placed directly above the tick marks, and interest
rates are shown directly below the time line

 The value of dollar in future
 It refers to the amount of money an investment will grow to
over some period of time at some given interest rate.
 Refer: http://www.transtutors.com/homework-
help/corporate-finance/money-time-value/future-
value/ for more details

 Application of Simple Interest
 Suppose that you have an extra $100 today that you wish to invest for one year.
If you can earn 10% per year on your investment, how much will you have in one
year?
0 1 2 3 4 5
-100 ?

 This process of leaving your money and any accumulated interest
in an investment for more than one period, thereby reinvesting
the interest, is called compounding.
 Compounding the interest means earning interest on interest,
so we call the result compound interest.
 With simple interest, the interest is not reinvested, so interest
is earned each period only on the original principal.
 Refer: http://www.transtutors.com/finance-homework-help/time-
value-of-money/compounding-and-discounting-future-value-of-
single-flow.aspx for more details

 If the investment is done for single period, which interest
will have higher value:
o Simple Interest
o Compound Interest
o Both will give same value

 The expression (1 + r)t is sometimes called the future value
interest factor (or just future value factor ) for $1 invested
at r percent for t periods and can be abbreviated as FVIF(r,
t).

 Assume that Mr. M has deposited $25000 in savings
account which will earn an interest of 12% per annum for
10 years

 Future values depend critically on the assumed interest
rate, particularly for long-lived investments.

 The expression (1 + r)t is called:
o Future value factor
o Future value annuity factor
o Present value factor
o Future value interest factor

 PV - Present value
 FV - Future value
 Pmt - Per period payment amount
 NPER - Either the total number of cash flows or the number
of a specific period
 Rate - The interest rate per period
 Type = 1 is beginning of period and 0 is end of period

 =FV (rate,nper,pmt,pv,fv,[type])
 Example: Assume that Mr. M has deposited $25000 in
savings account which will earn an interest of 12% per
annum for 10 years.
 Using excel formula:
 =FV (12%,10,0,-25000,0,[0])

 Why in calculating Future value, through excel formula, we
consider the value as negative
o Because it is a Present money
o It is assumed to be a cash outflow
o It is assumed to be a cash inflow

 Present value is thus just the reverse of future value.
Instead of compounding the money forward into the future,
we discount it back to the present.
 It is referred as the present worth of money
 Refer: http://www.transtutors.com/homework-
help/corporate-finance/money-time-value/present-value/
for further reference

 The present value of $1 to be received t periods into the
future at a discount rate of r is:
 The quantity in brackets, 1/ (1 + r)t, is called as discount
factor, discount rate, or present value interest factor or PVIF

 Suppose that your five-year old son who will be attending
the college on his 18th
birthday. It is assumed that for
attending the college sum of 100000 will be required. If you
can earn 8% per year on your investments, how much do
you need to invest today to achieve your goal?

 =PV (rate,nper,pmt,fv,[type])
 Example: Suppose that your five-year old son who will be
attending the college on his 18th
birthday. It is assumed that for
attending the college sum of 100000 will be required. If you can
earn 8% per year on your investments, how much do you need to
invest today to achieve your goal?
 =PV (8%,13,0,100000,[0])
 =36769.79

 As the length of time until payment grows, present values
decline.

 Calculating the present value of a future cash flow to
determine its worth today is commonly called
discounted cash flow (DCF) valuation.
 Present value factor is just the reciprocal of (that is, 1
divided by) the future value factor

 With increase in period and interest
o Present value increases
o Present value decreases
o Present value remains constant

 The rate at which the amount is discounted to the present
value.
 Apply PV formula

 =Rate (nper,pmt,pv,fv,[type])
 Example: Assume that Mr. M has $2000 now which he
wants to deposit for 15 years. He needs $25000 in 15
years
 =Rate(15,0,-2000,25000)
 =18%

 The time at which the amount is will have a certain value
 Apply PV formula

 =NPER (rate,pmt,pv,fv,[type])
 Example: Assume that Mr. M has $2000 now and he needs
$2500o. The interest rate is 18%.
 =NPER (18%, 0,-2000,25000,0,[0])
 =15 years

 Duration in which the amount is doubled
 Example: What is the time taken to double the money, rate
of interest is 12%

 Same as rule 72 is used to double money, rule of 114 and
144 are also used.
 Rule of 114 is used to triple the money
 Rule of 144 is used to quadruple the money

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