Final PPT - Time Value of Money

8/12/2019 Final PPT - Time Value of Money

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THE TIME VALUE OF

MONEY

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A Rupee received today is worth more than a Rupeereceived tomorrow

This is because a Rupee 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 Rupeethrough time

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Time Value of Money, or TVM, is a concept that isused in all aspects of finance including: Bond valuation

Stock valuation Accept/reject decisions for project management

Financial analysis of firms

And many others!

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There are many types of TVM calculations

We are Covering basic types

Present value of a lump sum Future value of a lump sum Present value of cash flow streams Future value of cash f low streams

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Common formulas that are used in TVM calculations:*

Present value of a lump sum:PV = PV = FVt / (1+r)

t

Future value of a lump sum:FVt= FVt= PV * (1+r)t

Variables

r = rate of return t = time period n = number of time periods PV = present value FV = future value

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Present value calculations determine what the valueof a cash flow received in the future would be worthtoday (time 0)

The process of finding a present value is calleddiscounting (hint: it gets smaller)

The interest rate used to discount cash flows is

generally called the discount rate

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How much would Rs.100 received five years from now beworth today if the current interest rate is 10%?

1. Draw a timeline

The arrow represents the flow of money and the

numbers under the timeline represent the time period.

Note that time period zero is today.7

0 1 2 3 4 5

Rs.100?i = 10%


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2. Write out the formula using symbols:

PV = FVt/ (1+r)t

FV = Rs. 100

n = 5i = 10%

PV = ?

3. Insert the appropriate numbers:

PV = 100 / (1 + 0.1)5

4. Solve the formula:

PV = Rs. 62.09

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You can think of future value as the opposite of presentvalue

Future value determines the amount that a sum ofmoney invested today will grow to in a given period of

time The process of finding a future value is called

compounding (hint: it gets larger)

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How much money will you have in 5 years if you invest Rs.100today at a 10% rate of return?

1. Draw a timeline

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0 1 2 3

Rs.100?

i = 10%

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2. Write out the formula using symbols:FVt= PV0* (1+r)

t

i = 10%

n = 5

PV = Rs.100FV = ?

3. Substitute the numbers into the formula:

FV = Rs.100 * (1+0.1)5

4. Solve for the future value:

FV = Rs.161.05

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In both of the examples, note that if you were toperform the opposite operation on the answers (i.e.,find the future value of Rs.62.09 or the present value ofRs.161.05) you will end up with your original investmentofRs.100.

This illustrates how present value and future valueconcepts are intertwined. In fact, they are the sameequation . . . Take PV = FVt / (1+r)

tand solve for FVt. You will get FVt= PV *

(1+r)t. As you get more comfortable with the formulas and

calculations, you may be able to do the calculations onyour calculator alone. Be sure you understand WHATyou are entering into each register and WHY.

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A cash flow stream is a finite set of payments that aninvestor will receive or invest over time.

The PV of the cash flow stream is equal to the sum of thepresent value of each of the individual cash flows in thestream.

The PV of a cash f low stream can also be found by takingthe FV of the cash flow stream and discounting the lumpsum at the appropriate discount rate for the appropriatenumber of periods.

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Joe made an investment that will pay Rs.100 the first year,Rs.300 the secondyear,Rs.500 the third year andRs.1000 the fourth year. If the interest rate is tenpercent, what is the present value of this cash flow stream?

Write out the formula using symbols:n

PV = S [FVt/ (1+r)t]

t=0

OR

PV = [FV1/(1+r)1

]+[FV2/(1+r)2

]+[FV3/(1+r)3

]+[FV4/(1+r)4

]

Substitute the appropriate numbers:

PV = [100/(1+.1)1]+[Rs.300/(1+.1)2]+[500/(1+.1)3]+[1000/(1.1)4]

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Solve for the present value:

PV = Rs.90.91 + Rs.247.93 + Rs.375.66 + Rs.683.01

PV = Rs.1397.51

Check using a calculator:Make sure to use the appropriate rate of return, number of periods, andfuture value for each of the calculations. To illustrate, for the first cash flow,you should enter FV=100, n=1, i=10, PMT=0, PV=?. Note that you will haveto do four separate calculations.

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The future value of a cash flow stream is equal to the sumof the future values of the individual cash flows.

The FV of a cash flow stream can also be found by takingthe PV of that same stream and finding the FV of that lumpsum using the appropriate rate of return for the appropriatenumber of periods.

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Assume Joe has the same cash flow stream from his investment butwants to know what it will be worth at the end of the fourth year

Write out the formula using symbols

n

FV = S [CFt* (1+r)n-t]

t=0

OR

FV = [CF1*(1+r)n-1]+[CF2*(1+r)

n-2]+[CF3*(1+r)n-3]+[CF4*(1+r)

n-4]

Substitute the appropriate numbers:

FV = [$100*(1+.1)4-1]+[$300*(1+.1)4-2]+[$500*(1+.1)4-3] +[$1000*(1+.1)4-4]


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Solve for the Future Value:

FV = $133.10 + $363.00 + $550.00 + $1000

FV = $2046.10

Check using the calculator:Make sure to use the appropriate interest rate, time period andpresent value for each of the four cash flows. To illustrate, for thefirst cash flow, you should enter PV=100, n=3, i=10, PMT=0, FV=?.Note that you will have to do four separate calculations.

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THANK YOU.

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Final PPT - Time Value of Money