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THE TIME VALUE OF

MONEY

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Refers to the appreciation and

depreciation of the value of a

capital asset over time

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Appreciation is the increase in value of a

property overtime due to inflation,

supply and demand, capitalimprovements and others.

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Depreciation refers to a physical

assets loss of value over time.

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Methods for Determining the depreciation

of an Asset:

Straight-line depreciation- assumes that the

asset will lose an equal amount of value each

year.

To calculate: purchase price

salvage value

estimated useful life

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For example, a washing machine that is

bought for $750 and expected to be worth

$210 after 15 years of use will depreciate $36

annually.

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Unit depreciation -this method

involves how much the asset is

used over a period of time

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For example, as the owner of a parcel delivery

company, you decide to purchase a delivery truckon 1/1/2005 for $50,000. After some calculationsbased on maintenance and repair factors youdetermine that for every mile the truck is driven itwill cost 10 cents in maintenance and repair. By12/31/2005 the truck has been driven 20,000 miles.To calculate the truck's depreciation that year,multiply 10 cents/mile by 20,000 miles. After oneyear, the truck that you bought for $50,000 hasdepreciated by $2,000. The next year you drive thetruck only 10,000 miles so it depreciates only$1,000 that year.

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Devaluation refers to a decline in the

value of a currency in relation to

another, usually brought about bythe actions of a central bank or

monetary authority.

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Market-driven devaluation, by contrast,is often the formal recognition by a

government, frequently during a

monetary crisis, that the value of itscurrency relative to major world

currencies has already depreciated

through trading in the foreign exchange

markets.

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Basic terminology:

Terminal value/ future value- how much what

you got now grows to when compounded at a

given rate

In determining the future value, we measure

the value of an amount that is allowed to

grow at a given interest rate over a period of

time

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Five factors to a TVM Calculation:

1. Number of time periods involved

2. Annual interest rate

3. Present value4. Payments

5. Future value

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Assume an investor has $1000 and wishes toknow its worth after 4 years if it grows at 10%

per year.

1st year $1000x 1.10=$1,100

2nd $1100x 1.10=$1,210

3rd $1210x 1.10=$1,331

4th

$1331x 1.10=$1,464

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FV= PV (1 + i )N

Where:

FV = Future Value

PV = Present Value

i = the interest rate per period

n= the number of compounding periods

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FV= PV (1 + i )N

=$1,000 ( 1+.10) 4

=$1,000(1.464)=$1,464

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Determine Future Value Compounded AnnuallyWhat is the future value of $34 in 5 years if the interest

rate is 5%? (i=.05)

FV= PV ( 1 + i ) N

FV= $ 34 ( 1+ .05 ) 5FV= $ 34 (1.2762815)

FV= $43.39

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Determine Future Value Compounded MonthlyWhat is the future value of $34 in 5 years if the interest rate is

5%? (i equals .05 divided by 12, because there are 12 months peryear. So 0.05/12=.004166, so i=.004166)

FV= PV ( 1 + i ) N

FV= $ 34 ( 1+ .004166 )60

FV= $ 34 (1.283307)

FV= $43.63

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Present Value - a sum payable in the future is

worth less today than the stated amount

It is the exact opposite of the future value.

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For example, we determined that the future

value of $1,000 for 4 periods at 10% was

$1,464. We could reverse the process to state

that $1,464 received 4 years into the future,

with 10% interest is worth only $1,000 today-

its present value.

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PV= FV[ ]

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Determine Present Value Compounded AnnuallyI will give you $1000 in 5 years. How much money should you

give me now to make it fair to me. You think a good interest ratewould be 6% . (i=.06)

PV= FV[ ]

=$1000[ ]

=$747.38

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Determine Present Value Compounded

Monthly

(i equals .06 divided by 12, because there are 12 months peryear so 0.06/12=.005 so i=.005)

PV= FV[ ]

=$1000 [ ]

=$741.37

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