Monday, March 21, 2011

Principles of Money-Time Relationship

Capital: Wealth in the form of money or property that can be used to produce more wealth.

Engineering economy studies involves the commitment of capital for extended periods of time. Since, money has its time value, and if money is not invested, the value suffer loses due to interest rates, inflation, currency exchange etc.

Interest: Money paid for the use of borrowed money. It is the rental charge for using an asset over some period of time and then, returning the asset in the same conditions as we received it.

Interest exists to encounter the risk of possibility that borrower will be unable to pay. Moreover, money repaid in the future faces inflation. Besides, the lender would need to undergo transaction costs and opportunity cost. This way, postponement of use of money occurred. On the other hand, interest is always a cost for borrowers.

An example of decision dilemma:
Take a Lump Sum or Annual Installments
A married couple won 4D and they had to choose between a single lump sum $104 million, or & 198 million paid out over 25 years ($7.92 million per year). The winning couple opted for the lump sum. Did they make the right choice? What basis do we make such an economic comparison?

We must be able to compare the value of money at different point in time. We need to develop a method for reducing a sequence of benefits and costs to a single point of time and make our comparison on that basis.

Time value of money is measured in terms of interest rate.

Key Terms
Interest rate (i)
Interest period (n)
Number of interest periods (N)
A plan for receipt (An)
Future amount of money (F)

Method of Calculating interest
Simple Interest: The practice of charging interest rate only to initial sum.
Compound interest: The practice of charging interest rate to initial sum and to any previously accumulated interest that has not been withdrawn.

Simple Interest
I = P x N x i
and he total amount repaid at the end is P + I

Example: If $5000 were loaned for five years at a simple interest rate of 7% per year, the interest earned would be...
I = $5000 x 5 x 0.07 = $1750
So, the total amount repaid at the end of five years would be the original amount plus the interest, $6750.

Compound Interest
n = N : F = P(1+i)^N

Example: If you deposit $100 now (n=0) and $200 two years from now (n=2) in a saving account that pays 10% interest, how much would you have at the end of year 10?
$100(1+0.1)^10 = $259
$200(1+0.1)^8 = $429
F = $259 + $429 = $688

Economic Equivalence exists between cash flow that have the same economic effect and could therefore be traded for one another. Although the amounts and timing of the cash flows may differ, the appropriate interest rate makes them equal.

Example: At an 8% interest, what is the equivalent worth of $3000 back in 5years.
F = $3000(1+0.08)^-5 = $2042

n=0, deposit $500
n=3, deposit $1000
find n=1 and n=2 at equivalent values(V)...
V,n2 = $500(1+0.1)^2 + $1000(1+0.1)^-1 = $1514.09
V,n2 = C(1+0.1)^1 + C
C = $721, for n=1 and n=2

Deferred annuities are uniform series that do not begin until some time in the future. Uniform series explains cash flows that changed by a constant amount each period.

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