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Time Value of Money and Economic Equivalence, Cash Flow Diagram, Series of…
Time Value of Money and Economic Equivalence
What is time value of money?
A sum of money is worth more now than the same sum will be at a future date due to its earnings potential
First principle of engineering economics
Over time money increases earning power due to interest but loses purchasing power due to inflation
Interest
The cost of money
Market interest rate: cost of money to borrowers and earnings from money to lenders
Simple interest
Interest rate charged only to an initial sum (principal amount)
F = P + I = P(1 + iN)
Compound interest
Interest rate charged on an initial sum and on any previously accumulated interest that has not been withdrawn
F = P(1 + i)^N
Principle
Initial amount of money
Interest Rate
Cost of money in percent per period of time
Interest Period
Length of time that determines how frequently interest is calculated
Number of Interest Periods
Length of time of the transaction
Future Amount of Money
The cumulative effects of the interest rate over a number of interest periods
Present Value of Money
The current value of a stream of payments over time discounted at a certain discount rate
N = total number of periods
i = interest rate per period n
P = sum of money at t = 0
present value, present worth, principal
F = future sum of money at period N future value
Fundamental Law of Engineering Economy
F = P(1 + i)^N
P = F(1 + i)^-N
End of Period Convention
Assumption that all cash flow transactions at the end of an interest period
Economic Equivalence
2+ cash flows that have the same economic effect are economically equivalent
Amounts and timing of the cash flows are different. The interest rate makes them equivalent.
Principle 1: need a common time basis and basis time period
Principle 2: depends on interest rates, timing, and magnitude of cash flows
Principle 3: is maintained regardless of point of view
Cash Flow Diagram
Graphical summary of timing and magnitude of a set of cash flows
Upward arrows = positive flows/receipts
Downward arrows = negative flows/disbursements
Money invested = negative Money withdrawn = positive
Series of Payments
An = a discrete payment occurring at the end of the interest period n
Vi = an equivalent sum of money that represents one or more payments An
i = interest rate per period
Equivalence Relationship Between P and F
Compounding Process
Finding an equivalent future value of a current cash payment
F = P(1 + i)^N
Discounting Process
Finding an equivalent present value of a future cash payment
P = F(1 + i)^-N