1. Cash Flow Analysis Construction Engineering 221 Economic Analysis

2. Cash Flow Analysis Assumptions –Year end convention is robust –Interest rates are real (no inflation) –Taxes are excluded –Interest rates are constant over term –Omit non-quantifiable factors –Funds for investment are available –Unused funds are invested at equal return

3. Cash Flow Analysis Equivalence –Method for comparing projects whose timing and magnitude of receipts and disbursements differ –Allows for the time value of money ($100 today is worth $105 one year from now at i=5%) therefore- the values are equivalent –Time value of money is represented by the effective interest rate. Convention is to use annual rates, although can be done qtr, daily,

4. Cash Flow Analysis Working backwards from a known future disbursement is called discounting (think of it as interest in reverse) Single payment equivalence (simplest case) * P = present amount * F = future amount * t = time * n = number of periods * i = effective interest rate

5. Cash Flow Analysis Future worth of a present sum is: –F = P(1 + i) n –(1 + i) n is the compounding factor and is contained in the tables in the back of the book for various rate and terms –Example- if I buy (today) $250,000 worth of 30 year bonds at 5% interest, how much will I get at maturity? F = 250,000 X 4.3219 = 1,080,475 (table p. 112)

6. Cash Flow Analysis Present worth of a future sum is: * P = F/(1 + i) n 1/(1 + i) n is called the present worth factor or the discount rate Example: If you want to be a millionaire by the time you are 50 years old, how much should you invest now (assume you are 20 years old and the effective interest rate is 5%) P = 1,000,000 X.2314= $231,400 (see table p. 112)

7. Homework Due Monday March 3 –Problems on worksheet handed out in class