Present Value Comparison Construction Engineering 221 Economic Analysis

Present Value Comparison Present Worth is used to establish a means for comparing projects with different cash flows over different periods. Discount all future receipts and disbursement to current dollars and choose project with highest worth, or Present Value

Present Value Comparison Can assume interest rate and compare present value or can assume cash flows and compare interest rates (rate of return method) ROI (return on investment) as used in the book is the same as interest rate Present worth is the excess present value of one project over another

Present Value Comparison Present value of $100 today is $100 Present value of $105 you will receive one year from now is $100 (assuming a 5% interest rate Therefore, the present worth of any investment that does not pay you more than 105 dollars one year from today is zero or less

Present Value Comparison Negative present worth projects use a minimization of loss criteria Positive present worth projects use a maximization of return on capital criteria Interest rate used in present worth can be taken from a variety of sources. Most common (conservative) is to use the risk- free rate

Present Value Comparison Calculate the risk free rate from government bond and note auctions (cnnfn.com)

Present Value Comparison Some companies have a hurdle rate or an average annual return rate that they use in their calculations Can vary the interest rate used based on risk associated with the project (higher risk = higher interest rate)

Present Value Comparison Compound interest is interest earned on principal AND interest earned to date If interest is paid only on the original investment, then it is simple interest Simple interest is uncommon in engineering problems, but can apply to certain payouts where interest is paid (literally) each year and the investment is re-started

Present Value Comparison The book uses a trial and error approach to solving ROR problems, but can also interpolate from the tables Also, many pocket calculators and on-line rate calculators can generate ROR comparisons

Present Value Comparison Example- which of the following options is best: –Option 1 requires $1000 initial investment and pays $120 per year for 10 years –Option 2 requires $2500 initial investment and pays $250 per year for 12 years –General form is P = A (P/A, i, n)

Present Value Comparison Option 1: 1000 = 120 (P/A, i, 10) –(P/A, i, 10) = 8.33, look at n = 10 lines in tables, find i where P/A is closest to 8.33, or i = 3.5% (page 106) –Option 2, same logic, (P/A. i, 12) = 10 (2500/250); look at n = 12 lines for P/A closest to 10, or i = 3% (page 104)

Present Value Comparison Therefore, Option 1 is the best choice, or provides the maximum rate or return FROM AMONG THE AVAILABLE CHOICES Tomorrow in class- sample problems on ROR and present worth