New Review Introduced a new magic number –P/A Present worth series The reciprocal of A/P Takes an annuity and sweeps it back to the present time –P/A * Annuity = Present Value

New Review Introduced Special Investor tools for evaluating the content of the POT –Net Present Value –Present Value Ratio

Net Present Value Follows the Special Pattern that runs all engineering econ problems First you write down the cash flow from the story problem –Trick #1 - Determine the perspective you will look from so you can tell when money moves in or out of your investors pocket –Trick #2 - Place the money pot at the point where the decision to go with the project is made (there is usually money moving at that point)

More NPV With the pot placed begin using magic numbers to sweep each cash flow in your picture back into the pot –Sweeping is done by multiplying each element of your cash flow by the appropriate magic number –Warning - You must use the right magic number

Getting the Right Magic Number Pick the super hero you think is appropriate to sweep your cash flow element back into the pot (you’ve met F/P, P/F, A/P, P/A) –Trick - Use the unit cancellation trick to make sure that you are not calling on the wrong super hero A/P * Present Cash Pile = Annuity of equal value

Tuning Up the Magic Number After Picking the Right Super Hero Get the value of n –it’s the number of compounding periods you need to sweep the cash to get it in the pot (count on the picture if you have to) For annuities its also the number of payments in the annuity

More Tuning Up Get the value of i –Its usually given in the problem as the rate of return needed for the investment Watch out for the booby trap –i is nearly always given as an annual rate of interest –Compounding period may be annually, quarterly, monthly, daily (or even continuous - special case)

Mismatch of the Interest Rate and Compounding Period Check for a mismatch If the Interest Rate Period is not the same as the compounding period –Divide the Interest Rate by the compounding period Example - Quarterly Compounding but annual interest rate of 8% –8% interest per year / 4 compounding periods per year = 2% interest per compounding period

More Checks on i There are real rates of return and nominal rates of return –real measures real buying power and does not consider inflation –nominal measures the number of cash units regardless of buying power and does consider inflation Make sure if you use a nominal rate the cash flow reflects inflation. Use a real rate if the cash flow does not reflect inflation –This is the hidden bug overlooked in the text

Solve for the Magic Number With n and I figured out - plug into the formula and crank out the magic number Use the magic number to sweep your cash flow element (multiply it by the magic number) back into the pot Move on to the next element of the cash flow until your done and have everything in the pot –Trick - sometimes temporary pots help with annuities

Total up all the money in the Pot Add up the sum of all the cash flow terms times there magic numbers This is the Net Present Value If its zero - you got your return (go for it) If its positive you got more than you hoped for (slobber profusely and go for it) If its negative - well

The PVR Pot Sniffing Method In PVR you do the same as with NPV except that you keep the red ink and green ink number separate You end up with a Pot that contains the NPV of all negative cash flows and the NPV of all positive cash flows –Divide the positive cash flow by the negative –(Ignore the negative sign on the bottom - ie get the absolute value)

Evaluating PVR If the number is 1 - that means the numerator is as big as the denominator –That means that the NPV of the money you earned is as great as the NPV of the money you invested This is good If the number is greater than 1 - that means the numerator is bigger than the denominator –That means the NPV of your earnings is greater than the investment Slobber profusely and go for it