1. 1 Economic Justification

2. 2 Used to evaluate project alternatives Compare projects Often a hurdle rate (eg. An IRR of > 20%) Variety of measurements: Net Present Worth, NPV IRR etc.

3. 3 Single Payment COMPOUND Interest P= (P)resent sum of money i= (i)nterest per time period (usually years) n= (n)umber of time periods (usually years) F= (F)uture sum of money that is equivalent to P given an interest rate i for n periods F=P(1+i) n P=F(1+i) -n Can also use tables, financial calculator, spreadsheet

4. 4 Example You invest $10,000 in a tax deferred retirement plan [401(k) or 403(b) or IRA]. What is the expected balance after a) 20 years b) 40 years with annual return of i) 5% fixed rate interest and ii) 12% return from stocks (equities)? Note can also calculate PW of future income or costs

5. 5 NPW Net Present Worth, NPW, may be used to establish the current market value of projected future benefits and costs associated with an investment opportunity at some i. (examples include real property and bond valuations.) NPW = PW of Benefits - PW of Costs = PWB - PWC For a project to be (barely) acceptable, the NPW must be > 0.

6. 6 Purchase of Manhattan PW C =24 PW B =12X10 9 (1+i)- n Calculate for given i NPW =PWB - PWC $24 $12,000,000,000 n=373

7. 7 Rate of Return Analysis Rate of return analysis is equivalent to other methods and is the most frequently used. Interest rate provides a common metric for comparison

8. 8 Internal Rate of Return Internal Rate of Return, IRR, is the interest rate at which the discounted present worth of benefits equals the discounted present worth of costs, i.e. the Net Present Worth, NPW, = 0.

9. 9 Purchase of Manhattan PW C =24 PW B =12X10 9 (1+i)- n PW C =PW B ln(1+i) =-ln(24/ 12X10 9 )/n i=5.55% $24 $12,000,000,000 n=373