Two sample problem: Same problem: 1) find the common multiple in years of the 2 project lengths (in this case 30 years). Hence, IRR must be solved for in iterative Atrial-and-error@ fashion. Two Methods for Comparing Projects of Unequal Length: 1.

3) for project A, the NPV of \$45000 will cover the first 10 years. Benefit Cost Ratio (B/C ratio) or Cost Benefit Ratio is another criteria for project investment and is defined as present value of net positive cash flow divided by net negative cash flow at i*. Thus, you cannot solve for i. She specializes in divorce, death, career changes, and caring for aging relatives. If you need \$200,000 in your account ten years from now, the present value, or the amount you need to start with today, changes based on various assumed rates of return: You can do these calculations on an HP12C calculator app, or any other financial calculator app that you can download to your smartphone or tablet. Thus 3-project As = 2-project Bs. It is easy to divide a 401k or other retirement account in the present because the balance of the account represents the value of the account. If the calculated i (IRR) is greater than the minimum acceptable rate of return (MARR) (i.e., you won=t accept an earning rate less than the MARR) then you will Ago@ with your project. 2) common multiple = 30 years. To do this calculation, you now have two unknown variables; the rate of return and your longevity. In the table you see the range of results: If your family and personal health history indicate you may be long-lived, you'll either need to save more or work longer than someone with a shorter life expectancy. 4) if not, repeat calculations with a new discount rate. The formula for NPV is: Where: NPV, t = year, B = benefits, C = cost, i=discount rate. (You must think of the terms Anet present value@ and Anet present benefits@ as being interchangeable.)