# 1.22 Personal Financial Planning Problem: Net Present Value (In-class Exercise)Â

Problem: Do you remember Shlomo, the soon-to-be retiree? He was unable to decide based on The Payback Method.

Solution: Shlomoâs choices are mutually exclusive. He has to decide between taking benefits now or later. He rightly figures that his expected lifespan is relevant and recognizes that his Payback analysis did not consider that. While it is true that it will take him a somewhat long time to break even, he expects to live a lot longer than that payback period. His parents both lived past 100 and he is in excellent health himself. He expects to live to 100, or 102, at least. He decides to do a (Net) Present Value calculation.

Shlomo assumes a 5% discount rate, based on the Treasury Yield Curve. He, rightly or wrongly, assumes that Social Security payments are as default-safe as Treasury debt. The present value of a 38-year annuity is (PVAF: N = 38; k = 0.05) (12) (\$800) = \$X, while the Present Value of a 34-year annuity is (PVAF: N = 34; k = 0.05) (12) (\$1,200) = \$Y, which has to be further discounted by four years to compare it, on a PV basis with his other choice.

Questions:

1. First, calculate these out. You may estimate this by hand, since there is no 34-year row in our tables. Or, you may use a financial calculator.
2. What should he do? Which option should he choose â based on NPV?

1. Now: (16.8679) (12) (800) = \$161,931.Â  Later: (16.1929) (12) (1,200) = \$233,177
2. Wait until later. The NPV is greater in the deferral instance.