# Discounted Present Value of Social Security Benefits

I just heard yet another “personal finance expert” offering some stupid advice on Social Security benefits. Social Security benefits generally become entitled at age 62. If the beneficiary defers receiving benefits for a few years, then higher monthly benefits are entitled. The so-called expert recommended NOT to elect to receive benefits at age 62, and to wait until age 67 or 70 in order to receive a higher monthly benefit.

That advice is stupid, because it ignores the Time Value of Money, as well as requiring the person to continue working up to age 70 at a job that may not be there.

Here is how to calculate the value of those varying benefit schedules. Suppose the monthly benefit at (1) age 62 is \$1200, at (2) age 67 is \$1700, and at (3) age 70 is \$2260. Also, suppose that regardless of when benefits begin, the recipient will die at age 80 and the cash flow stops.

(1) The total payment stream at age 62 to age 80 is \$259,200=216×\$1200.

(2) The total payment stream at age 67 to age 80 is \$265,200=156×\$1700.

(3) The total payment stream at age 70 to age 80 is \$271,200=120×\$2260.

This is where most “financial experts” stop and point to option (3) as the “most money”. That’s where they are wrong.

A cash flow stream has a discounted present value relative to a discount rate. Also, each cash flow stream starts at a different time. Therefore, to calculate the correct choice, a discount rate must be applied to calculate the discounted present value at the point when the stream starts and then applied again to calculate the discounted present value at age 62. This is how to compare apples to apples.

Choose a discount rate of, say, 6% to represent the average inflation rate over the entire time period from age 62 to age 80. Then discount each of the cash flow streams to present value at age 62:

(1) The age 62 to age 80 stream discounts at 6% to a present value of \$158,277.

(2a) The age 67 to age 80 stream discounts at 6% to a present value of \$183,839.

(2b) Now discount the \$183,839 at 6% from age 67 back to age 62 at \$0 per month to \$136,293. The present value \$183,839 won’t exist until 60 months in the future relative to age 62, so it must be discounted twice.

(3a) The age 70 to age 80 stream discounts at 6% to a present value of \$203,566.

(3b) Now discount the \$203,566 at 6% from age 70 back to age 62 at \$0 per month to \$126,114. The present value \$203,566 won’t exist until 96 months in the future relative to age 62, so it must be discounted twice.

Therefore, the true discounted present value at age 62 of the 3 choices are:

(1) \$158,277 for 216 monthly payments of \$1200 starting at age 62.

(2) \$136,293 for 156 monthly payments of \$1700 deferred 60 months after age 62.

(3) \$126,114 for 120 monthly payments of \$2260 deferred 96 months after age 62.

Clearly, choice (1) offers the largest discounted present value of the 3 cash flow streams. You can write a simple spreadsheet to perform the double discount calculation to experiment with different discount rates and timeframes. You will find the cash received sooner is more valuable than cash received later. That is a fundamental principle of the Time Value of Money (TVM).