Marcus is 50, earns a gross salary of 160,000 dollars a year and intends to retire at 65, which is 15 years away. His planner uses a wage replacement ratio of 75 percent of gross salary and assumes salaries and prices both rise at 3 percent a year. Social Security is expected to provide 42,000 dollars a year from age 65, stated in today's purchasing power, and that benefit will also have risen with inflation by the time he claims it. The remainder of the income is to come from his portfolio. What first year portfolio withdrawal must the plan fund at age 65, expressed in the dollars of that year?
- AAbout 121,521 dollars, the shortfall in today's money inflated at 3 percent for the 15 years to age 65 Correct
- BAbout 78,000 dollars, the shortfall measured in today's purchasing power at the date of the analysis
- CAbout 144,956 dollars, the inflated replacement need less the Social Security figure stated in today's money
- DAbout 186,956 dollars, the whole replacement income inflated for the 15 years to age 65
Why A is correct: The replacement need is 120,000 dollars and Social Security meets 42,000 dollars of it, leaving a 78,000 dollar shortfall in today's money that is then inflated over the 15 years to retirement.
Why B is wrong: This is the correct shortfall but it is left in today's money; the withdrawal is taken 15 years from now, so it must be inflated to the retirement date before the capital sum is calculated.
Why C is wrong: This inflates the 120,000 dollar replacement need correctly but then subtracts a Social Security benefit that has been left in today's dollars, so a future amount is reduced by a present one and the shortfall is overstated.
Why D is wrong: This inflates the full 120,000 dollar income need and ignores Social Security altogether, so the portfolio is asked to fund income that another source is already providing.