A defined benefit pension plan has expected payouts of $15 million per year for eight years and then $20 million per year over the following 15 years. Actuaries have estimated that the fund can be expected to earn an average of 5.25 percent on its assets. The fund currently has reserves of $185,475,000. The plan is ________ by about ________ million.

Question

Quizplus · Accepted Answer

The present value of the expected payouts can be calculated using the formula: PV = [(PMT/i) x (1 - (1+i)^-n)], where PMT is the annual payout, i is the interest rate, and n is the number of years. 
For the first 8 years: PV = [(15,000,000/1.0525) x (1 - (1/1.0525)^8)] = 101,095,362 
For the following 15 years: PV = [(20,000,000/1.0525) x (1 - (1/1.0525)^15)] = 205,338,310 
Total present value of expected payouts = 306,433,672 
The plan's reserves of $185,475,000 are less than the present value of expected payouts by $120,958,672. Therefore, the plan is underfunded by about $46 million (rounded to the nearest million). 
The correct answer is E) underfunded; $46.

A Defined Benefit Pension Plan Has Expected Payouts of $15