Yesterday we looked at a simple scenario to help illustrate how the funded ratio increases towards 100% over time as contributions are made and earnings are realized. It looked like the following, where the first number is the assets of the plan, the second number is the present value of accrued benefits, and the third number is the funded ratio:
Year 0: $80,000 ÷ $88,385 = 90.5% Year 1: $83,845 ÷ $90,595 = 92.5% Year 2: $87,786 ÷ $92,860 = 94.5% Year 3: $91,826 ÷ $95,182 = 96.5% Year 4: $95,967 ÷ $97,562 = 98.4% Year 5: $100,211 ÷ $100,000 = 100.2% This chart assumes a $1,800 contribution is made at the beginning of each year and that the annual investment return is 2.5%. Over this 5year period, the value of the assets grew by $20,211, of which $9,000 was contributed and $11,211 was earned on the investments. But what would it look like if our investment projection was too high, and the fund instead earned 1.5% per year, or 1.0% less than projected? Assuming the annual contribution of $1,8000 did not change, it would look something like this: Year 0: $80,000 ÷ $88,385 = 90.5% Year 1: $83,027 ÷ $90,595 = 91.6% Year 2: $86,099 ÷ $92,860 = 92.7% Year 3: $89,217 ÷ $95,182 = 93.7% Year 4: $92,382 ÷ $97,562 = 94.7% Year 5: $95,595 ÷ $100,000 = 95.6% If this happened, we would be $4,405 short of our goal. We contributed the same $9,000 but earned only $6,595 in investment income. But the purpose of having the actuarial valuation performed every year is to reassess where things stand and adjust contributions accordingly. So every year when the valuation is completed, the actuary would adjust the contribution for the fact that less investment income was received than anticipated. In this scenario, there is a hard target that must be hit  $100,000 in five years. So the impact on the contributions is a little more stark compared to an actual ongoing DB LOSAP that does not have to hit a certain asset value at a certain time. But the illustration is still helpful. Contributions would likely be adjusted as follows each year: Year 1: $1,800 Year 2: $2,000 (11% increase from Year 1) Year 3: $2,300 (15% increase from Year 2) Year 4: $2,700 (17% increase from Year 3) Year 5: $3,700 (37% increase from Year 4) By the end of Year 5, there would be about $99,200 in the account, leaving another $800 contribution required to get to the $100,000 goal. Over this 5year period, to meet the $20,000 shortfall, $13,300 will have been contributed and $6,700 earned on the investments. So you can see in this simple scenario how failing to meet the earnings target by 1% caused nearly a 50% increase in the total required contributions  from $9,000 to $13,300. The next post we'll look at what would happen if the rate of return assumption is adjusted to 1.5% after the first year.
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