This post is a piggy-back of the last post - go back one day to read that (you may want to read a few of the prior posts as well).

We saw in the last post that is we assumed a 2.5% rate of return on the investments but consistently earned only 1.5%, contributions would increase over our 5-year time frame to ensure we meet our $100,000 goal. The annual contributions looked like this:

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)

The total of these contributions is $13,300. You will notice how each year the increase in contribution became greater over time. That is partially due to the nature of the example - that $100,000 is due at the end of five years. In this instance, we were required to get to the $100,000 amount at year five. With a typical DB LOSAP, you aren't targeting a fixed number at a certain time, so you wouldn't see contributions increase as significantly as you see from year four to year five.

Now, what would happen if after year one, we recognized that our investments will not earn 2.5%, and that a 1.5% rate of return assumption is more realistic. A change to a 1.5% interest assumption would immediately increase the present value of the $100,000 payment owed. Remember, there is an inverse relationship to the interest rate and the present value - the lower the assumed interest, the higher the present value. The present value represents the amount of money needed today that will compound over time at the annual assumed interest rate to the $100,000 target. If we change the amount of interest we think we will earn - in this case going from 2.5% to 1.5% - then we'll need more in the bank today to reach our targeted amount due to lowered investment earnings. Hence, the present value increases.

The contribution requirement will also increase. Again, assuming the first contribution of $1,800 is made, the next four contributions would likely be around $2,860. This means over five years, a total of $13,240 would be contributed, or slightly less than if the rate was not lowered. 

In the first year that the rate is lowered, the contribution increases significantly - by just over $1,000, or nearly 60%. The funded ratio also decreases - it drops from 90.5% to about 88.1%. However, the total contributions made would end up being less than if the interest rate was not lowered. The reason is hopefully intuitive - the more you contribute up front, the more investment income can be earned, thus requiring lower contributions over time.

The short time period doesn't create a huge savings, but if this model was extracted over 20 years or longer, you would see a more significant long-term savings by using the lower assumed interest rate, despite the short-term increase in contribution.

Of course, the underlying factor here is that the interest rate should reasonably reflect the rate of return that is expected based on the investment policy. This assumption needs to be monitored annually, and it is important to try and set a reasonable assumption from the beginning. It is better to err on the low side than the high side, since if returns are greater than assumed, then contributions will decrease over time. Short-term volatility that results in a lower than anticipated investment return is not cause for a change. But if market conditions or expectations for the future indicate that lower returns are expected based on  the existing investment policy, then a change would then be considered and warranted.

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 5-year 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 re-assess 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 5-year 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.