Effective Interest Rate

[Pension RC]

I am looking at a 2012 SB created based upon software-generated results. It is clear that MAP-21 rates were used, but the effective rate of interest is lower than the lowest of the MAP-21 segment rates. Can anyone explain how this can be possible? Is there any allowance to use MAP-21 rates for funding, but to base the effective interest rate on non-MAP-21 rates?

Any thoughts would be appreciated!

[Hojo]

Check your software. If it's relius, you may have hit the bug that is producing faulity EIR's (usually the FT and TNC are correct, but its derivation of the EIR is messed up). You have to undo and rerun a few times to get it out of it.

[FAPInJax]

Well, theoretically, a plan paying lump sums at 5% would have values that could only be duplicated by using an effective interest rate of less than the first interest segment (when MAP rates are involved). However, I am not sure that it is permissible to have a result less than the first interest segment regardless.

I would guess that you have a very small plan and the population is very old (close to retirement). However, I would still vote for the effective interest rate to be no lower than the first interest segment.

[My 2 cents]

As I understand PPA, while you might use anticipated lump sum values based on 5% to get your anticipated cash flow (i.e., if the plan explicitly pays the greater of the 417(e) minimum lump sum and a 5% lump sum), the cash flow must then be discounted back to the present using the applicable segment rates, and you must then solve for a single rate (the effective interest rate) that produces an identical discounted value of that cash flow. I believe that the only acceptable methodology under PPA for determining the funding target is to (a) determine an expected cash flow and then (b) discount that cash flow using the relevant segment rates (or the full yield curve if that is being used). Presuming that you are not using the full yield curve, if you are getting an effective interest rate below the lowest segment rate, your software must either have a bug or lack sufficient sophistication to properly apply the PPA funding rules.

[Andy the Actuary]

Well, theoretically, a plan paying lump sums at 5% would have values that could only be duplicated by using an effective interest rate of less than the first interest segment (when MAP rates are involved). However, I am not sure that it is permissible to have a result less than the first interest segment regardless.

From proposed funding reg: "Under section 430(h)(2)(A), a plan’s effective interest rate for a plan year is defined as the single interest rate that, if used to determine the present value of the benefits taken into account in determining the plan’s funding target for the plan year, would result in an amount equal to the plan’s funding target determined for the plan year under section 430(d)."

Is there some guidance published elsewhere that would lead you to the statement that an effective rate lower than the first segment rate may be impermissible?

[My 2 cents]

It is not a matter of it being impermissible. If you calculate your anticipated cash flow for all future years and then discount the first five years' cashflow at x%, the next 15 years' cashflow at y% and the cashflow anticipated for 20+ years at z% (x%, y% and z% all being positive), and then solve for an interest rate w% that produces the same discounted value, is it possible, for any cash flow not involving negative (imaginary?) numbers to get a w% lower than the smallest of x%, y% and z%?

You could come up with an effective rate lower than the first segment rate, but only if the second or third segment rate is less than the first.

It all comes down to having to calculate a cash flow and then apply the discount rates to that cash flow. There is no other way to calculate a PPA Funding Target.

[Andy the Actuary]

Age 45

Segment 1 = 7.50%

Segment 2 = 8%

Lump sum in 20 years valued at 4.5%

Are you suggesting that effective rate won't be less than 7.50%?

Just for grins, (71GA,4.50%) used to value a65=123.79. 123.79/1.08^20=26.56 = PV @45

Single interest rate that produces this result=7.05%

Perhaps, I'm misunderstanding your 2-cents worth? Wouldn't be the first time.

[My 2 cents]

Suppose that your entire expected cash flow consists of a single payment of $X expected to be paid in 19 years.

FundingTarget (using your segment rates) = $X divided by 1.08% to the 19th power. Effective Interest rate (single interest rate that produces the same present value) = 8%, by default.

You don't give a third segment rate, so let's suppose that the third segment rate is 8.2%.

Suppose that your entire expected cash flow consists of a single payment of $Y expected to be paid in 21 years.

Funding Target = $Y divided by 1.082 to the 21st power. Effective interest rate (single interest rate that produces the same present value) = 8.2%.

Suppose that your entire expected cash flow consists of a payment of 0.5 times $X expected to be paid in 19 years and a payment of 0.5 times $Y expected to be paid in 21 years.

Funding Target = 0.5 times $X divided by 1.08 to the 19th power plus 0.5 times $Y divided by 1.082 to the 21st power. You need to solve for a single interest rate that produces the same discounted value. It will probably be very close to 8.1%.

The effective interest rate has nothing to do with the interest rates used to project the cash flow, only those used to discount the cash flow. In these examples, note that how one gets $X or $Y is not taken into account in calculating the Funding Target or the effective interest rate.

I hope this helps.

[Andy the Actuary]

It helps point out difference in interpretations. In my example, I valued a65 (pv of benefits at 65) at 4.50% to get funding target and then at 7.05% to get single effective interest rate. In short, in determining effective interest rate, I was not valuing 123.79 but rather the pv of the benefits at the effective interest rate. I believe that is how the actuary got to an effective rate less than the first segment rate. This is not a commentary on what should or should not be done.

[My 2 cents]

While it may be true that if you use 7.05% to both calculate the expected lump sum payable at t=20 and to discount it that you would get the same answer as using 4.5% to calculate the expected lump sum payable at t=20 and 8% to discount it, that does not make the Effective Interest Rate (for PPA purposes) equal to 7.05%.

Step one is construct the expected cash flow, taking into account whatever plan provisions and assumptions are appropriate (i.e., in this case the assumption/plan provision specifiying that lump sums are based on 4.5% interest). Step two is discount the expected cash flow from step one using the applicable segment rates to get the funding target. Step three is find a single interest rate such that discounting the expected cash flow from step one using that single rate gives you the same present value that you got in step two. It is my understanding that this approach to finding the effective interest rate is the approach required under PPA and the regulations.

[Andy the Actuary]

Not disagreeing with you. Simply trying to show an example of how someone may come up with the other answer.

[FAPInJax]

I was not aware of anything that permitted (off the top of my head when I wrote the response). However, I have had discussions where the topic was broached about redoing the calculations using the lower interest rate to match back to the AE calculations. I agree with My 2 cents but was commenting on a possible alternative approach.

So, a question that has been raised before, what happens to a 1 man plan where the participant is at NRA? The lump sum of the benefit is based on 5% and there is no discount using applicable rates (let's say 5.5, 6.5, 7.5)(taking steps 1 and 2). What is the effective interest rate? Any interest rate will work but can one argue it is 5% or does it floor at 5.5%?

[My 2 cents]

If the you are dealing with something like a 1 participant plan for someone at NRA and the objective is to bring the assets up to the amount that would be payable as a lump sum, would the 50% cushion amount, together with the fact that the deduction limit is explicitly not based on the MAP-21 funding relief rates, be enough to get you where you want to be? Remember, just because the minimum contribution won't be enough for such a plan does not mean that you cannot contribute more, probably on a tax-deductible basis.

As for the effective interest rate: Expected cash flow = 1 payment at time t=0. My guess is that, by default, since the entire cash flow is within the first 5 years, you get the first segment rate as the effective interest rate. To reiterate, the assumptions used to determine the expected cash flow do not determine what the effective interest rate is.