Am having difficulty understand the issue. How do you know if early retirement benefit and lump sum are "subsidized" or not? Have been asked many questions regarding this and honestly don't understand it myself.

Can someone give me an explanation and example?

You need to ask the Plan's actuary to make this determination.

Most early retirement benefits are subsidized, but the amount of the subsidy can vary a great deal depending on the factors used.

I'll give you a couple of generic answers, without regard to the regulations:

Subsidized Early retirement benefit:

Plan A says that if you retire early, you get your accrued benefit actuarially reduced in accordance with the plan's definition of actuarial equivalency.

Plan B says that if you retire early, you get the accrued benefit, reduced 3% per year for early commencement.

Plan C says that if you retire early after 25 years of service, you get your accrued benefit unreduced for early payment.

Plan A is not subsidized. Plan B and Plan C are.

Now, for a subsidized lump sum:

Plan D provides the same early retirement provision as plan C, an unreduced early retirement benefit.

Both plan C and Plan D offer lump sum benefits.

Plan C says the lump sum is equal to the present value of the accrued benefit, reduced actuarially from Normal Retirement Age to early retirement age.

Plan D says the lump sum is equal to the early retirement benefit, unreduced by early payment, multiplied by the annuity rate at the participant's current age.

Plan C does not have a subsidized lump sum. Plan D does.

These are extreme examples, but they illustrate the concept in general.