Reading 12 - Annuities Question

CFA Level III Equities
#1

Hi all,

I came across this following text from the CFA 2017 Level 3 Schweser Notes on annuities and I am kind of confused regarding the last sentence there.

In relations to annuities, the text states:

“The premium, which is normally paid once at purchase, could also be referred to as the value of the contract. The premium paid to the company is the price of the annuity. However, the convention is to keep the premium constant and adjust the stated annual payout. This means that a lower/higher quoted payout to the annuitant is equivalent to a higher/lower price for the annuity.”

I would’ve thought a lower/higher quoted payout to the annuitant is equivalent to a lower/higher price for the annuity?

Since if I buy an annuity, I would expect to receive a larger fixed payout during the duration of the annuity if I were to pay more upfront than if I were to pay less upfront?

Thanks all.

#2

You are ready to pay more upfront (higher price), but you cannot do it because the premium is kept constant therefore instead you quote a lower payout (receive less for the same money). As a result a lower quoted payout is equivalent to a higher price.

#3

You’re paying a fixed amount – say, $1,000,000 – for a 20-year annuity.

  • If the annual payout is $73,582 (4% discount rate), you’re paying $13.59 (= $1,000,000 ÷ $73,582) per $1.00 of annual payout.
  • If the annual payout is $80,243 (5% discount rate), you’re paying $12.46 (= $1,000,000 ÷ $80,243) per $1.00 of annual payout.

Thus, the higher payout ($80,243) corresponds to the lower price ($12.46 per $1.00), and vice-versa.

#4

Thanks for the responses Aylar and S2000, greatly appreciate it :slightly_smiling_face:

#5

My pleasure.

#6

Ok that makes A LOT of sense. Why didn’t they put that in the book?!