Ch 21 Alterations to contracts

Discussion in 'SP2' started by fischer, Jun 30, 2008.

  1. fischer

    fischer Member

    The notes on page 4 say that for with-profit, a retrospective reserve for the policy is determined and the surrender value is calculated using this.

    However, shouldn’t we use the prospective reserve because we would need to set a surrender value taking account of future distribution of profits that would be declared under with-profit contracts? The second last paragraph on page 3 seems to support my case.
     
  2. Mike Lewry

    Mike Lewry Member

    Ch21 - Alterations

    As it says on page 4, there are two values you can look at at, either a retrospective or prospective value, and both could be considered reasonable.

    For with-profits, assuming the aim is to pay out close to asset share, then a retrospective calculation is exactly aligned to this. Typically, any future bonuses would have been generated form the current asset share, so don't change things. However, if the current guaranteed benefits aren't supportable from the current asset share plus future premiums less expenses, then a prospective value of these cashflows might be considered more appropriate.

    Where a prospective value is being used for with-profits, this will often be too low if just the current guaranteed benefits are considered. If further bonuses are expected in future, the value of these should be included. If these are expected to be determined from asset share calculations, then we're back to using something equivalent to asset share, so might as well just use the retrospective calculation above.
     
  3. fischer

    fischer Member

    Surrender value respread to reduce future premiums

    I have not understood the Surrender value respread to reduce future premiums method of altering contracts.

    Suppose, the sum assured increases from S to S'. The premiums to be paid increase from P to P'. This is what point (i) in the core reading says.
    So, PV P' = PV S'

    Point (ii) says calculate a special surrender value of "existing" contract that makes allowance for intial expenses included in the prem in (i)
    Q01 - does "existing" here refer to pre or post alteration?
    pre-alt, SV = P.(adue.n) - e(adue.n) - S.A(term assurance factor) - I
    post-alt, SV = P.(adue.n) - e(adue.n) - S.A(term assurance factor) - I

    Point (iii) says reduce the premium by spreading the special SV over o/s term.
    Q02 - Will the reduced premium be sufficient to pay the benefit?
    i.e Will PV P' - SV spread = PV S'?

    cheers
     
    Last edited by a moderator: Jul 27, 2009
  4. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    Under the surrender value respread method, we start by ignoring the existing policy (ie the pre-alteration policy). We calculate the premium that would be charged for the new post-alteration policy P' based on the sum assured S' and expenses E'.

    So PV P' = PV S' + PV E'

    The surrender value is based on the pre-alteration policy, as this is the policy that the policyholder is giving up.

    The surrender value may be calculated on a prospective basis (as you show above), or as a retrospective asset share.

    You probably need to add some initial expenses to the surrender value, not subtract them as you have done. The expense of altering a contract is likely to be less than selling a new contract. For example, in part (i) you may have charged for initial expenses of 100 (eg commission, underwriting). But you may have only incurred expenses of 60 to alter the contract (eg the pre-alteration contract will already have paid commission so there may be no requirement to pay any more). Hence you would adjust the surrender value for intial expenses by adding 40.

    Yes, we can show that the reduced premium will be sufficient as follows.

    The policyholder pays a reduced premium P* given by

    P* = P' - (SV / annuity factor)

    So equivalently we have

    PV P* = PV P' - SV

    The insurance company receives the future premiums P*, plus it keeps the value of the surrendered pre-alteration policy. So the insurer receives

    PV P* + SV = PV P' = PV S' + PV E'

    So the insurer receives exactly what it needs to meet its new liabilities on the altered contract (I've ignored the initial expense adjustment here for simplicity).

    I hope this helps to clarify what's going on.

    Best wishes

    Mark
     
  5. fischer

    fischer Member

    Thanks Mark.
    Also had difficulty understanding the PUP pol val + Prem for balance of SA.

    I'm trying to work with the help of the following:
    Consider a policy with term = 10 years. SA = £1,200 (on death or survival). Premium payable = £100 p.a.

    After 5 years the PUSA is £700. The policyholder wants to increase term by another 10 yrs.

    Then, from the core-reading,
    PUSA after change = £700x(Ratio of assurance factors)
    PUSA after change = £1,500 (say).

    Q01 Would we then find the premium for a policy with a sum assured of £800? (i.e. 1,500-700)

    Q02 Suppose after the 5 year mark, if the PH holder wanted to keep the term unchanged but wanted to increase the sum assured from £1,200 to £2,000, would we then work out the premium for a policy with SA = £8,000 and term = 5 years?

    Q03 Is the first bullet point under Meeting the Principles saying the following:
    "If the benefit is unchanged and the term is unchanged, then we would end up with the paid-up value".

    Q04 Is the third bullet point under Meeting the Principles saying the following:
    "If the PUP value and the surrender value are calculated on the same basis & if the term "n" approaches "t" (where t is the date of alteration), then we would end up with the normal surrender value".

    I know the last 2 questions are not very intelligent, but was wondering if my understanding is correct.
    If it is, then could I use the bullet points as above, as I would be more comfortable in explaining how the principles are met in my own words rather than memorising the core reading.

    Any help would be much appreciated.

    Cheers
    ¦_____¦_____¦_____¦_____¦_____¦_____¦_____¦_____¦_____¦_____¦ P P P P P P* P* P* P*
     
    Last edited by a moderator: Jul 29, 2009
  6. fischer

    fischer Member

    Accumulation of premium arrears/ surplus
    Would like to use the following example:
    Consider a policy with term = 10 years. SA = £1,200 (on death or survival).
    Premium payable = £100 p.a.

    After 5 years the PH decides he wants a SA of £2,000 at the end of the next 5 years.
    So, then the company would need to work out the premium for a policy with term = 10 years and SA = £2,000 (on death or survival).
    The premium calculated works out to be = £125 p.a.

    Q01 Is the method saying,
    # Take the difference between the two premiums (100 & 125), -25 for each of the 5 previous years and accumulate it to the start of the 6th year.
    # Then spread the accumulated value over the remaining 5 premiums of £125 payable from 6th year to 10th year?

    Q02
    a) Under "Meeting the principles", is the second bullet point saying that if the basis for calculating both premiums is the same then there would be consistency between surrender values and paid-up values (if SV's and PUP values also followed premium basis)?
    b) Why does the second bullet point say we could ignore mortality and expenses?
    c) Can the entire second bullet point be explained from first principles? Using equations?

    As always, any help will be much appreciated.

    Cheers

    PLEASE TRY TO ANSWER POST #6 AS WELL
     
    Last edited by a moderator: Jul 29, 2009
  7. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    Yes, this sounds about right. First we calculate the paid-up sum assured (PUSA) on the original 10 year policy. The policyholder has paid half the premiums, but would probably get a PUSA a little higher than 50% because the first 5 premiums are invested for longer than the second 5 premiums. So take PUSA as £700.

    We then look at the new 20 year policy and ratio up the PUSA with assurance factors. If the policyholder survives to the end of the term we will be able to invest the premiums for an extra 10 years. Using a highish rate of interest we would get a new PUSA of £1,500.


    No, this calculation is not right.

    The good news for the policyholder is that they want a sum assured of £1,200, but they can actually get a sum assured of $1,500 without paying another penny! (£1,500 is the paid-up sum assured for a 20 year policy)

    Consider another example. The policyholder wants to extend the term by 10 years and increase the sum assured to £2,000. The paid-up policy provides the first £1,500 of cover. We now need to find the premium for a policy with a sum assured of £500 (ie 2,000 - 1,500).

    No. The paid-up sum assured on the original policy is £700. (There is no need to ratio this number as the term is unchanged.) We now calculate the premium for a 5 year policy with sum assured £1,300 (2,000 - 700).

    Alternatively, the policyholder could keep paying the premiums from the original policy and take out a new 5 year policy for the extra £800 of cover.

    No, the benefit must be changing if we stop paying premiums.

    The first bullet point is saying that under the paid-up value plus premium for balance method, that as the premium reduces to zero, the benefit will reduce to the paid-up sum assured (as long as the term is unchanged).

    Yes, I think this is saying the same as the third bullet. You could use this alternative explanation in the exam.

    Best wishes

    Mark
     
  8. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    Yes, we start by calculating the premium that should have been paid from outset on the new sum assured (ie 10 years and £2,000).

    Your new premium looks too low. By ratioing your original premium I would expect something like 100 x 2000 / 1200 = 166.67

    Yes. The policyholder owes the insurer £25 (or £67 using my numbers) from each of the first 5 years. So they must pay the nre premium of £125 from now on, plus an extra premium to cover the missing payments accumulated with interest.

    Yes, what you have said under a) is correct.

    Consider the following extension to your example. The policyholder wants to surrender his policy after 5 years. We calculate the sum assured that could have been bought for a premium of £100 and a 5 year term. The answer might be £500. The policyholder has paid a premium of £100, so there is no surplus or arrears to accumulate. Hence under this method we pay a surrender value of £500.

    £500 is only the right answer if we ignore expenses and mortality (and we always use the same basis). However, we probably paid higher commision and other initial expenses on the 10 year policy than we have valued on the 5 year policy. The policyholder has also benefitted from higher levels of life cover for the first five years. For both these reasons we could justify paying less than £500.

    Best wishes

    Mark
     
  9. Avviey

    Avviey Member

    Hi,

    For Accumulation of premium arrears/surplus method, 'Meeting the principle', point one, which says,' The method leaves the premium unchaged if the policy terms are unchanged. Hence good for small changes to duration or sum assured, particularly very near to entry.'

    The method leaves the premium unchaged if the policy terms are unchanged. I wonder under what scenario this happens.

    Many thanks.
     
  10. Mark Willder

    Mark Willder ActEd Tutor Staff Member

    In reality nobody ever asks for an alteration to change the policy to itself (ie to keep the policy terms unchanged). However, its a useful check of an alteration method. Any method which would calculate a different premium for an unchanged policy is badly flawed!

    Best wishes

    Mark
     

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