September 2005 Q11 (Calculating Provisions)

[scr123]

Could someone explain how to calculate the provision.

The given solution is:
provision required at start of year 3 = (1891.55-4138.821(1-p_24))/1.04=1768.192

=[(Profit)-(Maturity Cost)(1-p_24)]/1.04


I am trying to use the formula from the notes:
(NUFC)_t + (t-1)_V*(1+i) - p_(x+t+1) * t_V = PRO_t

Sub values gives:
-1891.55 + 2_V * (1.04) - p_64 *3_V = 0

The given solution has used:
3_V=4138.821 (Why isn't this 0?)
1-p_64 (Why isn't this just p_64?)

 

[Mark Mitchell]

If you're looking at the Examiners Report, I think it's a slightly odd presentation.

In particular, where the maturity cost is quoted it hasn't been multiplied by the probability that the company has to pay out on maturity.

It might make more sense to you as follows:

- expected maturity cost = 0.15*27592.14*p64 = 0.15*27592.14*(1-0.012716) = 4086.19.

- this changes the "profit" to -1838.92

- the you can use the standard formula to calculate the reserves at time 2 (with 3V=0):

2V = 1838.92/1.04 = 1768.19

as stated.