# EV and pvif

Discussion in 'SA2' started by dimitris13, Jun 18, 2019.

1. ### dimitris13Ton up Member

Hi,
can someone please explain by two eqs if possible the following two:
1. if prudential basis the emergence of prud margins =pvif
2. if bea pvif= 0.

i remember from st2 that pvif = pv netCf + res(t)-res(t+1) + int on reserve.

thanks

2. ### Em FrancisActEd TutorStaff Member

Hi

It may help to think of the following:

The PVIF is the present value of future profits on the in-force business. These profits arise from the release of the assets backing the reserves, over and above those which are needed to pay the net outward cashflows (NCF) arising on the business.

If we project those cashflows on the same basis (best estimate) as the reserves are calculated then there should be no excess assets to form the PVIF.

I’ll try and explain using your terminology:

· Let’s say res(t) represents supervisory reserves calculated on a best estimate, market-consistent basis at the start of year t

· int = interest rate which under market-consistent assumptions (as SII will be) int = discount rate = risk-free rate

· Assume NCF(t) occur at the start of the year t, and that these are projected on the same best estimate, market-consistent basis

Since res(t) = NCF(t) + NCF(t+1).v + NCF(t+2).v2 + … and res(t+1) = NCF(t+1) + NCF(t+2).v + …

then we have

· (1+i)res(t) = (1+i)NCF(t) + res(t+1)

which means that:

· (1+i)NCF(t)+res(t+1)-(1+i)res(t)=0

In other words, the investment return earned on the reserves held at the start of the year (= i.res(t)) plus the release of reserves over the year (= res(t) – res(t+1)) is exactly enough to cover the net outward cashflows arising during the year. So no ‘profit’ arises.

We can also see this as follows:

Profit arising in year t = net cashflows to the company (ie net inwards cashflows) + investment return earned on reserves held at start of year and on net cashflows received – increase in reserves over the year

= – NCF(t) + i.{res(t) – NCF(t)} – res(t+1) + res(t)

= – NCF(t).(1+i) + (1+i)res(t) – res(t+1)

Which, from the equivalent statement above, is zero.

So profit arising in year t = 0, for all years t. Thus PVIF = 0.

Does that help?

3. ### dimitris13Ton up Member

Thanks Em for this. Now i get it.
may i ask what about the release of margins in case of prud reserving ? how it is shown in equations (as you explained the above)?
it is pretty easy if some eqs are shown (at least for those that are not familiar with ev)

4. ### Lindsay SmithermanActEd TutorStaff Member

Hi

If there were prudential margins, say PM(t) in total in year t (expressed as a start year value), then:

res(t) = NCF(t) + PM(t) + NCF(t+1).v + PM(t+1).v + NCF(t+2).v^2 + PM(t+2).v^2 + … and res(t+1) = NCF(t+1) + PM(t+1)+ NCF(t+2).v + PM(t+2).v + …

then we have
(1+i)res(t) = (1+i)NCF(t) + (1+i)PM(t) + res(t+1)
etc
Following through in the other formulae, we now get that
Profit arising in year t = – NCF(t).(1+i) + (1+i)res(t) – res(t+1) [same as before]
= (1+i)PM(t)

So rather than 0 profit arising, we now have profit arising during the year = the prudential margins included in the reserving calculation for that year (here, stated as being the value as at the end of the year)

Hence now we would have PVIF = present value of the release of the prudential margins in the reserves

[This all assumes that the EV projection basis remains best estimate, ie that actual experience will be in line with the best estimate assumptions, not the prudent assumptions]

Hope that helps

dimitris13 likes this.
5. ### dimitris13Ton up Member

Hi, many thanks on this (although late). so this release of PMs is a profit. and every year's PM (t) after this t passes goes into the NAV (assuming without profit and no dividends)?

yes