Actuarial Notes

Deferred Policy Acquisition Expenses

Deferred Policy Acquisition Expenses (DPAE, also called DPAC or DAC) were, under pre-IFRS 17 Canadian P&C reporting, the balance-sheet asset for acquisition expenses paid when a policy is written that relate to its unexpired portion. They were expensed as the premium was earned, but only so far as they could be recovered from the equity in the net unearned premium, which the Appointed Actuary evaluated. The asset is off the current syllabus: under IFRS 17, Insurance Acquisition Cash Flows took its place.

\text{DPAE}_{\text{booked}} = \min\big(\text{DPAE}_{\text{initial}},\ \max(0,\ \text{EQUP})\big)

\text{EQUP} = \text{UPR}_{\text{net}} + \text{UC} - \text{PL}_{\text{net}}

  • The symbols. \text{DPAE}_{\text{initial}} is the amount the accounting department proposes, and EQUP is the equity in the net unearned premium. \text{UC} is the unearned reinsurance commissions. \text{PL}_{\text{net}} is the net policy liabilities in connection with unearned premium: future claims and adjustment expenses, expected reinsurance costs and maintenance expenses, at actuarial present value. Premium Deficiency shows how it is built. A negative EQUP takes the DPAE to zero and is carried as a premium deficiency, so a premium deficiency always means a booked DPAE of zero.
  • What is deferrable. Deferrable costs are acquisition expenses paid up front, and only the proportion relating to the unexpired portion of the policy:
    • Generally, broker and agent commissions and premium taxes.
    • Possibly an allocation of operating expenses such as renewal costs, advertising, licences and fees, and association dues.
    • Non-deferrable commissions are, in the CAS's published answer, those "that cannot be readily identified as exclusively relating to and varying with the acquisition of premiums and therefore are not recoverable". Page 80.10 of the old P&C-1 reported contingent commissions and other non-deferrable commissions outside the deferral.
    • Maintenance expenses, the cost of servicing policies already in force, are not acquisition costs. They are a future cost inside \text{PL}_{\text{net}}.
  • Purpose: matching. Deferral spreads the prepaid expenses over the policy term alongside the earned premium, so an expected profit emerges pro rata. Because the asset is capped at EQUP, an expected loss is recognised at once. The Standards of Practice build this into the premium liabilities themselves. Their amount "after deducting any deferred policy acquisition expense asset" is the present value of the cash flows still to come on the policies in force (paragraph 2230.01, as quoted in the CIA's 2007 note).
  • A write-down cuts both income and equity. The asset falls and the expense rises by the same amount, so net income and equity both fall. Examiners marked it wrong to reason that ROE falls simply because equity falls. One trigger for a write-down is a fall in the discount rate, which raises the premium liabilities and lowers the maximum DPAE.
  • The commission reconciliation on page 80.10 (old P&C-1), as the published answers use it:
    • Commission expense = deferred commissions at the start of the year + direct and assumed commissions written - deferred commissions at the end.
    • Ceded commission income = unearned commissions at the start + ceded commissions written - unearned commissions at the end.
    • Total net commissions = (expense - income) + net contingent commissions + net other non-deferrable commissions.
  • What replaced it. Under IFRS 17, in force in Canada from January 1, 2023:
    • Only acquisition cash flows directly attributable to the portfolio are deferred. Under the PAA, the LRC at issue is premiums received less, if applicable, the deferred acquisition costs, so the deferral sits inside the liability rather than beside it as an asset.
    • Where each contract's coverage period is a year or less, the insurer may instead expense them as incurred (IFRS 17.59(a)). That keeps them out of the onerous assessment but front-ends the expense.
    • Costs allocated to groups not yet recognised, such as expected renewals, are held as an asset subject to recoverability tests.
    • The 2023 returns have no page 80.10. Page 80.15 of the quarterly return reports total commissions by class only, and insurance service expenses include a column for the amortization of insurance acquisition cash flows (page 60.25).

Why Defer, and Where the Cap Bites An annual policy is written on October 1 for a premium of \$1{,}200. Commission and premium tax of \$240 are paid at issue. Expected claims and adjustment expenses are \$780 and maintenance expenses \$60, both incurred evenly over the term. Ignore discounting, margins and reinsurance.

(a) Find the DPAE at December 31, and the income in each calendar year with and without the deferral.

(b) Repeat with expected claims of \$1{,}000.

Answer (a) At December 31, three of twelve months are earned, so the UPR is \$900. The equity in it is:

\begin{align*}
\text{EQUP} &= 900 - 0.75(780) - 0.75(60) \\
&= 900 - 585 - 45 \\
&= 270
\end{align*}

The deferrable portion is 0.75 \times 240 = 180, which EQUP covers, so the DPAE is \$180.

\begin{align*}
\text{Year 1 income} &= 300 - 195 - 15 - (240 - 180) \\
&= 30 \\
\text{Year 2 income} &= 900 - 585 - 45 - 180 \\
&= 90
\end{align*}

The policy's \$120 profit emerges one-quarter in year 1, in step with the premium earned. Without the deferral, year 1 would show 300 - 195 - 15 - 240 = -\$150 and year 2 +\$270: a loss reported on a profitable policy.

(b) Future claims are now 0.75 \times 1{,}000 = 750:

\begin{align*}
\text{EQUP} &= 900 - 750 - 45 \\
&= 105
\end{align*}

This is below the \$180 deferrable, so the DPAE is capped at \$105.

\begin{align*}
\text{Year 1 income} &= 300 - 250 - 15 - (240 - 105) \\
&= -100 \\
\text{Year 2 income} &= 900 - 750 - 45 - 105 \\
&= 0
\end{align*}

The policy loses 1{,}200 - 1{,}000 - 60 - 240 = -\$100 in total, and all of it is recognised in year 1. The cap is what stops a deferral from carrying an expected loss forward.

Writing the DPAE Down The actuary finds net UPR of 80{,}000, unearned reinsurance commissions of 1{,}500 and net policy liabilities in connection with unearned premium of 74{,}300 ($000s). The accounting department proposed a DPAE of 9{,}000, on which basis net income for the year is 6{,}000 and year-end equity 60{,}000.

Ignoring tax, what is the effect on net income, equity and return on equity?

Answer

\begin{align*}
\text{EQUP} &= 80{,}000 + 1{,}500 - 74{,}300 \\
&= 7{,}200
\end{align*}

EQUP is positive but below 9{,}000, so the DPAE is written down by 1{,}800 to 7{,}200, with no premium deficiency. The 1{,}800 becomes expense this year:

\begin{align*}
\text{ROE before} &= \frac{6{,}000}{60{,}000} \\
&= 10.0\% \\
\text{ROE after} &= \frac{6{,}000 - 1{,}800}{60{,}000 - 1{,}800} \\
&= \frac{4{,}200}{58{,}200} \\
&= 7.2\%
\end{align*}

Both the numerator and the denominator fall by the same 1{,}800. The ratio (N - x)/(E - x) is below N/E whenever net income N is less than equity E, so for any ordinary insurer the write-down lowers ROE. The falling equity pushes ROE up, but by less than the falling income pulls it down.

Net Commissions on Page 80.10 From page 80.10 of an insurer's P&C-1 ($000s): deferred commissions were 21{,}000 at the start of the year and 23{,}500 at the end. Unearned commissions were 1{,}800 at the start and 2{,}100 at the end. Commissions written were 48{,}000 direct, 1{,}500 on reinsurance assumed and 6{,}000 on reinsurance ceded.

Contingent commissions were 2{,}400 gross and 400 ceded. Other non-deferrable commissions were 900 gross and 100 ceded.

Calculate the net commissions attributable to the period and the total net commissions.

Answer

\begin{align*}
\text{Commission expense} &= 21{,}000 + 48{,}000 + 1{,}500 - 23{,}500 \\
&= 47{,}000 \\
\text{Ceded commission income} &= 1{,}800 + 6{,}000 - 2{,}100 \\
&= 5{,}700 \\
\text{Net attributable to the period} &= 47{,}000 - 5{,}700 \\
&= 41{,}300
\end{align*}
\begin{align*}
\text{Total net commissions} &= 41{,}300 + (2{,}400 - 400) + (900 - 100) \\
&= 44{,}100
\end{align*}

Deferred commissions grew by 2{,}500: that much of the year's commissions written sits on the balance sheet as deferred commissions rather than in expense. Watch the signs, an error examiners reported: deferred commissions at the start add to the expense and those at the end reduce it, while unearned ceded commissions work the same way on the income side.