Projecting Solvency Under the Business Plan

Why Project Solvency Under the Business Plan?

A current solvency position is a snapshot; a business plan is a path. A plan to grow premiums, enter a new market, retain earnings, distribute dividends, or raise financing can change both sides of the balance sheet and the capital available to absorb losses. A useful baseline projection makes those changes explicit for each year, rather than assuming that today’s capital position will remain representative.

This tutorial focuses on a deterministic baseline: projected balances and earnings under the stated business-plan assumptions. It does not determine what the insurer’s internal capital target should be. Instead, where a capital requirement or planning benchmark is supplied, the projection can show how available capital compares with it over time. The approach is aligned with the CAS Exam 9 (Risk Management for Actuaries) syllabus.

Definition: At the end of year $t$, let $A_t$ be projected assets and $L_t$ be projected liabilities, measured on a consistent basis. Define available capital (or own funds in this simplified projection) as $C_t=A_t-L_t$. If $K_t$ is a stated capital requirement or planning benchmark, the coverage ratio is $C_t/K_t$, provided $K_t>0$. The ratio is a comparison against the specified benchmark; it is not, by itself, a universal definition of solvency.

Projection inputs commonly include expected premium and other income, claims and expenses, investment income, changes in insurance liabilities, taxes, dividends, planned equity issuance, liability growth, and the benchmark $K_t$. The projection should identify the measurement basis and timing of each input. For example, an end-of-year liability balance should be compared with end-of-year assets valued on the same basis. A projection that mixes valuation bases or timing conventions can create an apparent change in capital that is only a modeling inconsistency.

The Capital Roll-Forward

Let $P_t$ denote comprehensive earnings for year $t$, after tax and including any gains, losses, or liability remeasurement effects included in the projection. Let $D_t$ be dividends paid during the year and $Q_t$ be new paid-in equity. If there are no other capital movements, available capital rolls forward as follows:

C_t=C_{t-1}+P_t-D_t+Q_t.

This equation follows directly from the balance-sheet identity. If retained earnings increase equity by earnings, dividends reduce equity, and new shares add equity, then the change in $A-L$ is earnings less dividends plus new equity. Any other capital movement, such as a valuation change not included in $P_t$, must be added separately; it must not be silently omitted or counted twice.

\begin{aligned} C_t &=A_t-L_t\\ &=(A_{t-1}-L_{t-1})+P_t-D_t+Q_t\\ &=C_{t-1}+P_t-D_t+Q_t. \end{aligned}

Once the liability projection and capital roll-forward are established, the balance sheet gives $A_t=L_t+C_t$. This is a useful consistency check. It also clarifies that liabilities increasing does not, by itself, imply that available capital falls: the corresponding assets may also increase. The effect on capital depends on the net change in assets and liabilities, including earnings, losses, distributions, and financing.

Set the opening position.
Record opening assets, liabilities, and available capital using a consistent valuation basis. Check that $C_0=A_0-L_0$.

Project business results and liabilities.
Use the plan’s assumptions to calculate comprehensive earnings and the closing liability balance for each year.

Apply distributions and financing.
Subtract dividends and add paid-in equity in the capital roll-forward. Treat debt separately from equity.

Reconcile and compare.
Calculate closing assets as liabilities plus available capital, then compare available capital with any stated benchmark.

Worked Projections

Worked Example: Retained Earnings and a Growing Balance Sheet

A hypothetical insurer has opening assets of $1,200 thousand and liabilities of $1,000 thousand. Its deterministic business plan forecasts comprehensive after-tax earnings of $30 thousand in year 1 and $40 thousand in year 2. It will pay dividends of $10 thousand and $15 thousand, respectively, and will issue no equity. Closing liabilities are forecast to be $1,050 thousand and $1,100 thousand. The stated capital benchmarks are $180 thousand and $210 thousand. Project available capital, assets, and coverage ratios for both years.

Method and assumptions. Amounts are in thousands of dollars. Treat the earnings, dividends, liability balances, and benchmarks as end-of-year projection inputs. There are no other capital movements, financing transactions, or valuation changes outside comprehensive earnings.

Opening available capital is $C_0=1{,}200-1{,}000=200$.

Year 1. Available capital is $C_1=200+30-10=220$. Closing assets are $A_1=L_1+C_1=1{,}050+220=1{,}270$. The coverage ratio is $220/180=1.2222$, or 122.2% to one decimal place.

Year 2. Available capital is $C_2=220+40-15=245$. Closing assets are $A_2=L_2+C_2=1{,}100+245=1{,}345$. The coverage ratio is $245/210=1.1667$, or 116.7% to one decimal place.

Check. In each year, subtracting liabilities from projected assets returns projected available capital: $1{,}270-1{,}050=220$ and $1{,}345-1{,}100=245$. The ratio declines from year 1 to year 2 even though capital increases, because the stated benchmark grows faster relative to available capital.

Worked Example: Equity Issue Versus Borrowing

A hypothetical insurer starts with assets of $800 thousand and liabilities of $700 thousand. In year 1, it expects comprehensive after-tax earnings of $18 thousand and pays a $8 thousand dividend. Its insurance liabilities then increase by $70 thousand under the growth plan. The plan considers either a $15 thousand equity issue or a $15 thousand borrowing. For this example, the borrowing is an additional liability. The year-end capital benchmark is $105 thousand. Compare projected available capital, assets, and coverage under the two alternatives.

Method and assumptions. All amounts are in thousands of dollars. Assume no other capital movements or valuation changes. The borrowing adds $15 thousand to both assets and liabilities; the equity issue adds $15 thousand to assets and available capital, with no new liability.

Opening available capital is $800-700=100$. Before either financing alternative, the year-end capital after earnings and dividends is $100+18-8=110$. The insurance liability balance before any borrowing is $700+70=770$.

Equity issue. Available capital is $110+15=125$. Total liabilities are $770 thousand, so assets are $770+125=895$. The coverage ratio is $125/105=1.1905$, or 119.0% to one decimal place.

Borrowing. Borrowing does not add available capital because it creates an equal asset and liability. Available capital remains $110 thousand. Total liabilities are $770+15=785$, and assets are $785+110=895$. The coverage ratio is $110/105=1.0476$, or 104.8% to one decimal place.

Check. Both alternatives produce assets of $895 thousand, but their liability and capital amounts differ. The equity issue increases available capital by $15 thousand; borrowing increases assets and liabilities by the same amount, leaving their difference unchanged.

Worked Example: Building Earnings from the Business Plan

A hypothetical insurer has opening assets of $900 thousand and liabilities of $800 thousand. Its year 1 plan forecasts premiums of $300 thousand, investment income of $45 thousand, claims paid of $180 thousand, expenses of $60 thousand, taxes of $15 thousand, and an increase in insurance liabilities of $30 thousand. It pays a $10 thousand dividend and issues no equity. The closing insurance liability balance is therefore forecast at $830 thousand. Its stated year-end benchmark is $125 thousand. Calculate year 1 earnings, available capital, assets, and coverage.

Method and assumptions. All amounts are in thousands of dollars. Assume the listed items are the complete earnings calculation: premiums and investment income increase earnings; claims, expenses, taxes, and the increase in insurance liabilities reduce earnings. There are no other gains, losses, or capital transactions.

Comprehensive after-tax earnings are $300+45-180-60-15-30=60$. The liability increase is subtracted because the plan recognizes a larger obligation in the earnings calculation. Opening available capital is $900-800=100$.

The capital roll-forward gives $C_1=100+60-10=150$. With closing liabilities of $830 thousand, projected assets are $A_1=830+150=980$. The coverage ratio is $150/125=1.2$, or 120.0% to one decimal place.

Cash-flow reconciliation. The listed cash inflows less cash outflows and dividends are $300+45-180-60-15-10=80$. Thus assets increase from $900 thousand to $980 thousand. Liabilities increase by $30 thousand, while available capital increases by $50 thousand, so their combined increase is also $30+50=80$. This verifies that the earnings treatment and balance-sheet projection are consistent.

Check. Closing assets less closing liabilities equal $980-830=150$, matching the capital roll-forward. The coverage ratio uses available capital divided by the benchmark, not the reverse.

Growth, Dividends, and Financing in the Baseline

Business growth affects the projection through the assumptions it changes. More business may increase premiums, expenses, claims, and insurance liabilities; it may also require investment in assets or produce earnings that build capital. Therefore, “growth” is not itself a capital adjustment with a fixed sign. Its effect is captured by the projected earnings and closing balance sheet. The plan should make the underlying assumptions visible rather than treating growth as a single unexplained percentage.

Dividends reduce both assets and available capital when paid, all else equal. Retained earnings do the opposite: positive earnings not distributed increase available capital. An equity issue adds assets and capital. Borrowing can provide funds for operations or investment, but, on initial recognition in this simplified balance-sheet view, it also adds a liability and does not create available capital.

A year-by-year schedule is preferable to a single horizon-end estimate. It makes the timing of earnings, distributions, liability growth, and financing visible, and helps identify when a planned action changes the path. For each projected year, a compact schedule can show opening capital, earnings, dividends, equity issuance, closing capital, closing liabilities, closing assets, the benchmark, and the resulting coverage ratio.

Common Projection Errors

Counting financing incorrectly. Treating a loan as if it were an equity contribution overstates available capital. Debt adds an asset and a liability; equity adds an asset and capital.
Double counting earnings. If comprehensive earnings already include investment income and liability remeasurement, do not add those items a second time in the capital roll-forward.
Applying dividends twice. Subtract dividends once from available capital. If closing assets are then calculated as liabilities plus available capital, do not also subtract the dividend again from that balancing asset amount.
Confusing balance-sheet growth with capital growth. An increase in liabilities alone does not determine the change in available capital. The change in assets and the earnings and financing associated with that growth also matter.
Reversing the coverage ratio. Under the definition used here, coverage is available capital divided by the stated benchmark. Dividing the benchmark by available capital answers a different question.

Key takeaway: A defensible baseline projection connects the business plan to earnings, liabilities, available capital, and assets year by year. Reconcile $A_t-L_t=C_t$, distinguish equity from debt, and state clearly what benchmark is used for any coverage comparison.

Check Your Understanding

For each problem, treat the stated amounts and assumptions as complete for the requested calculation. Amounts are in thousands of dollars unless otherwise noted.

A hypothetical insurer has opening assets of 700 and liabilities of 550. It forecasts after-tax earnings of 28, dividends of 8, no new equity, and closing liabilities of 620. Find closing available capital and assets. (Answer: Available capital is 170; assets are 790.)
A company begins with available capital of 90. It projects earnings of 14, dividends of 6, and an equity issue of 12. If the year-end benchmark is 100, calculate closing available capital and the coverage ratio. (Answer: Available capital is 110; coverage is 110.0%.)
A firm begins with assets of 500 and liabilities of 440. It earns 10, pays dividends of 4, and borrows 20, which increases both assets and liabilities. If the benchmark is 60, calculate closing available capital and coverage. (Answer: Available capital is 66; coverage is 110.0%.)
A hypothetical insurer forecasts premiums of 200, investment income of 20, claims of 120, expenses of 40, taxes of 5, and an increase in insurance liabilities of 15. Opening available capital is 80, and the insurer pays a dividend of 10 with no equity issue. Calculate earnings and closing available capital. (Answer: Earnings are 40; closing available capital is 110.)
An insurer starts with available capital of 200 and liabilities of 1,000. In year 1 it earns 25, pays a dividend of 5, and has closing liabilities of 1,060. In year 2 it earns 30, pays a dividend of 10, and has closing liabilities of 1,120. There is no other capital movement. Calculate year 2 available capital and assets. (Answer: Available capital is 240; assets are 1,360.)

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