Using Capital Returns in Business Planning

Turning Capital Returns Into Plan Targets

A business plan should connect operating ambitions to the capital needed to support them. A projected profit increase can look attractive in isolation but fail to earn the required return if the plan also consumes substantial capital. Conversely, a contraction may reduce profit while releasing enough capital to improve the return on the business that remains. The planning question is therefore not just “How much profit will this unit produce?” but “How much profit will it produce relative to its allocated capital, and what target follows from the hurdle rate?”

The calculations in this tutorial use a single planning horizon and hypothetical projections. They show how to set targets and track the effect of business-plan changes; they do not imply that projected profits or capital requirements are certain. This approach is aligned with the CAS Exam 9 (Risk Management for Actuaries) syllabus.

Definition: Let $\Pi$ be projected annual risk-adjusted profit, $K$ be the unit’s allocated economic capital, and $h$ be its annual hurdle rate. For $K>0$, the capital return is $\operatorname{RAROC}=\Pi/K$. Economic profit is $\operatorname{EP}=\Pi-hK$. The hurdle profit, or profit required to meet the hurdle, is $hK$. A unit meets the hurdle exactly when $\Pi=hK$, equivalently when $\operatorname{RAROC}=h$ or $\operatorname{EP}=0$.

Use profit and capital measured on a consistent basis: the same currency, business scope, and planning horizon. In the examples, amounts are in millions of dollars and profits are annual projections. No interest discounting, mortality assumption, or loss distribution is used; the figures are deterministic planning inputs. In practice, the profit definition, capital measure, and hurdle rate should follow the organization’s approved framework.

From a Hurdle Rate to an Operating Target

Once a unit’s capital allocation and hurdle rate are set, the minimum profit target follows directly. Multiply the capital by the hurdle rate. The difference between this target and projected profit indicates the size of the planning gap; it does not, by itself, specify which operating action will close that gap.

\Pi_{\text{target}}=hK,\qquad \text{profit gap}=hK-\Pi=-\operatorname{EP}.

A positive gap means projected profit is below the hurdle target. A negative gap means projected profit exceeds that target. Business plans can address a positive gap through suitable profit improvements, changes in the amount or mix of business, or a reduction in capital needs. Any change must be evaluated using both its effect on profit and its effect on allocated capital.

Worked Example: Setting Targets Across Two Units

A hypothetical insurer uses a 10% annual hurdle for two product units. Unit A has projected annual risk-adjusted profit of $12.0 million and allocated capital of $100 million. Unit B has projected profit of $7.2 million and allocated capital of $80 million. Calculate each unit’s target profit and economic profit, then assess a proposed growth plan for Unit A that adds $1.1 million of annual profit and $15 million of capital. All figures are one-year deterministic planning projections; no interest rate, mortality assumption, or probability distribution is applied.

Method. Apply the hurdle to each unit’s capital, then recalculate profit and capital together for the proposed plan. The common mistake to avoid is counting additional profit while leaving the associated capital unchanged.

For Unit A, the hurdle profit is $0.10(100)=\$10.0$ million. Its economic profit is $12.0-10.0=\$2.0$ million, and its RAROC is $12.0/100=12.0\%$.

For Unit B, the hurdle profit is $0.10(80)=\$8.0$ million. Its economic profit is $7.2-8.0=-\$0.8$ million, and its RAROC is $7.2/80=9.0\%$. Unit B’s projected profit is therefore $0.8 million below its hurdle target.

Under Unit A’s growth plan, profit becomes $12.0+1.1=\$13.1$ million and capital becomes $100+15=\$115$ million. The new hurdle profit is $0.10(115)=\$11.5$ million. Economic profit is $13.1-11.5=\$1.6$ million, and RAROC is $13.1/115\approx11.3913\%$, or 11.39% to two decimal places.

The growth adds $1.1-0.10(15)=-\$0.4$ million of economic profit relative to Unit A’s original plan. Thus, the unit still exceeds the hurdle overall, but this particular growth increment reduces its economic profit. As a check, the total for both units before the growth plan is profit $12.0+7.2=\$19.2$ million and capital $100+80=\$180$ million, giving economic profit $19.2-0.10(180)=\$1.2$ million. After adding Unit A’s growth, the total is profit $20.3 million and capital $195 million, so economic profit is $20.3-19.5=\$0.8$ million, a decrease of $0.4 million as calculated.

How Plan Changes Affect Economic Profit

Let a proposed plan change projected profit by $\Delta\Pi$ and allocated capital by $\Delta K$, where a contraction can have negative values for both. If the hurdle $h$ remains fixed, the new economic profit is:

\operatorname{EP}_{\text{new}} =(\Pi+\Delta\Pi)-h(K+\Delta K) =\operatorname{EP}_{\text{old}}+\Delta\Pi-h\Delta K.

This identity is a useful planning check. It follows by substituting the changed profit and capital into the definition of economic profit and rearranging terms. If the hurdle also changes, use the new hurdle directly: $\operatorname{EP}_{\text{new}}=(\Pi+\Delta\Pi)-h_{\text{new}}(K+\Delta K)$; the fixed-hurdle change identity no longer applies as written.

Establish the baseline.
Record current projected profit, allocated capital, hurdle rate, RAROC, and economic profit on a consistent basis.

Specify the plan’s effects.
Estimate the change in profit and the change in allocated capital. Do not infer capital relief from a profit reduction or assume capital changes in the same proportion as exposure.

Recalculate the target and return.
Apply the appropriate hurdle to post-plan capital, then calculate post-plan profit, RAROC, and economic profit.

Reconcile the result.
Check that the change in economic profit equals $\Delta\Pi-h\Delta K$ when the hurdle is unchanged.

The calculation does not establish that a proposed plan is operationally feasible or that the assigned capital change is correct. Capital may reflect diversification, limits, risk mix, or other features of the portfolio. Use the capital allocation produced under the organization’s approved method; do not treat unit capital as automatically additive or assume a departing segment releases exactly its prior allocation without support.

Worked Example: Planning a Hypothetical Contraction

A hypothetical specialty unit has projected annual risk-adjusted profit of $8.4 million and allocated capital of $90 million. Its hurdle rate is 9%. A proposed contraction is expected to reduce unit profit by $2.7 million and allocated capital by $30 million, based on the approved planning allocation. Find the original and post-contraction RAROC and economic profit. All amounts are in millions of dollars; the projections are deterministic for one year, with no interest, mortality, or loss-distribution assumption.

Method. Recalculate the whole unit after applying both changes. The common mistake to avoid is comparing the post-contraction return with the contribution-to-capital ratio of the segment being removed as though that ratio were the original unit’s RAROC.

Before contraction, the unit’s RAROC is $8.4/90=9.333\ldots\%$, or 9.33% to two decimal places. Its hurdle profit is $0.09(90)=\$8.1$ million, so its economic profit is $8.4-8.1=\$0.3$ million.

After contraction, projected profit is $8.4-2.7=\$5.7$ million and allocated capital is $90-30=\$60$ million. The post-contraction RAROC is $5.7/60=9.5\%$. The new hurdle profit is $0.09(60)=\$5.4$ million, so post-contraction economic profit is $5.7-5.4=\$0.3$ million.

The whole unit’s RAROC rises from 9.33% to 9.50%, while its economic profit is unchanged. The removed segment’s contribution-to-capital ratio is $2.7/30=9.0\%$, not the specialty unit’s original RAROC. As a check, the removed segment’s economic-profit contribution at the 9% hurdle is $2.7-0.09(30)=0$, consistent with the remaining unit retaining the original $0.3 million of economic profit. This conclusion depends on the stated $30 million capital release being valid under the approved allocation.

Growth Plans Must Include Their Capital Requirement

A plan can increase profit and still miss its return target. For growth, calculate the new target from the new capital requirement, not from the baseline capital. The plan’s overall RAROC uses total post-plan profit over total post-plan capital; the change in economic profit shows whether that plan raises or lowers value relative to the hurdle.

Worked Example: Correcting a Growth-Plan Target

A hypothetical business unit has annual projected risk-adjusted profit of $6.3 million, allocated capital of $90 million, and a 9% hurdle. A growth plan adds $2.0 million of annual profit and $20 million of capital. Calculate the baseline target and shortfall, then find the post-growth profit, capital, hurdle profit, economic profit, and RAROC. The one-year figures are deterministic planning inputs; no interest rate, mortality assumption, or distribution is used.

Method. First calculate the target on current capital, then add both effects of growth before reassessing the hurdle. The common mistake to avoid is applying the hurdle to the original $90 million after the plan has raised capital to $110 million.

The baseline hurdle profit is $0.09(90)=\$8.1$ million. The current projected profit is $6.3 million, so the shortfall is $8.1-6.3=\$1.8$ million. Baseline economic profit is $6.3-8.1=-\$1.8$ million.

After growth, projected profit is $6.3+2.0=\$8.3$ million and allocated capital is $90+20=\$110$ million. The post-growth hurdle profit is $0.09(110)=\$9.9$ million. Therefore, economic profit is $8.3-9.9=-\$1.6$ million, and RAROC is $8.3/110\approx7.5455\%$, or 7.55% to two decimal places.

The growth improves economic profit by $2.0-0.09(20)=\$0.2$ million, from $-\$1.8$ million to $-\$1.6$ million, but the unit still falls short of the hurdle. The incorrect calculation $8.3-0.09(90)=\$0.2$ million leaves capital unchanged despite the stated $20 million addition. Using the correct $110 million post-growth capital gives $-\$1.6$ million. The post-plan target and shortfall reconcile: $9.9-8.3=\$1.6$ million.

Common Planning Traps

Holding capital fixed when the plan changes it. Recalculate the hurdle profit using post-plan capital.
Comparing unlike ratios. A segment’s profit-to-capital contribution is not the same as the whole unit’s RAROC. Name the numerator and denominator before making a comparison.
Treating a higher RAROC as proof of higher economic profit. RAROC is a ratio; economic profit is an amount. A change can affect them differently, so calculate both when the plan calls for both.
Assuming allocated capital releases mechanically. Use an approved post-change allocation; capital can depend on portfolio composition and diversification.
Mixing planning bases. Compare annual profit with the annual hurdle applied to consistently defined capital, and keep the business scope consistent before and after the plan.

Key takeaway: Set the profit target as hurdle rate times allocated capital. For any growth, retention, or contraction plan, update both profit and capital, then check the post-plan return and economic profit. At a fixed hurdle, the change in economic profit is exactly $\Delta\Pi-h\Delta K$.

Check Your Understanding

Use annual amounts in millions of dollars. Unless a question says otherwise, treat projections as deterministic one-year planning inputs with no interest, mortality, or loss-distribution assumption.

A unit has allocated capital of $64 million, projected annual risk-adjusted profit of $5.12 million, and an 8.5% hurdle. Find its hurdle-profit target, profit gap, and economic profit. (Answer: target $5.44 million; gap $0.32 million; economic profit $-\$0.32$ million.)
A unit earns projected profit of $9.6 million on $120 million of capital at an 8% hurdle. A plan adds $1.4 million of profit and $25 million of capital. Find post-plan profit, capital, RAROC, and economic profit. (Answer: profit $11.0 million; capital $145 million; RAROC $11/145\approx7.586\%$; economic profit $-\$0.60$ million.)
A unit has profit of $4.8 million and capital of $50 million at a 9% hurdle. A hypothetical contraction reduces profit by $1.35 million and capital by $15 million. Find post-contraction RAROC and economic profit, and compare its economic profit with the baseline. (Answer: post-contraction profit $3.45 million and capital $35 million; RAROC $3.45/35\approx9.857\%$; economic profit $0.30 million, unchanged from baseline.)
Two units have, respectively, profit/capital of $7.0/$70 million and $4.5/$60 million. At a common 9% hurdle, a plan for the second unit adds $0.8 million of profit and $5 million of capital. Find combined post-plan profit, capital, and economic profit. (Answer: profit $12.3 million; capital $135 million; economic profit $12.3-0.09(135)=\$0.15$ million.)
A unit has profit of $12 million and capital of $150 million at an 8% hurdle. A contraction reduces profit by $1.1 million and capital by $20 million. Calculate the change in economic profit and confirm it using the post-plan figures. (Answer: economic profit increases by $0.50 million; post-plan profit $10.9 million, capital $130 million, and economic profit $10.9-0.08(130)=\$0.50$ million.)

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