0 Allocating the Cost of Capital Practical Examples Daniel Isaac CAS Spring Meeting May 19-22, 2002.

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Allocating the Cost of CapitalPractical Examples

Daniel Isaac

CAS Spring MeetingMay 19-22, 2002

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Practical Applications

You’ve Determined how to Allocate the Cost of Capital

Now what?

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Practical Applications

Two Primary Actuarial Applications

• New Business Pricing

• Acquisition and/or Divestiture

Other Possible Uses

• Performance Measurement

• Incentive Compensation

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New Business Pricing Example

DFAIC Company

• Basis for 2001 DFA Call Paper

• Results Presented in “DFA Insurance Company Case Study: Parts I and II”

• Available on the CAS web site at: http://www.casact.org/pubs/forum/01spforum/01spftoc.htm

http://www.casact.org/pubs/forum/01spforum/01spftoc.htm




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Key Information

• Five Main Lines of Business

• Allocated Capital to Lines based on

- Tail Conditional Expectations (TCE)

- Shapley Methodology

• Estimated Cost of Capital at 7.7%

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Recap of DFAIC

Asset SummaryInvested Assets

Book Value: $4,702 millionMarket Value: $4,746 million

Fixed Income Analysis Average Maturity: 9.2 yearsDuration: 5.3 years

Asset Mix

7%6%

5%

17% 1%

64% Cash

Common Stock

Preferred Stocks

Governments

Corporates

Other

1999 Underwriting Summary• Loss & LAE Reserves

$ 2,330 million

• Direct Written Premium $ 2,565 million

• Net Written Premium $ 2,350 million

• Booked Accident Year Loss&LAE Ratio

Gross

86.3%Net

82.0%

• Expense Ratio (including

policyholder dividends)

29.5%

9%

28%

10%

22%

31% Workers CompAuto LiabHome/CMP(Prop)Auto Phys DamGL/CMP(Liab)

Distribution of Net Earned Premium1999

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Step 1: Calculate Underwriting NPV

• Project Underwriting Cash Flows

• Discount After-Tax Results at Cost of Capital

• Need a Positive NPV at this stage, regardless of Allocation Methodology

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Line NPV % of PremiumWC 1,378 0.6%Auto Liab -46,671 -6.1%Prop -24,486 -4.1%Auto Phys Dam 18,198 2.9%GL 31,372 11.9%

Step 1 - Results:

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Step 2: Calculate Net Capital Cost

• Allocate Capital based on Selected Methodology

• Determine timing of Capital flows

- For this example, entire amount is held for one year

• Determine Net Cost of Carrying Capital

- Capital can be invested in assets

- Net cost is excess of cost of capital over after-tax returns

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Step 2 - Results

Line % of Capital CapitalWC 39.6% 739,341Auto Liab 25.5% 474,984Prop 11.0% 204,564Auto Phys Dam 3.1% 57,923GL 20.9% 389,084

Total 100.0% 1,865,896

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Step 2 - Results

Line Net Capital Cost Excess Profit % of PremiumWC -19,839 -18,461 -8.0%Auto Liab -12,746 -59,417 -7.7%Prop -5,489 -29,975 -5.0%Auto Phys Dam -1,554 16,644 2.6%GL -10,441 20,932 7.9%

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Step 3: Calculate Indicated Rate Change

• Price to no Excess Profit

- At that level, prices meet company’s cost of capital

• Change in Excess Profit = Rate Change * (1 - Variable Expense Ratio) * (1 - Tax Rate ) * Discount Factor

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Step 3 - Results

Line Excess Profit Rate ChangeWC -18,461 16.9%Auto Liab -59,417 16.4%Prop -29,975 10.5%Auto Phys Dam 16,644 -5.5%GL 20,932 -16.8%

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Refined Approach

• Capital is Needed to Support Risk

- Therefore, some capital should back reserves

• Associated Cost arises Directly out of the Decision to Write the Business

- Needs to be factored into the pricing

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Refined Approach (cont.)

• Proposed Fix

- Split each line’s allocation between reserves and premium

- Convert reserve capital to a portion of current reserves

- Capital cash flows now include:

– An initial (smaller) amount due to premium

– Ongoing amounts associated with reserves

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Refined Approach - Results

LinePremium

CapitalReserve Capital % of Reserves

WC 15.3% 24.3% 81.0%Auto Liab 15.0% 10.4% 21.1%Prop 7.8% 3.2% 18.8%Auto Phys Dam 2.3% 0.8% 17.4%GL 8.9% 12.0% 49.4%

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Impact on Indicated Rate Change

Line Baseline RevisedWC 16.9% 14.6%Auto Liab 16.4% 16.5%Prop 10.5% 10.4%Auto Phys Dam -5.5% -5.6%GL -16.8% -17.2%

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Impact on Workers Comp

Item Baseline RevisedInitial Capital 739,341 286,254Total Capital 739,341 786,789Capital Cost -19,839 -17,371Rate Change 16.9% 14.6%

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Question: Why bother?

Answer: Reduces Pricing Distortions across Accident Years and Lines of Business

Example: What would happen to indications if DFAIC didn’t write any new Workers Comp?

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No New Workers Comp - Results

Line BaselinePremium

CapitalReserve Capital

WC N/A N/A 28.7%Auto Liab 42.2% 17.8% 12.3%Prop 18.2% 9.2% 3.8%Auto Phys Dam 5.1% 2.8% 0.9%GL 34.5% 10.5% 14.2%

Total 1,579,642

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No New Workers Comp - Results


Line Baseline RevisedAuto Liab 1.4% 0.0%Prop 0.8% 0.0%Auto Phys Dam 0.2% 0.0%GL 3.4% 0.0%

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Divestiture Example

Question: What if you can’t get the rates you need?

• Another Option is to shut down or sell off the Line

• Becoming Increasingly common in Today’s fast paced Market

Key to Analysis is Comparing Results Before and After Decision

• In this case, consider DFAIC with and without Workers Comp

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Divestiture Example

Results

Item Baseline Without WCRequired Capital 1,865,896 1,205,693Non-WC Capital 1,126,555 1,205,693Excess Profit -67,289 -58,155Without WC -51,296 -58,155

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Divestiture Example

Results


Line Baseline Without WCAuto Liab 16.5% 17.2%Prop 10.4% 10.9%Auto Phys Dam -5.6% -5.0%GL -17.2% -16.2%

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Divestiture Example

Reason for Differences

• Capital Calculation

- Pricing uses allocated capital

- M&A uses marginal capital

- Can get even bigger differences between lines if the “after” capital is reallocated

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Divestiture Example

Reason for Differences (cont.)

• Costing Methodology

- Pricing uses full costing

- M&A uses marginal costing

– No change in total fixed costs

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Allocating the Cost of CapitalPractical Examples

Daniel Isaac

CAS Spring MeetingMay 19-22, 2002

0 Allocating the Cost of Capital Practical Examples Daniel Isaac CAS Spring Meeting May 19-22, 2002.

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