Download - 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
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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
Refined Approach - Results
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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New Business Pricing Example
Refined Approach - Results
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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New Business Pricing Example
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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New Business Pricing Example
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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New Business Pricing Example
No New Workers Comp - Results
Impact on Indicated Rate Change
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
Impact on Indicated Rate Change
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