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

1 Practical Applications  You’ve Determined how to Allocate the Cost of Capital  Now what?

2 Practical Applications  Two Primary Actuarial Applications New Business Pricing Acquisition and/or Divestiture  Other Possible Uses Performance Measurement Incentive Compensation

3 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:

4 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%

5 New Business Pricing Example Recap of DFAIC Asset Summary Invested Assets Book Value: $4,702 million Market Value: $4,746 million Fixed Income Analysis Average Maturity:9.2 years Duration: 5.3 years 1999 Underwriting Summary Loss & LAE Reserves$ 2,330 million Direct Written Premium $ 2,565 million Net Written Premium $ 2,350 million Booked Accident Year Loss&LAE Ratio Gross86.3% Net82.0% Expense Ratio (including policyholder dividends) 29.5% Distribution of Net Earned Premium 1999

6 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

7 New Business Pricing Example  Step 1 - Results:

8 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

9 New Business Pricing Example  Step 2 - Results

10 New Business Pricing Example  Step 2 - Results

11 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

12 New Business Pricing Example  Step 3 - Results

13 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

14 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

15 New Business Pricing Example  Refined Approach - Results

16 New Business Pricing Example  Refined Approach - Results Impact on Indicated Rate Change

17 New Business Pricing Example  Refined Approach - Results Impact on Workers Comp

18 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?

19 New Business Pricing Example  No New Workers Comp - Results

20 New Business Pricing Example  No New Workers Comp - Results Impact on Indicated Rate Change

21 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

22 Divestiture Example  Results

23 Divestiture Example  Results Impact on Indicated Rate Change

24 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

25 Divestiture Example  Reason for Differences (cont.) Costing Methodology -Pricing uses full costing -M&A uses marginal costing –No change in total fixed costs

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