Analysis 5 and 6

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Risk Analysis Applications I

Learning Objectives

1. Explain the purpose of a net present value cost-benefit analysis and its importance to a risk management program. (p. 2)

2. Understand how to calculate a net present value cost-benefit analysis in risk management applications. (p. 5)

3. Understand how to calculate ultimate total losses by applying development and inflation factors to total incurred losses. (p. 21)

4. Discuss the importance of exposure bases in forecasting and trending and calculate indexed ultimate total loss rates. (p. 24)

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Learning Objective #1: Explain the purpose of a net present value cost-benefit analysis and its importance to a risk management program.

I. Review of Analytical Techniques

A. The purpose of a NPV cost-benefit analysis is to evaluate a project or option by determining if the PV of expected inflows exceeds the PV of expected outflows

B. Examples of cash flows

1. Inflows

a. Premium reductions – a reduction in a cash expense has the same effect as an increase in revenues

b. Tax reductions – a reduction in tax has the same effect as an increase in revenues

c. Loss payment reductions resulting from an investment in safety equipment or training – a reduction in loss payments has the same effect as an increase in revenues

d. Non-cash expenses (ex. depreciation) – have the same effect as an increase in revenue; the expense deduction lowers tax but there is no reduction in cash from the expense itself

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2. Outflows

a. Cost of safety equipment

b. Cost of training

c. Paid losses, premiums, expenses

C. Important risk management applications

1. Decisions related to investments in equipment and training

2. Decisions related to risk financing options

D. General risk treatment option analysis

1. Develop losses

a. Develop losses through triangulation using an organization’s own data

b. Develop losses using industry factors

c. Combination and weighting of both

2. Forecast or project losses

a. Develop incident rates using exposures and losses

b. Project frequency using average incident rates or regression

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c. Trend severity (index for inflation)

d. Project severity, using average severity or regression

e. Project expected total losses (frequency times severity)

f. Consider using ranges based on confidence intervals or high-low estimates

g. Consider capping losses

3. Determine payout pattern of projected losses

a. Using organization’s data

b. Using industry factors

c. Combination and weighting of both

4. Calculate and compare NPV of each option

E. Approaches to analysis

1. External – outsource the actual work; be sure to understand the process and results

2. Internal – use software, e.g., Excel, or specific application computer software, e.g., “@Risk,” “Instant Actuary,” etc.

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Learning Objective #2: Understand how to calculate a net present value cost-benefit analysis in risk management applications.

II. NPV Cost-Benefit Analysis in Risk Management Applications

A. Steps in the process

1. Determine cash outflows, such as

a. Cost of safety equipment

b. Cost of training and professional fees

c. Paid losses and related expenses or premiums

2. Determine cash inflows, such as

a. Premium reductions (reduction in premiums has the same effect as an increase in revenues)

b. Tax reductions (reduction in taxes has the same effect as an increase in revenues)

c. Loss savings specifically tied to safety equipment or training investments

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3. Calculate NPV using the organization’s discount rate (WACC or CFO’s prerogative) and compare PV of cash outflows to PV of cash inflows

4. Calculate the impact of taxes on cash outflows and inflows including the after-tax effect of depreciation

5. Calculate PV of tax impact on cash outflows and inflows

6. Determine after-tax NPV by comparing after-tax PV of cash outflows and inflows

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Skills Application Scenario #12

1. Incurred losses (valued as of 12/31/X5), including reserves for loss adjustment expenses, are as follows:

01/01/X3  12/31/X3 $67,000 01/01/X4  12/31/X4 $49,000 01/01/X5  12/31/X5 $41,000

Revenues have been stable. Frequency has been relatively consistent.

a. Are you satisfied that losses are improving?

b. Development factors (to ultimate total loss) are 1.2, 1.4, and 1.8 for the three years. Compute developed losses.

c. Adjust the losses for inflation (based on 5% annually) to reflect X6 dollars.

2. Total projected losses for next year are $82,000, assuming operations are the same as in the past.

You believe you can install various safety measures, e.g., new machine guards, strips on floors for traction, and new ergonomic computer tables, which will significantly reduce losses.

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As a result, consider a $1,000 deductible program. Presume the deductible losses are remitted to the carrier after an average of one year’s use of funds.

The insurance program will change as follows, assuming loss improvement occurs as expected. Over time, less frequency should also result in less severity.

X6 Deductible credit of $15,000

X7 Deductible credit of $15,000 and experience credit of $15,000

X8 Deductible credit of $15,000 and experience credit of $20,000

Calculate the combined results of both introducing loss control measures and accepting a deductible. Assume a 10% cost of capital (discount rate).

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Net Present Value Cost-Benefit Analysis

Mary Donner, the risk manager, is concerned about the cost of injuries to the employees working on the receiving dock and in storage areas caused by improper lifting techniques. She thinks she has finally discovered a way to address the problem. The problem, as is often the case, is that the solution will cost a great deal of money.

An external safety consultant suggested that DCRI introduce the use of new high-tech lifting devices. Since these devices cost from $10,000 to $25,000 each, Mary agreed to try two units on a three- month trial basis at the Lake Tahoe location. The initial results seemed to be quite positive. The consultant and the manufacturer’s rep for the lifting units estimated a total cost of $300,000 to properly outfit all DCRI locations. The consultant projected a reduction in losses of 20% from the current level once the units are in place and the staff is trained in their use. Mary is assured the installation, training, and improvement in results can happen overnight. The expected life of the machines is five years. Mary decides to calculate the financial cost-benefit effects of purchasing the lifting devices.

DCRI has consistently experienced about 150 losses per year for the past five years, with three or four each year exceeding $25,000 ultimate costs except in year X3 when seven losses exceeded $25,000. Mary developed the loss data for those five years for these types of losses and determined average and expected losses of $500,414. She expects a reduction in the losses by 20%, regardless of size or frequency, in keeping with the representations made by the loss consultant and manufacturer’s rep.

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Working with her brokers, Rachel and Ralph, Mary learned the current premium allocated to that particular exposure is $400,000 annually.

Mary is preparing to make an analysis of this option, but she realizes she does not have adequate information.

1. What discount rate should she use?

2. What pattern of premium reduction might she expect, assuming the reduction of losses occurs as suggested?

3. What are the depreciation charges and effect of taxes?

Mary knows Sarah Parker, the CFO, should have this information. Sarah asks Mary to make the analysis using a discount rate of 12%, tax rate of 40% and the straight-line depreciation method.

Mary knows that 100% of the costs will be incurred immediately. She assumes, for simplicity in analysis, that savings, when they occur, will be received at the beginning of the appropriate year as well. Also, she assumes the tax savings will be received at the beginning of each appropriate year.

Rachel and Ralph tell Mary that the current insurance market for this class of business is “tough”. Underwriters will not reduce the premium this year, particularly since the last year was a loser. The underwriter feels that if the suggested improvement actually occurs, premiums will be reduced 10% the second year, then an additional 20% each of the next two years. No additional credit is likely in the fifth year, but a substantial premium reduction should have occurred by then, and premiums should be stable.

When she completed her analysis, Mary gave a copy of the report to Sarah, the CFO.

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INSURANCE SAVINGS CALCULATIONS

Year Estimated Prem.

Reduction (off prior year)

Estimated Projected

Premium $

Estimated Dollar

Savings $

X6 0% 400,000 -

X7 10% 360,000 40,000

X8 20% 288,000 112,000

X9 20% 230,400 169,600

X10 0% 230,400 169,600

Total Savings 491,200

Calculations

X7 X7 estimated premium reduction x X6 estimated projected premium = estimated dollar savings

10% x $400,000 = $40,000

X6 estimated projected premium – X7 estimated dollar savings = X7 estimated projected premium

$400,000 – $40,000 = $360,000 X8 [X8 estimated premium reduction x X7 estimated projected premium]

+ previous savings = estimated dollar savings in X8

[20% x $360,000] + $40,000 = $112,000

X7 estimated projected premium – [20% of X7 estimated projected premium] = X8 estimated projected premium

$360,000 – [20% x $360,000] = $288,000

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X9 [X9 estimated premium reduction x X8 estimated projected premium] + previous savings = X9 estimated dollar savings

[20% x $288,000] + $112,000 = $169,600

X8 estimated projected premium – [20% of X8 estimated projected premium] = X9 estimated projected premium

$288,000 – [20% x $288,000] = $230,400 X10 [X10 estimated premium reduction x X9 estimated projected

premium] + previous savings = X10 estimated dollar savings

[0% x $230,400] + $169,600 = $169,600

X9 estimated projected premium – [0% of X9 estimated projected premium] = X10 estimated projected premium

$230,400 – [0% x $230,400] = $230,400

Present Value Factors for Future Calculations

n 12% 15% 20% 1 0.893 0.870 0.833 2 0.797 0.756 0.694 3 0.712 0.658 0.579 4 0.636 0.572 0.482

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Notes

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NET PRESENT VALUE CALCULATIONS Discount Rate = 12%

Year Cost of Lifts

($) PV of Lifts

($) Insurance Savings $

Discount Factor

PV of Insurance Savings $

NPV ($)

X6 (300,000) (300,000) - -

X7 40,000 0.893 35,720

X8 112,000 0.797 89,264

X9 169,600 0.712 120,755

X10 169,600 0.636 107,866

Total (300,000) 353,605 53,605

X7 Insurance savings x discount factor = PV insurance savings $40,000 x 0.893 = $35,720

X8 Insurance savings x discount factor = PV insurance savings $112,000 x 0.797 = $89,264

X9 Insurance savings x discount factor = PV insurance savings $169,600 x 0.712 = $120,755

X10 Insurance savings x discount factor = PV insurance savings $169,600 x 0.636 = $107,866

Net Present Value

NPV = sum of PV of the lifts and PV of insurance savings ($300,000) + $353,605 = $53,605

Since the savings in insurance premiums is greater than the cost of the lifts resulting in a positive NPV, the project should be accepted.

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TAXATION CALCULATIONS (Assume Straight-line Depreciation)

Tax Rate = 40% Discount Rate = 12%

Depreciation of Lifts

Year Depreciation of

Lifts ($) Tax Savings $ Discount Factor

PV @12% ($)

X6 60,000 24,000 24,000

X7 60,000 24,000 0.893 21,432

X8 60,000 24,000 0.797 19,128

X9 60,000 24,000 0.712 17,088

X10 60,000 24,000 0.636 15,264

Total 96,912

Insurance Savings

PV insurance savings $ 353,605 Tax on the PV insurance savings (141,442) After-tax PV insurance savings $ 212,163

After-tax NPV

After-tax NPV = PV of lifts + PV tax savings + after-tax PV insurance savings

Outflows: PV of lifts $ (300,000) Inflows: PV of tax savings (depreciation) 96,912 After-tax PV of insurance savings 212,163

Total Inflows: $ 309,075

After-tax NPV $ 9,075

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NET PRESENT VALUE (NPV) CALCULATIONS Discount Rate = 15%

Year Cost of Lifts

($) PV

of Lifts Insurance Savings $

Discount Factor

PV of Insurance Savings $

NPV ($)

X6 (300,000) (300,000)

X7 40,000 0.870 34,800

X8 112,000 0.756 84,672

X9 169,600 0.658 111,597

X10 169,600 0.572 97,011

Total (300,000) 328,080 28,080

X7 Insurance savings x discount factor = PV insurance savings $40,000 x 0.870 = $34,800

X8 Insurance savings x discount factor = PV insurance savings $112,000 x 0.756 = $84,672

X9 Insurance savings x discount factor = PV insurance savings $169,600 x 0.658 = $111,597

X10 Insurance savings x discount factor = PV insurance savings $169,600 x 0.572 = $97,011

Net Present Value

NPV = sum of PV of the lifts and PV of insurance savings

$(300,000) + $328,080 = $28,080

Since the savings in insurance premiums is greater than the cost of the lifts resulting in a positive NPV, the project should be accepted.

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TAXATION CALCULATIONS (Assume Straight-line Depreciation)

Tax Rate = 40%

Discount Rate = 15%

Depreciation of Lifts

Year Depreciation of

Lifts ($) Tax Savings $ Discount Factor

PV @ 15% ($)

X6 60,000 24,000 24,000

X7 60,000 24,000 0.870 20,880

X8 60,000 24,000 0.756 18,144

X9 60,000 24,000 0.658 15,792

X10 60,000 24,000 0.572 13,728

Total 92,544

Insurance Savings PV insurance savings $ 328,080 Tax on the PV insurance savings (131,232) After-tax PV insurance savings $ 196,848

After-tax NPV

After-tax NPV = PV of lifts + PV tax savings + after-tax PV insurance savings

Outflows: PV of lifts $ (300,000) Inflows: PV of tax savings (depreciation) 92,544 After-tax PV of insurance savings 196,848 Total Inflows: $ 289,392

After-tax NPV $ (10,608)

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NET PRESENT VALUE (NPV) CALCULATIONS Discount Rate = 20%

Year Cost of Lifts

($)

PV of Lifts

($)

Insurance Savings ($)

Discount Factor

PV of Insurance Savings

($)

NPV ($)

X6 (300,000) (300,000) - -

X7 40,000 0.833 33,320

X8 112,000 0.694 77,728

X9 169,600 0.579 98,198

X10 169,600 0.482 81,747

Totals (300,000) 290,993 (9,007)

X7 Insurance savings x discount factor = PV insurance savings $40,000 x 0.833 = $33,320

X8 Insurance savings x discount factor = PV insurance savings $112,000 x 0.694 = $77,728

X9 Insurance savings x discount factor = PV insurance savings $169,600 x 0.579 = $98,198

X10 Insurance savings x discount factor = PV insurance savings $169,600 x 0.482 = $81,747

Net Present Value

NPV = sum of PV of the lifts and PV of insurance savings

$(300,000) + $290,993 = $(9,007)

Since the savings in insurance premiums are less than the cost of the lifts resulting in a negative NPV, it is a project that should not be accepted.

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TAXATION CALCULATIONS

(Assume Straight-line Depreciation) Tax Rate = 40%

Discount Rate = 20%

Depreciation of Lifts

Year Depreciation of

Lifts ($) Tax Savings

($) Discount Factor

PV @ 20% ($)

X6 60,000 24,000 24,000

X7 60,000 24,000 0.833 19,992

X8 60,000 24,000 0.694 16,656

X9 60,000 24,000 0.579 13,896

X10 60,000 24,000 0.482 11,568

Total 86,112

Insurance Savings PV insurance savings $ 290,993 Tax on the PV insurance savings (116,397) After-tax PV insurance savings $ 174,596

AFTER-TAX NPV

After-tax NPV = PV of lifts + PV tax savings + after-tax PV insurance savings

Outflows: PV of lifts $ ( 300,000) Inflows: PV of tax savings (depreciation) 86,112 After-tax PV of insurance savings 174,596

Total Inflows: $ 260,708

After-tax NPV $ (39,292)

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Recap of Previous Pages

Discount Rate

Non-Taxable Entity NPV

($)

Taxable Entity NPV

($)

12% 53,605 9,075

15% 28,080 (10,608)

20% (9,007) (39,292)

Effect of Discount Rates and Taxation

A. The higher the discount rate, the lower the NPV; the lower the discount rate, the higher the NPV

B. At any discount rate, a non-taxable entity has a higher NPV than a taxable entity

As discount rate increases, NPV decreases!

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Learning Objective #3: Understand how to calculate ultimate total losses by applying development and inflation factors to total incurred losses.

Self-Funding Analysis: DCRI

Sarah, the CFO, asked Mary, the risk manager, to perform an analysis to determine if self-funding the workers compensation exposures across the organization would make financial sense. Mary used the last five years of DCRI loss experience and exposures to calculate a projection. After consulting with the Human Resources department and Sarah, she learned that the payroll (exposures) was expected to increase by 9% for the next year. Mary also asked for a funding status review from the insurance carrier so she could perform the calculation as if the program had been funded for the past five years.

Self-Funding Analysis Exhibit SF-1

Year

Frequency Total

Incurred* ($) (a) (b)

X1 156 125,986

X2 115 469,091

X3 148 386,550

X4 192 291,555

X5 138 357,171

* Data is taken from the chart in Section 4, pg.3. Losses are from loss run with valuation

date of 12/31/X5 (not developed and not indexed for inflation).

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Self-Funding Analysis Exhibit SF-2

Year Freq. Total Incurred

($) Development

Factor

Ultimate Total Loss

($) (b  c)

(a) (b) (c) (d)

X1 156 125,986 1.00 125,986

X2 115 469,091 1.11 520,691

X3 148 386,550 1.30 502,515

X4 192 291,555 1.57 457,741

X5 138 357,171 2.51 896,499

Note: Development factors were calculated by triangulation in Section 4, pg. 26.

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Self-Funding Analysis

Exhibit SF-3

* A 12% inflation rate is used because of the high rate of inflation on medical costs. This rate would vary based on geographical location.

Year Freq. Total

Incurred $

Development Factor

Ultimate Total Loss $ (b  c)

Inflation Index

Factor*

Indexed Ultimate

Total Loss $ (d  e)

(a) (b) (c) (d) (e) (f)

X1 156 125,986 1.00 125,986 1.762 221,987

X2 115 469,091 1.11 520,691 1.574 819,568

X3 148 386,550 1.30 502,515 1.405 706,034

X4 192 291,555 1.57 457,741 1.254 574,007

X5 138 357,171 2.51 896,499 1.120 1,004,079

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Learning Objective #4: Discuss the importance of exposure bases in forecasting and trending and calculate indexed ultimate total loss rates.

Self-Funding Analysis

Exhibit SF-4

Year Freq. Total

Incurred $

Dev. Factor

Ultimate Total Loss $ (b  c)

Inflation Index Factor

Indexed Ultimate

Total Loss $ (d  e)

Exposure (Payroll $)

Indexed Ultimate

Total Loss Rate* (f / g)

(a) (b) (c) (d) (e) (f) (g) (h)

X1 156 125,986 1.00 125,986 1.762 221,987 12,350,000 0.0180

X2 115 469,091 1.11 520,691 1.574 819,568 13,910,000 0.0589

X3 148 386,550 1.30 502,515 1.405 706,034 15,204,000 0.0464

X4 192 291,555 1.57 457,741 1.254 574,007 17,112,000 0.0335

X5 138 357,171 2.51 896,499 1.120 1,004,079 18,080,000 0.0555

* Indexed Ultimate Total Loss Rate = the cost in losses per $1 in payroll adjusted for inflation

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Regression Analysis for Indexed Ultimate Loss Rates

SUMMARY OUTPUT Regression Statistics Multiple R 0.46699555 R Square 0.218084843 Adjusted R Square -0.042553542 Standard Error 0.01718157 Observations 5 ANOVA df SS MS F Significance F Regression 1 0.000247009 0.000247009 0.836733403 0.427783647 Residual 3 0.000885619 0.000295206 Total 4 0.001132628

Coefficients Standard Error t Stat P-value Lower 95% Intercept 0.03254 0.013308787 2.445001265 0.092088622 -0.009814538 X Variable 1 0.00497 0.005433289 0.914731329 0.427783647 -0.012321168

r2 = 0.218 is too low!

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Average of Indexed Ultimate Total Loss Rates

(0.0180 + 0.0589 + 0.0464 + 0.0335 + 0.0555)  5 = 0.0425 Projected payroll = $18,080,000  1.09 = $19,707,200 (1.09 represents expected increase in payroll) Projected losses for X6 are approximately: $19,707,200  0.0425 = $837,556

Self-Funding Analysis

Exhibit SF-5

Year

Indexed Ultimate

Total Loss $

Exposure (Payroll $)

Indexed Ultimate

Total Loss Rate (f / g)

(f) (g) (h)

X1 221,987 12,350,000 0.0180

X2 819,568 13,910,000 0.0589

X3 706,034 15,204,000 0.0464

X4 574,007 17,112,000 0.0335

X5 1,004,079 18,080,000 0.0555

(Projection) X6 837,556 19,707,200 0.0425

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Self-Funding Analysis Exhibit SF-6

Year Ultimate

Total Loss $* (b  c)

Losses Paid to Date ($)

Remaining Liabilities ($)

(d - i) ( d ) ( i ) ( j )

X1 125,986 74,581 51,405

X2 520,691 468,692 51,999

X3 502,515 205,474 297,041

X4 457,741 140,835 316,906

X5 896,499 142,895 753,604

(Projection) X6 837,556 - 837,556 * Ultimate Total Loss is the Total Incurred Losses times the Development Factor.

Losses are developed but not adjusted for inflation.

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Self-Funding Analysis Exhibit SF-7

Projected Losses ($)

Payout Periods

(months)

Est. Payout

Projected Payout

per Period ($)

(a x c)

12% Discount Factor

Discounted Payout $

(d x e)

Combined Discount Payout Factor

(c x e)

(a) (b) (c) (d) (e) (f) (g)

837,556 12 24% 201,013 0.893 179,505 21.4%

24 27% 226,140 0.797 180,234 21.5%

36 9% 75,380 0.712 53,671 6.4%

48 29% 242,891 0.636 154,479 18.5%

60 11% 92,131 0.567 52,238 6.2%

Total 100% 837,556 620,126 74% The difference between the projected payout of all losses (Col D) and those losses’ discounted payout (Col F) is specific to DCRI’s account specific payout patterns (calculated in Chapter 4, pg 28) and the given discount factor (12%). This combined discount payout factor allows the estimation of any future loss projection for DCRI in today’s dollars. The 74% factor will again be utilized in the deductible case study in Section 7.

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III. Additional Considerations

A. Certain payment of fixed premium on a date versus uncertain possible future payments, date, and amounts

B. Enough information to make an informed decision

C. Identify trends over a given period

1. Changes in exposure

2. Changes in loss rate

D. Confidence interval (standard deviation)

E. Ultimate total losses versus ultimate total losses plus confidence interval

F. Ability and willingness to pay

G. Other non-financial factors

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Skills Application Scenario #13

DCRI’s automobile liability program is renewing in several months. The current fleet of 206 vehicles consists of private passenger autos (100), limousines (52), vans (30), and SUVs (24).

The following data is from premium audits and loss reports:

Year # of Units Total Incurred

Liability Losses ($) # of Losses

X3 140 250,000 13 X4 145 277,000 15 X5 163 224,000 20

X6 206

Mary, the risk manager, calls Lucas Pacioli, the actuary with whom she has a business relationship, and Lucas gives her the loss development factors of 1.1, 1.3, and 2.0 for severity and an index (inflation) factor of 4% each year. How should Mary develop the Indexed Ultimate Total Loss Rate projected for year X6, the coming year?

How would Mary develop Indexed Ultimate Total Losses projected for year X6?

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Skills Application Scenario #14

Mary has received two renewal quotes for the payroll and loss data in Exhibit SF-5.

Quote #1 is for a fully insured plan. The premium is $950,000 payable the first of the month in 12 equal installments.

Quote #2 is for a deductible plan having a $25,000 deductible per loss with no aggregate. The underwriter believes that of the $837,556 of total losses expected in X6 that $217,500 will fall within the deductible range. The premium for this deductible plan is $625,000 and is to be paid in 12 equal installments. The projected payout of losses within the deductible is as follows:

0-12 mths 12-24 mths 24-36 mths 36-48 mths 48-60 mths

$52,200 $58,725 $19,575 $63,075 $23,925

Mary makes the assumption that the payout is made at year-end of each case.

Sarah, the CFO, advised Mary that the discount rate she should use is 12%.

Hints:

1. Consider using the PV of an annuity when calculating the discounted payment streams.

2. Assume the annual 12% discount rate will translate to a monthly discount rate of 1%.

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Review of Learning Objectives

1. Explain the purpose of a net present value cost-benefit analysis and its importance to a risk management program. (p. 2)

2. Understand how to calculate a net present value cost-benefit analysis in risk management applications. (p. 5)

3. Understand how to calculate ultimate total losses by applying development and inflation factors to total incurred losses. (p. 21)

4. Discuss the importance of exposure bases in forecasting and trending and calculate indexed ultimate total loss rates. (p. 24)

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Risk Analysis Applications I Appendix

© 2010. The National Alliance for Insurance Education & Research. All Rights Reserved. This outline or any part thereof may not be reproduced in any form or by any means or stored in any information retrieval system without the express written consent of the author.

This publication includes copyrighted material of Insurance Services Office, Inc. with its permission.

ANA:6:11/10 Appendix Page 1

Skills Application Scenario #12

1. Incurred losses (valued as of December 31st in third year), including reserves for loss adjustment expenses, are as follows:

01/01/X3  12/31/X3 $67,000 01/01/X4  12/31/X4 $49,000 01/01/X5  12/31/X5 $41,000

Revenues have been stable. Frequency has been relatively consistent.

a. Are you satisfied that losses are improving?

b. Development factors (to ultimate total loss) are 1.2, 1.4, and 1.8 for the three years. Compute developed losses.

c. Adjust the losses for inflation (based on 5% annually) to reflect X6 dollars.

Answer:

Year Loss $  Dev = Ultimate

Total Loss $  Index = Indexed Ultimate

Total Loss $

X3 67,000 1.2 80,400 1.158 93,103

X4 49,000 1.4 68,600 1.103 75,666

X5 41,000 1.8 73,800 1.050 77,490

ANA:6:11/10 Appendix Page 2

2. Total projected losses for next year are $82,000, assuming operations are the same as in the past.

You believe you can install various safety measures (new machine guards, strips on floors for traction, and new ergonomic computer tables) which will significantly reduce losses.

Cost of these measures is $50,000 (assume this is paid immediately). Assume losses less than $1,000 per occurrence will be reduced to $10,000 annually for each of the next three years, which is much lower than in the past. As a result, consider a $1,000 deductible program. Presume the deductible losses are remitted to the carrier after an average of one year’s use of funds.

The insurance program will change as follows, assuming loss improvement occurs as expected. Over time, less frequency should also result in less severity.

X6 Deductible credit of $15,000

X7 Deductible credit of $15,000 and experience credit of $15,000

X8 Deductible credit of $15,000 and experience credit of $20,000

Calculate the combined results of both introducing loss control measures and accepting a deductible. Assume a 10% cost of capital (discount rate).

ANA:6:11/10 Appendix Page 3

Answer:

Inflows: $ Discount Factor PV $ of Inflows X6 (current) 15,000 1.000 15,000

X7 30,000 0.909 27,270 X8 35,000 0.826 28,910

Total 71,180

Outflows: $ Discount Factor PV $ of Outflows

X6 (current) 50,000 1.000 ( 50,000) X7 10,000 0.909 ( 9,090) X8 10,000 0.826 ( 8,260) X9 10,000 0.751 ( 7,510)

Total ( 74,860)

NPV ( 3,680)

ANA:6:11/10 Appendix Page 4

Skills Application Scenario #13

DCRI’s automobile liability program is renewing in several months. The current fleet of 206 vehicles consists of private passenger autos (100), limousines (52), vans (30), and SUVs (24).

The following data is from premium audits and loss reports.

Year # of Units Total Incurred

Liability Losses ($) # of Losses

X3 140 250,000 13 X4 145 277,000 15 X5 163 224,000 20 X6 206

ANA:6:11/10 Appendix Page 5

Answer:

Year Freq Total

Incurred Dev.

Factor

Ultimate Total Loss $

Inflation Index Factor

Indexed Ultimate

Total Loss $

Exposure Units

Indexed Ultimate

Total Loss Rate

X3 13 250,000 1.1 275,000 1.125 309,375 140 2,210

X4 15 277,000 1.3 360,100 1.082 389,628 145 2,687

X5 20 224,000 2.0 448,000 1.040 465,920 163 2,858

X6 206

How would Mary develop Indexed Ultimate Total Losses projected for year X6?

500

1000

1500

2000

2500

3000

3500

X3 X4 X5 X6

Projected Indexed Ultimate Total Loss Rate for X6 is approximated (eyeballed) at $3,200 per vehicle. Therefore, projected total incurred losses are 3,200 x 206 = $659,200.

Ultimate Total Loss

Rate

Years

ANA:6:11/10 Appendix Page 6

Skills Application Scenario #14

Mary has received two renewal quotes for the payroll and loss data in Exhibit SF-5.

Quote #1: the first quote is for a fully insured plan. The premium is $950,000 payable the first of the month in 12 equal installments.

Quote #2: the second quote is for a deductible plan having a $25,000 deductible per accident with no aggregate. The underwriter believes that of the $837,556 of total losses expected in X6 that $217,500 will fall within the deductible range. The premium for this deductible plan is $625,000 and is to be paid in 12 equal installments. The projected payout of losses within the deductible is as follows:

0-12 mths 12-24 mths 24-36 mths 36-48 mths 48-60 mths

$52,200 $58,725 $19,575 $63,075 $23,925

Mary makes the assumption that the payout is made at year-end of each case.

Sarah, the CFO, advised Mary that the discount rate she should use is 12%.

Hints: Consider using the PV of an annuity when calculating the discounted payment streams. Also, assume the annual 12% discount rate will translate to a monthly discount rate of 1%.

ANA:6:11/10 Appendix Page 7

Answer: Fully Insured Plan (Quote 1) $950,000 annual premium paid in monthly installment of $79,167 per month. We will be assuming monthly premium installments are paid at the beginning of each month. Premium first month $950,000  12 = $ 79,167 (not discounted) 11 following months $ 79,167  10.368 = $ 820,803 (PV of Annuity, i = 1%, n = 11)

Total Discounted Payments $ 899,970

Deductible Plan (Quote 2)

$625,000 paid in monthly installment of $52,083 per month. Again we will be assuming the monthly installments are paid at the beginning of each month. We are also assuming that losses are paid at the end of the year. Premium first month $625,000  12 = $ 52,083 (not discounted) 11 following months $ 52,083  10.368 = $ 539,997 (PV of Annuity, i = 1%, n = 11)

Total Discounted Payments $ 592,080

Losses (assuming payout made at year end) Paid 0-12 months $ 52,200  0.893 = $ 46,615 (PV, i = 12%, n = 1) Paid 12-24 months $ 58,725  0.797 = $ 46,804 (PV, i = 12%, n = 2) Paid 24-36 months $ 19,575  0.712 = $ 13,937 (PV, i = 12%, n = 3) Paid 36-48 months $ 63,075  0.636 = $ 40,116 (PV, i = 12%, n = 4) Paid 48-60 months $ 23,925  0.567 = $ 13,565 (PV, i = 12%, n = 5)

Total Discounted Paid Losses $ 161,037

Total $ 753,117

ANA:6:11/10 Appendix Page 8

SIR Analysis: DCRI

Unlike workers compensation, DCRI has a history of retaining and self- administering its liability losses. Because of its nature, loss frequency is low but severity is always a concern.

Currently DCRI retains $1,000,000 per occurrence and $3,000,000 aggregate. There has been one loss that exceeded the per-occurrence retention and three other losses that exceeded $300,000 each.

Mary, the risk manager, senses she needs a “better plan”, as Sarah, the CFO, said in a meeting that DCRI needed a “better plan” in managing its cash flow. (Mary suspects that DCRI is preparing to expand or acquire another company.) However, Mary is not certain where to start.

DCRI has always carried high limits of general liability coverage in excess of the retentions, and Mary would like to see the impact of retaining $2,000,000 and $3,000,000 per occurrence.

She collected the loss and exposure data and began her analysis. After reviewing the insurance policies and discussing the account with her broker and the underwriter, Mary negotiated a composite rating basis of the average number of guests per day, or “heads on beds”, a term used in the hotel industry.

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