Background

//CAVISor (CEI)is a rental agency witha number oflocations in the NY,NJ,PA areaand is currentlyowned by a VC firm from Chicago called WindyCity Investments, LLC. WindyCity specializesinregional firms and has investments inmanyregions and in many product areas. It has over$500millionincash reserves which it can use for strategic purchases of new regional companies.Nearly 100 percentof its revenue comes from rental receipts. A small portion also comes from insurance offered to clients if they desire coverage.

//CAVISisa big-smallcompany.AVIS Car Rental, for example,has 550,000 cars worldwide while//CAVIShas 15,000total cars all withinin the Tri-State area.In the Tri-State area, //CAVIS is well known with about a 5% market share.The CEO, Maria Garcia, has convincedthe board that the company's strength is local ownership and control over its fleet.There are more airports in the region, so there is room for growth. The business is one basedalmost solelyon price, so//CAVISneeds to be aware of costs.//CAVISisattempting to attract a bigger percentage of the business travel market as there is less price sensitivity for business travel. However, recent concerns about inflation are again making Ms. Garcia concerned about costs.

WindyCity is think of selling //CAVIS to a Sky Resorts Inc. a family-owned business with operations in the Poconos. The company runs a couple ofresorthotels and restaurants in the region. Sky Resorts has four major shareholders withanapproximately equalownershipshare and is run byErica Hoffman. Ms. Hoffman has 30 years' experience in the tourism industry and was hired to take Sky Resorts to the next level. Sky Resorts would finance the purchase of //CAVIS from cash and a loan.The company wouldbehighly leveraged after the purchase.

//CAVISundertooksomeanalysis ofitsoperationswith the help of Phillis-Powers (PP) a well-known actuarial consulting firm.PP has estimated that//CAVIS'scashflow "Beta" suggests thatitscash flows areriskierthan the market's cash flows. Normally a beta is estimated for a publicly traded company and that is the relationship between our returns and the markets returns. In our case, since we are privatelyowned,we do not have a stock price and thus PP has attempted to see how our cash flow relates to the market portfolio cash flows.PPestimatesthebeta to be 1.5 which suggests that//CAVIS'scash flows are more volatilethanthemarket's.

Analysis

PPbuilta Monte-Carlo simulationmodelfor//CAVISto help in decision making. ...

Page 2 contains a number of exhibits for the company. At the top of the page there are two items of note.PP prepared this document not knowing our risk attitudes or risk appetite, so it gave us a little bit of latitude by allowing us to change the z score and talk about the different results.The first is a grey area with a user input. In this gray are you can change the critical value for a risk tolerance exercise.As the probability increase the z score increases and this z score measures the distance from the mean of a distribution. Thus, the higher the probability, the higher the z-score and the larger is the loss at that level relative to the mean.The second item is the total number of cars inthefleet. It is for information purposes only.

Exhibit1.

From this fiscal year's loss analysis, we have found the following.//CAVIS'sfleetexperienced 2,212 accidents with an average damage per car of $3,055. Our total losses across our fleet of 15,000 cars was $6.76 million.Our problem is that we do not really know our standard deviation of our total losses.PPhave estimated it to be about $770,000 and havealsoestimatedour standard deviation for our accidents to be about45.But there is a good deal of uncertainty about these estimates. PP permits us to change these estimates to see how sensitive our results are to change in the "risk".

Exhibit2.

The exhibit has three main parts. Part 1 shows the results of a Monte Carlo analysis of our total lossesgiven the assumptions about the standard deviation for the number of accidents per year and the standard deviation of the losses. These are then allocated to eh cost per damaged car and the cost per car. The cost per car is like the expected cost of an accident to any given car, while the cost per damaged car is the actual cost per damaged car.(PressingF9 will update the analysis, if you change anything, please press F9 for an update).

//CAVIShas the PP principal for this project come in. This is a summary of ColleenO'Grady's presentation.

"PP presents two methods of assessing the potential size of the risk. Recall, a definition of risk is the deviation from what is expected. If one assumes the distribution oflossesis normally distributedone might worry about losses greater than what we would expect 95 (or 99) percent of the time. The Red line on the two graphs shows that level of loss. It is chosen by theanalystin Cell E4 and is used as a guide point for discussion.

The other metrics are percentiles. The 99^thpercentile, for example,would be the loss at the 99^thoutof 100 losses. Thismetricis not based on probability but a mere rank from 1to 100. We might use this if we 1) wanted to look at absolute loss levels rather than the loss is the top x% in terms of probability.Or 2) the data is not normally distributed ... and thus we need a metric for extreme risks.

Graph 2a is part 3 shows the distribution of the losses. With our current assumptions of the number of accidents having a std deviation of45and the standard deviation of total losses having a standard deviation of $770,000,Graph 2A looks normal. But it might not be normal looking if the assumptions are changed.

Graph 2B shows the same data in a different way. This is a cumulative distribution of the probability of a loss. Where the various horizontal lines intersect the cumulative distribution is the probability of a loss of that size. For example, the red linewhich reflects the z score 95 percent probability and the teal line which is the 90^thpercentile in terms of rank shows up around the 77^thpercent of probability. This is becausemost ofthe losses are near the mean and the percentile will be closer to the mean than the 95^th% in terms of probability. If you changeassumptions,you might see different results.

Finally, the Amt above Expected is the level oflossat a given level (corresponding to the colored lines) above the average. One can use this as a measure of risk to help us understand our tolerance for risk."

77%

95%

Exhibit3

Ms. O'Grady also provided data from our annual report she thought might be useful. This includes revenues and expenditures for last year.

Exhibit4

This exhibit is PP's analysis of LBI's pricing for last year. Since we haveallthe loss data, PP had to estimate the other components of//CAVIS'sbilledpremium.This is presented on a per car basis for convenience.

Ms.O'Grady gave an overview of how insurance companies set the priceriskas she shows LBIs price in Part A.

Insuranceis a mark-up business. The mark up is based upon the Expectedlosses,butthe components of the markup differ. Firstthereare claims adjustment expenses. This is the cost ofdeterminingthe loss and paying the claim. For a company like//CAVISthereare few (or no disputes)with theinsurer and thus this is just the cost of managing the repair of the car. Second, there is a risk charge. This is a serious charge and covers the insurer for the likelihood that the losses areactually higherthan expected. So, business with large variances willhavebigger risk charges. Automobile property damage is alowvariance business where the variance is driven by weather conditions and damage from robbery. From discussion with LBI, PP believes that//CAVISis charged the samerisk charge as all other customers. Profit is amakeupthat issupposedto cover thereturn to shareholders. Commissions are paid to the broker who arranges the coverage and shops and negotiates on//CAVIS'sbehalf. Taxes are paid to the state where the contract is signed and is1-2% in most states. The taxes are based on premiums and operate like a sales tax.

During this period//CAVISreceived two quotes for renewal. One was the same contract, but it had a premium increase ofabout 21%. The broker told us that this wasa fair priceand that most commercial carriers lost money last year and with the expectations concerning inflation the price would have to increase.

However, the broker also said the LBI could offer//CAVISanother contract with a deductible of $1 Million and it would have a price of $604 per car.

Ms.O'Grady went on to talk about a self-insurance solution.

In part B, PP put together an analysis of how much it would cost to self-insure. She thought that since//CAVISonly had three cars types the costs of claims adjustments would be lower. In addition, there were no negotiating costs or delay is assessment of the claims, so the mark-up wouldbelower. She also thought thatthe risk charge could be lower for//CAVIS.

Ken Brett, the CFO, said that he thought thatmaybe therisk charge should be higher since LBI hada largepool of cars and that//CAVISonly had 15,000 cars. She said, that may be true, but that risk charge is really based upon what//CAVISthought the risk charge should be based uponitsown numbersand risk tolerance.Ms. O'Grady mentioned that the owner'sof//CAVIStolerated a good deal of risk. She went on tosay she thought the//CAVIScash flow beta was high relative to LBIs.In addition, Ms. O'Grady mentioned that//CAVISwould"keep"the risk charge anyway.

Ms. O'Grady concluded by saying that self-insurance would save//CAVISmoney and PP's estimates were about $4 million plus a risk charge of nearly 60,000.

Exhibit5.

Mr. Brett provided Exhibit 5. These are the expected insurance revues which amount to about $200 per car. Mr. Brett state that he though this was a good estimate as it was based on historical data. He did not provide any information about the standard deviation.The industry rental rate of a car ranges from 70-80 percent,whichis a car is likely to be rented about 70-80 percent of the time. For Mr. Brett this means that the typical car is rented almost 274 days a year.//CAVIScharges $20/day to cover property damage to the car. About 1 in 20 clients purchasedthe insurance.This providesanexpectation of about $205 per car each year of insurance revenue which translates into about3million in additional revenue for the fleet.

Auto Physical Damage

Z Score

Dashboard

prob: User Input {.90,.99}

A measurement of deviaton from the mean

Size of Fleet

15,000

cars

CAVIS

0.95

1.645

Exhibit 1

User Input Std Deviation

N of accidents in Fleet per year

2212

45

<-Any Number can go here

Average Damage per car

3,055

Annual Expected Loss per car

450.511

15000

cars

6,757,660

770,000

<-Any Number can go here

Exhibit 2

1)

Results

Loss severity

Per damaged car

Per all cars

Average per simulation

6,790,021.152

3,216.195

6,829,482.771

Std deviation =sqrt(variance)

1,000,000

342.975

50.577

Level of Losses At prob or p-tile

Amount Above Expected

2)

Assuming Normal Distribution, "Risk Tolerance" =f(prob)

8,434,874.779

Red line in Chart

1,644,853.627

Percentile loss = 99 percentile

8,500,000

Green

1,709,978.848

Percentile loss = 95 percentile

8,000,000

Purple

1,209,978.848

Percentile loss = 90 percentile

7,750,000

Teal

959,978.848

3)

Exhibit 3

Fiscal Year

Revenues and Expenditures

July 2021-June 2022

Revenue

218,000,000

Revenue /car

14,533.333

Expenditures

178,100,000

Net Income

39,000,000

Net Income/ Car

2,600

Exhibit 4

Part A

Liberty-Bibity, INC (LBI)

Profits are a mark up of

3%

percent

Commissions are a markup of

6%

percent

Typical Commission rate

Claims Adjustment Cost are a mark up of

17.00%

percent

Based on Industry Loss adjustment expenses

Risk Charge is based upon LBI's risk tolerance

9%

percent

Based on an industry average for commercial auto business

Premium taxes are a percentage of premiums

2%

percent

Based on typical state rate

Allocated Costs per car

Per Car Premium

E[L]

Claims Adjust

0

Profit

Commissions

Taxes

Premium this Year

594.983

=

455.299

77.401

4.552

13.659

33.055

44.073

Option for renweal with same terms except premium

Per Car Premium Next Year

716

Option w/ 1 Million deductable

Per Car Premium Next Year

603.6

Part B

CAVIS Self Insurance Options

Profits are a mark up of

0%

percent

Commissions are a markup of

0%

percent

Claims Adjustment Cost are a mark up of

9.0%

percent

Risk Charge is based upon LBI's risk tolerance

8.0%

percent

Premium taxes are a percentage of premiums

0%

percent

Per Car

E[L]

Claims Adjust

0

Profit

Commissions

Taxes

Prem

500.322

=

455.299

40.977

4.046

0

0

0

Difference: LBI Quote - Self Insurance

Difference (per car)

94.661

Total Fleet Savings

1,419,922.417

Risk Charge Captured

60,692.864

Exhibit 5

Part C.

Sources of Revenues

"Insurance" Payments to CAVIS from client Per Car

Typical rental rate of a car per year

0.75

Typical Days Rented

273.75

Typical Daily Insurance premium

20

Likelihood of Client Insurance Purchase

5%

Expected "insurance" revenue per car

205.313

Expected Fleet Insurance Revenue

3,079,687.5

Questions

1.How would you assess //CAVIS's risk tolerance?

1.Is //CAVIS able to bear the risk it currently has? On what basis do you make that conclusion?

2.What more would you like to know?

3.How would your answer change if Sky Resorts purchased //CAVIS?

2.In last week's handout, we saw that //CAVIS has different classes of cars andperhaps differenttypes of loss. Is this information relevant? What might you ask PP to do next?

3.Let'spretend there is no lost revenue for a rental car being repaired as we know that cars can be rented approximately 70-80 percent of the time. Should //CAVIS self-insure, take the high-cost contract, or should it take the contract with a deductible? Does the choice affect the cost of risk to //CAVIS? Provide a rationale for your conclusion.