Maximum probable yearly aggregate loss

ASSIGNMENT02: RSK4803

Question 1 [50 Marks] Question 1 consists of 5 sub-questions, with a total of 50 marks. All the questions are based on the following case study.

Big Boy Ltd is a successful transport company with a network of customers mainly based in Gauteng, but has recently started to expand its operations nationally. The board of directors of Big Boy Ltd has decided to submit a tender to provide fuel to a new power plant in the Western Cape. The new plant was developed by a large national electricity supplier for providing additional electricity during peak periods. A subsidiary of Big Boy Ltd, Enron (Pty) Ltd was established to tender for the contract and to fulfil the contract if the tender was successful. Enron (Pty) Ltd won the tender 18 months ago to transport fuel to a new Open Cycle Gas Turbine (OCGT) power plant in Rheebok in the Western Cape.

Problems experienced

Enron has experienced a number of problems since the inception of the business. The media was scathing in their reports on the negative impact on the environment that may be caused by possible oil leaks which could pollute the beaches and negatively influence the marine life. The community is demanding compensation from Enron in this regard and has also threatened to damage the pipeline. The pipeline, which is visible on the beach, is easily accessible and anyone could interfere with the effective operation of pumping oil to the tanks.

The insurance premiums on the trucks has increased with 15% due to theft of fuel after the trucks left the depot and the number of accidents caused by Enron’s drivers. Fuel consumption of the trucks are also 10% higher than budget. A preliminary investigation indicated that possible causes are the road condition and driver practices.

Enron is defending a legal claim to repair the roads between Mossel Bay and Rheebok and the quantum is estimated at R20m. A community pressure group has also commissioned an environmental impact assessment on the noise pollution caused by the trucks.

Due to a low pay increase for blue collar workers, the competition is recruiting these workers at a higher compensation rate, which is negatively influencing Enron’s staff turnover (currently 15%). An acceptable rate for staff turnover is closer to 3%. Another problem detected was the high frequency of electricity outages. As a result Enron is losing critical management information which has a negative effect on monitoring and business decisions.

©

UNISA 2017

2

ASSIGNMENT02: RSK4803

The Board of Big Boy has instructed the Chief Financial Officer (CFO) and the Chief Risk Officer (CRO) to assist Enron with projections for the next 10 years on claims of the Enron

motor fleet to determine the appropriate risk

YEAR

CPI

ZAR

PERFORMANCE

financing strategies for the fleet. The CFO has

USD/ZAR

consulted with Two Hands Econometrics

2016

6.56

13.8

2017

6.89

14.5

Consultancy Services for estimations of the CPI

2018

7.00

15

and ZAR/USD for the period. Exchange rates

2019

7.32

16.5

have a significant effect on claims inflation as

2020

7.42

16.85

2021

6.95

15.89

40% of claims cost is in foreign currency. Refer

2022

6.83

15.5

to the table for the projections provided by the

2023

6.67

14.5

consultants.

2024

6.43

11.48

2025

6.38

15.81

To determine the risk financing alternatives, the CRO recommended that the maximum probable yearly aggregate loss (MPY) must be calculated for the fleet. An analysis of the fleet showed the following:

YEAR

PLANNED NUMBER OF

BUDGETED COST PER

EXPECTED NUMBER

VEHICLES

VEHICLE

OF ACCIDENTS

2016

30

R 500 000

5

2017

30

R 500 000

6

2018

30

R 500 000

6

2019

35

R 505 000

7

2020

35

R 505 000

7

2021

35

R 512 000

7

2022

35

R 512 000

7

2023

35

R 512 000

7

2024

40

R 518 000

10

2025

40

R 518 000

10

Question 1.1

(5 Marks)

The administration cost per claim was R8 000 in 2016. Calculate the claims administration cost per claim for the projected period by incorporating the information provided by Two Hands Econometrics Consultancy Services. (Show all calculations)

Question 1.2 (15 Marks)

The average damage per accident in 2016 was R100 000 and the administration cost R8 000 per claim, which gives an average of R108 000 for 2016, and total claims cost of R540 000 for the year. Claims inflation forms a significant component of the total claims cost per accident and for that reason it is important to include claims inflation in the projections. For the purpose of this exercise, the CRO defined claims inflation as the administration cost and effect of

©

UNISA 2017

(3 Marks)

0.1

0.09

0.1

0.11

0.08

0.12

0.1

0.1

0.1

0.1

2016

2017

2018

2019

2020

2021

2022

2023

2024

2025

EXPECTED PROBABILITY

OF LOSSES

YEAR

3

ASSIGNMENT02: RSK4803

exchange rate fluctuation. Calculate the expected aggregate total claims cost per annum for the projected period by incorporating the information provided by Two Hands Econometrics Consultancy Services. (Show all calculations).

Question 1.3 (15 Marks)

Calculate the expected total claims cost for the projected period by incorporating the information of the calculations above. (Show all calculations)

To determine the probability, the Risk Management team has developed a number of scenarios by using the Delphi-technique. Although the probabilities were determined on a qualitative basis, the CRO and her team were satisfied that the values appear to be

reasonable. Factors that were considered in the scenarios were past experience, the current

situation and future trends as discussed with Two Hands Econometrics Consultancy Services. The CRO and her team determined the probability of

the expected losses for the period as indicated in the box. The CRO is of the opinion that the Chebyshev theorem is the most appropriate

method to calculate the MPY. The k-value as determined by the Risk Department is 1.25.

Question 1.4

Argue on which basis the CRO has decided that the Chebyshev theorem is the most appropriate method in this instance.

Question 1.5 (12 Marks) Calculate the MPY according to the Chebyshev method. To simplify the calculations for purposes of this examination, use for example R100 instead of R 100 000. (Show all calculations)

Question 2 [20 Marks]

Identify the forms of risk sharing in a commercial insurance contract. Argue and illustrate where appropriate with diagrams the benefits to the insurer for each method.