Question $1[40$ Marks$]$

SA Logistix is a transport company that operates across South Africa. The company has a fleet of specialised vehicles to transport a wide range of products such as fresh foodstuffs, chemicals, and hazardous products.

The company is preparing for the annual insurance review. The Board of SA Logistix has instructed the Chief Financial Officer $($CFO$)$ and the Chief Risk Officer $($CRO$)$ to determine the appropriate risk financing strategies for the fleet. To determine the risk financing alternatives, the CRO recommended that the maximum probable yearly aggregate loss $($MPY$)$ must be calculated for the fleet. The historical financial data of the fleet is incomplete and certain critical components need to be calculated.

Exchange rates have a significant effect on claims inflation as $40\%$ of claims cost is in foreign currency. Refer to the table for the annual inflation rate and appropriate exchange rate. The historical information available for the fleet is as follows:

$1.$a$.$ The administration cost per claim was R$9000$ in $2013.$ Calculate the claims administration cost per claim for the period by incorporating the information provided in the table above. $($Show all calculations$).$

$1.$b$.$ The average damage per accident in $2013$ was R$100000$ and the administration cost R$9000$ per claim, which gives an average of R$109000$ for $2013,$ and total claims cost of R$5450000$ 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 data. For the purpose of this exercise, the CRO defined claims inflation as the administration cost and effect of exchange rate fluctuation. Calculate the expected total claims cost per annum for the projected period by incorporating the information provided in the table above. $($Show all calculations$).(15)$

$1.$c$.$ The board of Logistix stated in the last annual report that the company adopted a conservative risk appetite. Advise the board on the three methods to calculate the MPY$.$ Which method will you recommend given the risk appetite of the company? $(15)$

$1.$d$.$ Calculate the MPY according to the Chebyshev method. The k$-$value as determined by the Risk Department is $1\mathrm{.}05.($Show all calculations$)$