The managing director of XYZ plc has delegated some decisions making to the the operating divisions of the firm.Heis anxious to extend this process but first wishes to be assured that decisions are being taken properly in accordance with group policy.

As a check on existing practice he has asked for an investigation to be made into a recentdecision to increase the price of the sole product of Z division to K $14\mathrm{.}50$ per unit due to rising costs.

The following information and estimates were available for the management of Z division.

$(1)$ Last year $75,000$ units were sold at K$12$ each with a total unit cost of K$9$ of which K$6$ were variable costs.

$(2)$ For the year ahead the following cost and demand estimates have been made.

UNIT variable costs

Pessimistic probability $0\mathrm{.}5$ K$7\mathrm{.}00$ per unit

Most likely probability $0\mathrm{.}65$ K$6\mathrm{.}50$ per unit

Optimistic probability $0\mathrm{.}20$ K$6\mathrm{.}20$ per unit

Total fixed costs

Pessimitic probability $0\mathrm{.}3$ increase by $50\%$

Most likely probability $0\mathrm{.}5$ increase by $25\%$

Optimistic probability $0\mathrm{.}2$ increase by $10\%$

$($Unit variablee costs, fixed costs and demand are stistically independent.$)$

For this type of decision the group has decided that the option should be chosen which has the highest expected outcome with at least an $80$ per cent chance of breaking even.

Required

$($a$)$ Assess whether the decision was made in accordance with group guidelines

$($b$)$ Comments on the estimates for the decision