Question

Jupiter plc (Jupiter) owns a chain of pet shops in Geeland. As the economy in Geeland develops, pet ownership has increased and Jupiter now has the opportunity to expand its operation. The nature of this expansion includes developing both the range of pets and associated pet products sold as well as the number of physical stores.

Jupiter has commissioned some market research into the viability of undertaking this additional investment. There are three potential levels of investment and two potential market conditions. The returns within one year are highlighted in the table below:

	Investment $25m	Investment $35m	Investment $50m
Market Demand	Forecast Contribution per store	Forecast Contribution per store	Forecast Contribution per store
Medium	$2,000,000	$3,500,000	$4,250,000
High	$3,000,000	$4,500,000	$5,000,000

The investment would be for 25 new stores in all cases and the additional investment relates to the range of new pets and associated products stocked.

The fixed costs per store will change depending upon the level of investment. These are listed below:

	Investment $25m	Investment $35m	Investment $50m
Fixed costs per store	$700,000	$1,200,000	$1,700,000

Required:

1. Prepare a profit table for each outcome.

2. Advise Jupiter which investment level should be chosen if the maximin decision criteria is applied. Justify your answer.

Explain how probabilities can be used to calculate expected value and the limitations of expected value in risk assessment

Answer 1

Part (a)

Profit per store ($) = Forecast Contribution per store - Fixed costs per store

Investment	$ 25 mn	$ 35 mn	$ 50 mn
Market Demand
Medium	$1,300,000	$2,300,000	$2,550,000
High	$2,300,000	$3,300,000	$3,300,000

Part (b)

Investment	$ 25 mn	$ 35 mn	$ 50 mn
Market Demand
Medium (A)	$1,300,000	$2,300,000	$2,550,000
High (B)	$2,300,000	$3,300,000	$3,300,000
Minimum (C = Min (A, B))	$1,300,000	$2,300,000	$2,550,000
Maximin (= max of all Cs)	$2,550,000

The decision should be to choose the investment of $ 50 million.

Explain how probabilities can be used to calculate expected value and the limitations of expected value in risk assessment

Expected value is the probability weighted average of potential values associated with various probable outcomes of an exposure.

E(V) = p1 x V1 + p2 x V2 + p3 x V3 + ......+ pn x Vn

where pi is the probability of occurrence of state i and Vi is the value the variable V takes in the state i.

Limitations:

• Expected value is a theoretical value. When actual value occurs, it will be one of the probable values and not the expected value.
• Probabilities used in the calculation of expected value are usually based on historical data and hence may not be a reliable estimate for prediction of future.