Three Different Designs Are Being Considered for a New Refrigerator

question 47

Essay

Three different designs are being considered for a new refrigerator, and profits will depend on the combination of the refrigerator design and market condition. The following payoff table summarises the decision situation, with amounts in millions of dollars. $\begin{array} { ccc }&\text { Alternative }\\\text { State of Nature }& a_{1} & a_{2} & a_{3}\\\text { (Market condition) }\\s_{1} & \$ 30 & \$ 20 & \$ 10 \\s_{2} & \$ 19 & \$ 21 & \$ 15 \\s_{3} & \$ 11 & \$ 23 & \$ 35\end{array}$
Assume that the following probabilities are assigned to the three market conditions:
P( $S _ { 1 }$ ) = 0.2, P( $S _ { 2 }$ ) = 0.4, P( $S _ { 3 }$ ) = 0.4.
a. Calculate the expected monetary value for each design with present information. Which design should be selected in order to maximise the firm's expected profit?
b. Convert the payoff table to an opportunity loss table.
c. Calculate the expected opportunity loss for each design with present information. Which design should be selected in order to minimise the firm's expected loss?
d. Determine the expected payoff that would be realised if perfect information were available.
e. What is the most the firm would be willing to pay for a research study designed to reduce its uncertainty about market conditions?

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Definitions:

Return on Equity

A measure of a corporation's profitability, expressed as a percentage of the total amount of equity.

Year 2

Referring to the second year in a given context, often referring to financial or operational timelines.

Return on Total Assets

A financial metric indicating how profitable a company is relative to its total assets, measuring the efficiency in using assets to generate earnings.

Net Profit Margin Percentage

A financial ratio that shows what percentage of sales has turned into profits, indicating overall profitability.