The Johnson sisters are planning on opening an upscale catering business in Down

Question

The Johnson sisters are planning on opening an upscale catering business in Downtown Durham that can accommodate large weddings and corporate events. They arc renovating space in the old Tobacco District but need to decide if the size of the renovated space should be 4000 sq. ft, 8000 sq. ft. or 15,000 sq. ft. The payoffs received for each size of development will depend on the market demand which could be classified as low, medium or high. They payoff matrix (in $1000's) for this decision problem is Based on historical information about the area and potential for catering, the probability that the market demand will be low, medium, or high is estimated at 0.20, 0.20, and 0.60 respectively. Suppose the risk profile of the sisters can be estimated by the following utility function: where x is in 1000s and the risk tolerance value R = 1000. What decision should the sisters take according to the expected utility criterion? What is the certainty equivalent and risk premium associated with the alternative of building an 8000 sq. ft. space? Are the sisters risk averse, risk neutral or risk-seeking?

Explanation / Answer

For 4000 Sqft, the expected payoff is = 0.2*225+0.2*600+0.6*600 = 45+120+360 = 525 (1000$)

For 8000 sqft, expected payoff = 0.2*300+0.2*750+0.6*975 = 60+150+585=795 (1000$)

For 15000 sqft, expected payoff = 0.2*(-600)+0.2*450+1200*0.6=-120+90+720 = 690 (1000$)

So, Expected Payoff (ROI) is highest at 8000 sqft. Hence they should go for 8000 sqft (Ans a)

Ans B) Certainity equivalent is the guaranteed return, Here if they choose 8000 sqft area, then at low demand also, the return = 300 (1000$). Hence, Certainity Eqv = $300000.

Risk premium = Expected return for other options - guaranteed return for choosen option

= Expected return from 4000 sqft+Expected return from 15000 sqft - Certainity eqv of 8000 sqft

= 525 + 690 - 300= 915 (1000$) or rather $915000.

c) Here, choosing the highest expected return option (8000 sqft) will also lead to highest guaranteed return (300). Thus it makes them Risk averse, since the other 2 options have no gain on the risk.

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