Question

Scenario 6.1 - The Big Box Bahouth Ltd. is planning for the next two years of production and debating whether to construct a large cross-dock facility with 40 truck bays or a smaller one with 20 truck bays. The cost to build the large facility is $2 million and the cost to build the small one is $1.2 million. If they construct a large facility and demand is as high as they hope, then operating costs are $450,000 annually. If they construct a large facility and demand is low, then operating costs are $300,000. If they construct a small facility and demand is low, the operating costs are $275,000 but if they experience high demand, the operating cost of a small facility increases to $600,000. After having conducted some market research, they feel that the likelihood of high demand is 0.7 and the likelihood of small demand is 0.3. -Suppose the contractor has found some materials on Craigslist that can drop the construction cost of a large facility to $1,500,000. These materials cannot be used in the construction of the small facility, so its price remains as indicated in Scenario 6.1. Determine the likelihood of high demand that would make the decision maker indifferent between the two alternatives for a two year time period.

A) 1.0 B) 0.72 C) 0.92 D) 0.86

Answer 1

Ans:

Large Facility Cost;

One time Investment = $1500000 ( since some materials from craigslist can be used)

Operating Costs = $450000 per annum => $900000 for 2years

Probable Operating costs to be incurred for 2 years = $900000 * Probability for high demand (say x)

(this is only for decision. We probably incur 900000*x cost if we choose this option because we don't know if we will select large facility. Here the cost is dependent on demand. If the probability of demand being high is 100% then we will incur 450000 per annum but if probability of high demand is 50% then we make a decision using 450000*50% as cost. This is purely for decision making.)

Small Facility Cost;

One time Investment = $1200000

Operating Costs = $600000per annum => $1200000 for 2years

Probable Operating costs to be incurred for 2 years = $1200000* Probability for high demand

Indifference:

The decision-maker will be indifferent if two facilities yield same result i.e., same cost in our case.

=> 1500000 + (900000*x) = 1200000 + (1200000*x)

1500000 - 1200000 = 1200000x - 900000x

300000 = 300000x

:. x = 1.0

Therefore when the probability of high demand is 1.0 the company would be incurring the same costs in two facilities i.e., when we have 100% high demand the company can go with any of the options. So he can choose any of the options. This holds good only for a two year period. If the company plans for a higher period again the decision has to be taken.