3. A construction company has signed a contract to build an office tower. The co

Question

3. A construction company has signed a contract to build an office tower. The contract stipulates that the project will be completed in 1500 days from today and also includes a penalty on the construction company of S30,000 per day the project is late. In addition, the construction company estimates that its internal cost is S60,000 for each day the project is late. However, completing the project early is costly to the firm as well: each day the project is early costs the firm $45,000. (This includes opportunity cost of capital and idle capacity.) The firm estimates the project will take 1200 days to complete. The following are data on the ratios of the firm's actual completion times to forecasted completion times on previous projects with comparable complexity. (For example, one project's actual completion time was only 69% of forecasted time whereas another project's actual completion time was 210% ofthe forecast. Note, these 20 observations have been already sorted in ascending order.) 0.69 0.89 1.11 1.44 0.71 0.9 1.17 1.50 0.75 0.95 1.2 1.75 0.77 1.05 1.26 1.91 0.81 1.08 1.31 2.10 (a) Given these data, how many days should the firm wait to begin construction? (10)

Explanation / Answer

Expected Value of %Forcast Time = Summation of all times/ No. of observation = 23.37/20 = 1.1685

So Expected Time of Project Completion = Expected Value of %Forcast Time * Projected Project Time

=1.1685 * 1200 = 1402.2 ~1402

Thus the firm can delay the start of project by = 1500-1402 = 98 days.

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