# Mat 543 | Probability homework help

12-1 Using the information in Table 12-7, construct a PERT network and answer each of the following questions:

a. What is the expected project completion data?

b. What is the scheduled start and completion date for each activity?

c. Which activities are on the critical path?

d. How long can noncritical path activities be delayed without jeopardizing the overall completion date for this project?

12-2 Assess the impact of the following changes to the time estimates provided in question 12-1. Individually, what is the impact if: Activity Predecessor New Time Estimate O. Advertise for new staff N 4 P. Interview for new staff O 6 Q. Select new staff P 1 Collectively, what is the impact of these changes?

12-3 As project manager for the example included in question 12-1, what would you recommend to preserve the original project completion date if activity A was reestimated to take 8 weeks, not the original 4 weeks? Provide details.

13-1 A representative of a reputable financial services company has approached you as manager of a four-person group of anesthesiologists with an opportunity to purchase a 10-year annuity due for each member of the group. The annuity due would pay \$40,000 each year beginning 5 years from now (i.e., at time = 5). What is the most you would be willing to pay now, per each physician, for this investment? Assume an appropriate discount rate of 7%.

13-2 The hospital’s marketing and finance departments have just provided you, as chief financial officer, with pro forma income statements for your proposed sonogram center. These statements appear in the following. Pro forma Income Statement (000) Time t + 1 t + 2 t + 3 t + 4 Service Revenues (net) \$425 \$500 \$580 \$700 Expenses \$400 \$450 \$525 \$600 Depreciation Expense \$ 35 \$ 35 \$ 35 \$ 35 Net Income (\$ 10) \$ 15 \$ 20 \$ 65 What is the project’s IRR? Assume an initial investment of \$175,000 and an appropriate discount rate of 6%. The hospital is operated as a not-for-profit facility.

13-3 The chief operating officer (COO) of a small, not-for-profit community hospital has to make a recommendation to the board of trustees on choosing among three project options for an unrestricted gift of \$250,000 that has just been received. The board has established a time horizon of 5 years on this project. The options are described in the following. a. Purchase a 5-year treasury note at an interest rate (annual) of 7%. b. Purchase the practice of a young physician (the hospital’s third highest admitter). Estimates of projected cash flows for the practice (post-purchase), are: Probability of Cash Flow Time 60% 20% 20% t + 1 \$ 40,000 \$20,000 \$ 60,000 t + 2 \$ 60,000 \$30,000 \$ 80,000 t + 3 \$  75,000 \$40,000 \$100,000 t + 4 \$100,000 \$50,000 \$125,000 t + 5 \$100,000 \$50,000 \$125,000 c. Purchase an upgraded analyzer for the laboratory. Based on forecasts of laboratory utilization, the net cash flows for this project are: Time Net Cash Flow t + 1 \$75,000 t + 2 \$75,000 t + 3 \$50,000 t + 4 \$50,000 t + 5 \$50,000 Which investment should the COO recommend and why?

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