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Sox Engineering designs and constructs air conditioning and heating (HVAC) systems for hospitals and clinics. Currently the company’s staff is overloaded with design work. There is a major design project due in 9 weeks. The penalty for completing the design late is $14,000 per week, since any delay will cause the facility to open later than anticipated, and cost the client significant revenue. If the company uses its inside engineers to complete the design, it will have to pay them overtime for all work. Sox has estimated that it will cost $10,000 per week (wages and overhead), including late weeks, to have company engineers complete the design. Sox is also considering having an outside engineering firm do the design. A bid of $85,000 has been received for the completed design. Yet another option for completing the design is to conduct a joint design by having a third engineering company complete all electromechanical components of the design at a cost of $52,000. Sox would then complete the rest of the design and control systems at an estimated cost of $30,000. Sox has estimated the following probabilities of completing the project within various time frames when using each of the three options. Those estimates are shown in the following table:
| Probability of Completing the Design | ||||
| Option | On Time | One Week Late | Two Weeks Late | Three Weeks Late |
| Internal Engineers | 0.4 | 0.5 | 0.1 | — |
| External Engineers | 0.2 | 0.5 | 0.2 | 0.1 |
| Joint Design | 0.2 | 0.2 | 0.4 | 0.2 |
The expected monetary value using inside engineers to complete the design is $______(Enter your response as an integer.)
The expected monetary value using outside engineers to complete the design is $______(Enter your response as an integer.)
The expected monetary value of conducting a joint design is $______(Enter your response as an integer.)
Expert Answer
Internal Engineers Option:
Wages per week = $10,000
Late Penalty cost = $14,000 beyond 9 weeks
For Internal Engineers the payoff or cost for the project as per week schedule is as follows:
| Events | Cost Structure | Payoff | Probability of completion | Expected Payoff |
| On time (in 9 weeks) | Wages and OH for 9 days | 9 x 10,000
= 90,000 |
0.4 | (0.4)(90,000)
= 36,000 |
| One week late (in 10 weeks) | Wages and OH for 10 days + penalty for 1 week delay | (10)(10,000) + (1)(14,000)
= 114,000 |
0.5 | (0.5)(114,000)
= 57,000 |
| Two weeks late (in 11 weeks) | Wages and OH for 11 days + penalty for 2 week delay | (11)(10,000) + (2)(14,000)
= 138,000 |
0.1 | (0.1)(138,000)
= 13,800 |
| Three weeks late (in 12 weeks) | Wages and OH for 12 days + penalty for 3 week delay | (12)(10,000) + (3)(14,000)
= 162,000 |
0 | (0)(139,000)
= 0 |
| Expected Monetary Value | 106,800 | |||
EMV using Inside Engineers to complete design = $106,800
External Engineers Option:
Bid Cost = $85,000
Late Penalty cost = $14,000 beyond 9 weeks
For Internal Engineers the payoff or cost for the project as per week schedule is as follows:
| Events | Cost Structure | Payoff | Probability of completion | Expected Payoff |
| On time (in 9 weeks) | Bid Cost | 85,000 | 0.2 | (0.2)(85,000)
= 17,000 |
| One week late (in 10 weeks) | Bid Cost + penalty for 1 week delay | 85,000 + (1)(14,000)
= 99,000 |
0.5 | (0.5)(99,000)
= 49,500 |
| Two weeks late (in 11 weeks) | Bid Cost + penalty for 2 week delay | 85,000 + (2)(14,000)
= 113,000 |
0.2 | (0.2)(113,000)
= 22,600 |
| Three weeks late (in 12 weeks) | Bid Cost + penalty for 3 week delay | 85,000 + (3)(14,000)
= 127,000 |
0.1 | (0.1)(127,000)
= 12,700 |
| Expected Monetary Value | 101,800 | |||
EMV using External Engineers to complete design = $101,800
Joint Design Option:
Total Cost of project = $52,000 + $30,000 = $82,000
Late Penalty cost = $14,000 beyond 9 weeks
For Internal Engineers the payoff or cost for the project as per week schedule is as follows:
| Events | Cost Structure | Payoff | Probability of completion | Expected Payoff |
| On time (in 9 weeks) | Total Joint Cost | 82,000 | 0.2 | (0.2)(82,000)
= 16,400 |
| One week late (in 10 weeks) | Total Joint Cost + penalty for 1 week delay | 82,000 + (1)(14,000)
= 96,000 |
0.2 | (0.2)(96,000)
= 19,200 |
| Two weeks late (in 11 weeks) | Total Joint Cost + penalty for 2 week delay | 82,000 + (2)(14,000)
= 110,000 |
0.4 | (0.4)(110,000)
= 44,000 |
| Three weeks late (in 12 weeks) | Total Joint Cost + penalty for 3 week delay | 82,000 + (3)(14,000)
= 124,000 |
0.2 | (0.2)(124,000)
= 24,800 |
| Expected Monetary Value | 104,400 | |||
EMV using Joint Design option to complete design = $104,400
