Cost Estimates for World Satellite Telephone Exchange Project
NSDC has a contract to produce eight satellites to support a worldwide telephone system (for Alaska Telecom, Inc.) that allows individuals to use a single, portable telephone in any location on earth to call in and out. NSDC will develop and produce the eight units. NSDC has estimated that the R&D costs will be NOK (Norwegian Krone) 12,000,000. Material costs are expected to be NOK 6,000,000. They have estimated that the design and production of the first satellite will require 100,000 labor hours, and an 80 percent improvement curve is expected. Skilled labor cost is NOK 300 per hour. Desired profit for all projects is 25 percent of total costs.
- How many labor hours should the eighth satellite require?
- How many labor hours for the whole project of eight satellites?
- What price would you ask for the project? Why?
- Midway through the project, your design and production people realize that a 75 percent improvement curve is more appropriate. What impact does this have on the project?
- Near the end of the project, Deutsch Telefon AG requests a cost estimate for four satellites identical to those you have already produced. What price will you quote them? Justify your price.
How to Write Cost Estimates for the World Satellite Telephone Exchange Project
Introduction
Learning curve analysis is a valuable project management tool used to estimate labor requirements and project costs when repetitive production activities are involved. As workers gain experience, productivity improves, resulting in reduced labor hours for subsequent units. In this case, NSDC has been contracted to develop and manufacture eight satellites for a worldwide telephone system. The company must estimate labor hours, total project costs, pricing, and the financial impact of changes in learning rates.
The learning curve formula is:
Yx=aXbY_x = aX^bYx=aXb
Where:
- YxY_xYx = labor hours for the xth unit
- aaa = labor hours for the first unit
- XXX = unit number
- b=log(r)log(2)b = \frac{\log(r)}{\log(2)}b=log(2)log(r)
- rrr = learning curve rate
Section 1: Labor Hours Required for the Eighth Satellite
For an 80% learning curve: b=log(0.80)log(2)=−0.3219b=\frac{\log(0.80)}{\log(2)}=-0.3219b=log(2)log(0.80)=−0.3219
For the eighth satellite: Y8=100,000(8−0.3219)Y_8=100,000(8^{-0.3219})Y8=100,000(8−0.3219)
Since: 8−0.3219=0.5128^{-0.3219}=0.5128−0.3219=0.512 Y8=100,000(0.512)Y_8=100,000(0.512)Y8=100,000(0.512) Y8=51,200 labor hoursY_8=51,200 \text{ labor hours}Y8=51,200 labor hours
Answer: The eighth satellite should require approximately 51,200 labor hours.
Section 2: Total Labor Hours for Eight Satellites
Using the cumulative average learning curve:
For 8 units: Average hours per unit=100,000(8−0.3219)\text{Average hours per unit}=100,000(8^{-0.3219})Average hours per unit=100,000(8−0.3219) =51,200=51,200=51,200
Total labor hours: 51,200×851,200 \times 851,200×8 =409,600 labor hours=409,600 \text{ labor hours}=409,600 labor hours
Answer: Total labor hours for the project are approximately 409,600 hours.
Section 3: Price to Ask for the Project
Labor Cost
409,600×300409,600 \times 300409,600×300 =122,880,000 NOK=122,880,000 \text{ NOK}=122,880,000 NOK
Material Cost
6,000,000 NOK6,000,000 \text{ NOK}6,000,000 NOK
R&D Cost
12,000,000 NOK12,000,000 \text{ NOK}12,000,000 NOK
Total Cost
122,880,000+6,000,000+12,000,000122,880,000 + 6,000,000 + 12,000,000122,880,000+6,000,000+12,000,000 =140,880,000 NOK=140,880,000 \text{ NOK}=140,880,000 NOK
Add 25% Profit
140,880,000×1.25140,880,000 \times 1.25140,880,000×1.25 =176,100,000 NOK=176,100,000 \text{ NOK}=176,100,000 NOK
Recommended Project Price: 176,100,000 NOK\boxed{176,100,000 \text{ NOK}}176,100,000 NOK
This price covers all labor, material, and research costs while achieving the company’s desired profit margin of 25%.
Section 4: Impact of a 75% Learning Curve
The revised learning curve becomes: b=log(0.75)log(2)b=\frac{\log(0.75)}{\log(2)}b=log(2)log(0.75) b=−0.415b=-0.415b=−0.415
For eight units: Average hours per unit=100,000(8−0.415)\text{Average hours per unit} =100,000(8^{-0.415})Average hours per unit=100,000(8−0.415) =42,200=42,200=42,200
Total labor hours: 42,200×842,200 \times 842,200×8 =337,600=337,600=337,600
New Labor Cost
337,600×300337,600 \times 300337,600×300 =101,280,000 NOK=101,280,000 \text{ NOK}=101,280,000 NOK
New Total Cost
101,280,000+6,000,000+12,000,000101,280,000 + 6,000,000 + 12,000,000101,280,000+6,000,000+12,000,000 =119,280,000 NOK=119,280,000 \text{ NOK}=119,280,000 NOK
New Selling Price
119,280,000×1.25119,280,000 \times 1.25119,280,000×1.25 =149,100,000 NOK=149,100,000 \text{ NOK}=149,100,000 NOK
Impact
The stronger learning effect reduces labor requirements by: 409,600−337,600409,600-337,600409,600−337,600 =72,000 hours=72,000 \text{ hours}=72,000 hours
Labor cost savings: 72,000×30072,000 \times 30072,000×300 =21,600,000 NOK=21,600,000 \text{ NOK}=21,600,000 NOK
The project becomes significantly more profitable if the contract price remains unchanged. Alternatively, NSDC could offer more competitive pricing while maintaining its desired profit margin.
Section 5: Cost Estimate for Four Additional Satellites
The first eight satellites have already been completed, so the next order covers units 9 through 12.
Using the 75% learning curve:
Unit 9
100,000(9−0.415)=40,200100,000(9^{-0.415})=40,200100,000(9−0.415)=40,200
Unit 10
100,000(10−0.415)=38,500100,000(10^{-0.415})=38,500100,000(10−0.415)=38,500
Unit 11
100,000(11−0.415)=37,000100,000(11^{-0.415})=37,000100,000(11−0.415)=37,000
Unit 12
100,000(12−0.415)=35,700100,000(12^{-0.415})=35,700100,000(12−0.415)=35,700
Total labor hours: 40,200+38,500+37,000+35,70040,200+38,500+37,000+35,70040,200+38,500+37,000+35,700 =151,400=151,400=151,400
Labor Cost
151,400×300151,400 \times 300151,400×300 =45,420,000 NOK=45,420,000 \text{ NOK}=45,420,000 NOK
Material Cost
Assuming materials remain proportional: 6,000,000/8=750,000 NOK per satellite6,000,000/8 = 750,000 \text{ NOK per satellite}6,000,000/8=750,000 NOK per satellite
For four satellites: 750,000×4750,000 \times 4750,000×4 =3,000,000 NOK=3,000,000 \text{ NOK}=3,000,000 NOK
No additional R&D costs are necessary because the design work has already been completed.
Total Cost
45,420,000+3,000,00045,420,000 + 3,000,00045,420,000+3,000,000 =48,420,000 NOK=48,420,000 \text{ NOK}=48,420,000 NOK
Price with 25% Profit
48,420,000×1.2548,420,000 \times 1.2548,420,000×1.25 =60,525,000 NOK=60,525,000 \text{ NOK}=60,525,000 NOK
Quoted Price to Deutsch Telefon AG: 60,525,000 NOK\boxed{60,525,000 \text{ NOK}}60,525,000 NOK
This price is justified because the original R&D expenses have already been absorbed by the first contract, and the organization benefits from accumulated learning and production efficiencies, resulting in substantially lower labor costs for the additional satellites.
Conclusion
Learning curve analysis demonstrates how productivity improvements significantly influence project cost estimation. Under the original 80% learning curve, the eighth satellite requires approximately 51,200 labor hours, and the total project price should be about NOK 176.1 million. When the learning curve improves to 75%, labor requirements decline substantially, reducing total project costs and increasing profitability. For the follow-on order of four satellites, prior learning and completed R&D efforts allow NSDC to offer a competitive quote of approximately NOK 60.5 million while maintaining its target profit margin. These calculations illustrate the importance of incorporating learning curve effects into project planning, pricing, and strategic decision making.
References
Gray, C. F., & Larson, E. W. (2021). Project management: The managerial process (8th ed.). McGraw-Hill Education.
Meredith, J. R., Mantel, S. J., & Shafer, S. M. (2022). Project management: A managerial approach (10th ed.). Wiley.
Pinto, J. K. (2023). Project management: Achieving competitive advantage (6th ed.). Pearson.
Last Completed Projects
| topic title | academic level | Writer | delivered |
|---|