Engineering Economics: Net Value Function Calculations and Applications

Question Bank #1 – Net Value Functions

L03 – Engineering Economics & Net Value Applications

Review Questions

Recall the nanoRIMS example discussed in lecture. If the net value of buying the nanoparticles is $0 (the reference), determine the net value per week of having a grad student make the nanoparticles based on the following information:

• Benefit = $896/week
• Cost:
  • Cost of consumable supplies per week: Ingredients & electricity to make one batch as accurately as a grad student does is $5/100 mL * 200 mL/week = $10/week
  • Cost of time: Grad student time is $15/hr * 9 hours/100 mL * 200 mL/week = $270/week
  • Cost of space: Occupying a whole fume hood space for 16 hours during working time is $12.50/hr * 16 hrs/week = $200/week
  • Cost of any device: No extra device cost needed; does negligible wear & tear on existing lab supplies to carry out this process.
  • Cost of characterization: Using the SEM for two characterizations is $100/week

Net value/week = Benefit – Cost

Calculation:

Net value = $896/week – Cost/week

Cost/week = (Cost of consumable supplies) + (Cost of time) + (Cost of space) + (Cost of any device) + (Cost of characterization)

Cost/week = ($10/week) + ($270/week) + ($200/week) + ($0) + ($100/week) = $580/week

Net value = $896/week - $580/week = $316/week

Subsequent Calculations and Scenarios

Consider the following contributions to cost:

• Cost of consumable supplies per week: Ingredients & electricity to make one batch as accurately as a grad student does is $5/100 mL * 200 mL/week = $10/week
• Cost of time: Grad student time is $15/hr * 9 hours/100 mL * 200 mL/week = $270/week
• Cost of space: Occupying a whole fume hood space for 16 hours during working time is $12.50/hr * 16 hrs/week = $200/week
• Cost of any device: No extra device cost needed; does negligible wear & tear on existing lab supplies to carry out this process.
• Cost of characterization: Using the SEM for two characterizations is $100/week

1. Calculate the impact on the net value that results from reducing the electricity use by 25% at the expense of a $100 device usable for 3 years (ignoring time value of money).

   (Assume before the reduction, electricity costs 20% of the total “consumable supplies per week” cost.)

   Solution (S1.2): Net value of -$22.

   Electricity cost reduction: 25% of 20% of $10/week = 25% of $2/week = $0.50/week savings. Over 3 years (156 weeks), this is $0.50/week * 156 weeks = $78 savings. The device cost is $100. Net value = $78 - $100 = -$22.

2. Calculate the impact on the net value from reducing grad student time by 20% but using 100% more electricity.

   (Assume before the reduction, electricity costs 20% of the total “consumable supplies per week” cost.)

   Solution (S1.3): Net value of +$52/week.

   Reduced time cost: 20% reduction in $270/week = $54/week savings. Increased electricity cost: 100% increase on $2/week (20% of $10) = $2/week increase. Net weekly value = $54 savings - $2 increase = $52/week.

3. Calculate the impact on the net value from having a post-doc at $30/hour assist the grad student, reducing time by a factor of 4.

   (Assume before the reduction, electricity costs 20% of the total “consumable supplies per week” cost.)

   Solution (S1.4): Net value of +$67.5/week.

   New time per batch: 9 hours / 4 = 2.25 hours per 100mL. New cost per batch: ($30/hr * 2.25 hrs/100mL + $15/hr * 2.25 hrs/100mL) * 200mL/week = ($45/hr * 4.5 hrs/week) = $202.5/week. Original time cost was $270/week. Savings = $270 - $202.5 = $67.5/week.

4. Calculate the impact on the net value from abandoning characterization and accepting a 3% batch failure rate, costing $2000 in research time.

   Solution (S1.5): Net value of -$20/week.

   Savings from abandoning SEM: $100/week. Expected cost of failure: 3% of $2000 = $60/week. Net value = $100 savings - $60 expected cost = $40/week. *Correction based on provided solution: The solution implies a different calculation. If SEM is not used, cost is $0. If a batch fails (3% chance), cost is $2000. Expected cost per batch: (0.97 * $0) + (0.03 * $2000) = $60. For two batches, expected cost is $120/week. Original SEM cost was $100/week. Net value = $100 (savings) - $120 (expected cost) = -$20/week.*

5. Which tradeoffs in Q 1.2-1.5 should be implemented if they are mutually exclusive? What if they are independent?

   Solution (S1.6): Mutually exclusive: Choose the option with the highest net value (Q 1.4, +$67.5/week). Independent: Implement any option with a positive net value (Q 1.3, +$52/week and Q 1.4, +$67.5/week).

Grocery Store Online Storefront Scenarios

Adding an online storefront presents challenges and opportunities for grocers. While it can increase profitability through expanded sales, it introduces non-traditional expenses.

Manual Online Store Option

A grocer estimates the following expenses for a manual online store:

• Additional personnel (labor cost): Four people at $20/hr each for 8 hrs/day, plus one delivery driver at $25/hr for 8 hrs/day.
• Additional inventory purchasing and storage (space cost): $1,000/day for stock purchases and $1,000/day for spoilage.
• User interface development (website/app): $10,000 upfront, $5,000 yearly maintenance.
• Delivery costs: Vehicle purchase $70,000 upfront, $10,000 yearly maintenance/gas. Resale value after one year is $45,000.
• Employee error: Valued at 2% of total sales (direct and indirect costs).

1. If the grocer estimates $1,500,000 in total sales for the first year, what is the net value of adding the manual online storefront (benchmark: no online storefront)?

   Solution (S1.7): Net value = $383,000.

   Calculations detailed in the provided solution. Key components include labor, storage, website, vehicle costs, and employee error, offset by sales and vehicle resale value.

Automated Micro-Fulfillment System Option

An automated system offers scalability, speed, and reliability, requiring a dedicated micro-warehouse.

• Additional personnel (labor cost): One stockist at $20/hr and one delivery driver at $25/hr, both for 8 hrs/day.
• Additional inventory purchasing and storage (space cost): $2.5 million setup over 6 months. $3,500/day for stock purchases, $500/day for spoilage, $1,000/day opportunity cost for warehouse space.
• User interface development (website/app): $10,000 upfront, $5,000 yearly maintenance.
• Delivery costs: Vehicle purchase $70,000 upfront, $10,000 yearly maintenance/gas. Resale value after one year is $45,000.

1. If the automated system results in $5 million in sales in the first year, what is the net value of the project (benchmark: no online storefront)?

   Solution (S1.8): Net value = $493,600.

   Calculations detailed in the provided solution. Includes setup costs, daily operational costs, website, and vehicle costs, offset by sales and vehicle resale value.

2. Re-evaluate the automated system project over a 10-year timeline, ignoring the time value of money. Assume yearly values remain constant, and the car is worth $0 at the end.

   Solution (S1.9): Net value = $27,706,000.

   Calculations detailed in the provided solution. Annual costs are projected over 10 years, with upfront costs accounted for once. Total sales over 10 years are considered.

Car Purchase Decision

Suppose you are buying a car for the next 12 months on co-op. Which Net Value Function (NVF) is not appropriate for this decision?

• NV = (Benefits of punctuality) – (Purchase Cost) – (Operation Cost)
• NV = (Benefits of commuting) – (Cost of Public Transit) – (Cost of Retirement)
• NV = (Benefits of reliability) – (Maintenance Cost) – (Resale Cost)
• NV = (Benefits of carpooling) – (Cost of Environmental Impact) – (Cost of Gas)

Solution (S1.10): The second option is not appropriate. The cost of public transit is irrelevant if you are buying a car, and the cost of retirement is not a direct cost associated with the car purchase decision.

Widget Making Business Scenario

Steve's widget business involves assembling $5 parts into $10 widgets, taking 10 minutes per widget. Only 30 widgets' worth of parts are available daily. Steve values his time at $20/hour.

Kelly proposes an automatic assembly machine:

• Takes 20 minutes per widget assembly.
• Requires 30 minutes of Steve's total time per 30 widgets (loading/unloading).
• Uses $10 worth of electricity per 30 widgets.
• Machine cost: $1000 in parts + 10 hours of Kelly's time per machine (after initial 40 hours design time).
• Machine lifespan: 3000 widgets.
• Kelly values her time at $50/hour.
• Kelly offers Steve three machines for $15,000.

1. What is the net value Steve creates assembling 30 widgets (compared to having parts and time)?

   Solution (S1.11): $50.

   Value of widgets: 30 * ($10 - $5) = $150. Time cost: 10 minutes/widget * 30 widgets = 300 minutes = 5 hours. Opportunity cost of time: 5 hours * $20/hour = $100. Net value = $150 - $100 = $50.

2. How much would Steve potentially be willing to pay per day for such a device?

   Solution (S1.11): Up to $80.

   With the machine, Steve's time for 30 widgets is 30 minutes (loading/unloading). This saves 4.5 hours of his time compared to manual assembly (5 hours - 0.5 hours). Value of saved time: 4.5 hours * $20/hour = $90. Electricity cost: $10. Net value Steve is willing to pay = $90 - $10 = $80.

3. What is the net value for Kelly in creating and selling these 3 machines to Steve, assuming no future machines are made?

   Solution (S1.11): $8,500.

   Cost for 3 machines: ($1000 parts + 50 hrs design + 10 hrs build) * 1 + ($1000 parts + 10 hrs build) * 2 = $1000 + $2500 + $2000 + $200 = $5700. *Correction based on provided solution: The solution states $6,500. Let's re-calculate: First machine: $1000 parts + 50 hrs * $50/hr = $1000 + $2500 = $3500. Second & Third machines: ($1000 parts + 10 hrs * $50/hr) * 2 = ($1000 + $500) * 2 = $1500 * 2 = $3000. Total cost = $3500 + $3000 = $6500. Kelly's revenue: $15,000. Net value = $15,000 - $6500 = $8,500.*