13.7: End-of-Chapter Assignments

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Problem 1: Time Value of Money (TVM)

An industrial engineering firm is evaluating an automated quality-inspection robot to replace manual inspection on an assembly line. The robot is projected to reduce labor costs by $15,000 annually over its useful life of 6 years.

Part A: If the firm's Minimum Attractive Rate of Return (MARR) is 8% per year, calculate the maximum initial purchase price (Present Worth, PW) the firm should be willing to pay for the robot.
Part B: Calculate the Future Worth (FW) of these cumulative annual savings at the end of Year 6 at an 8% interest rate.

Problem 2: Break-Even Point (BEP) Analysis

A manufacturing plant produces custom composite turbine blades. The facility incurs annual fixed costs of $240,000 (including facility leases, equipment depreciation, and administrative salaries). The direct variable cost (materials and direct labor) to produce each turbine blade is $350. The market selling price per blade is $750.

Part A: Determine the annual break-even production volume (number of blades).
Part B: Calculate total revenue and total production cost at the break-even point.
Part C: If the plant produces and sells 800 blades in a year, determine the anticipated annual net profit or loss.

Problem 3: Return on Investment (ROI) & Net Present Value (NPV)

An energy engineering team proposes installing a rooftop solar array with waste-heat recovery at a manufacturing plant. The total initial capital investment required is $180,000. The project has an expected service life of 5 years and is projected to deliver the following financial streams:

Net Annual Energy Cost Savings: $48,000 per year for 5 years.
Equipment Salvage Value (End of Year 5): $20,000.

Part A: Calculate the Simple Annualized Return on Investment (Simple ROI) based on the average annual net profit relative to initial capital investment.
Part B (Challenge Problem): Assuming a corporate discount rate (MARR) of 10%, calculate the project's Net Present Value (NPV). State whether the project is economically justified.
Part C (Challenge Problem): Calculate the Net Discounted ROI percentage (NPV divided by Initial Investment).

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