Present Worth Analysis

Introduction

Present Worth (PW) Analysis is a fundamental technique in engineering economic analysis and financial accounting for evaluating the value of cash flows over time. It allows decision-makers to compare alternatives by converting future amounts to their equivalent present values using a specified interest rate.

Assumptions in Solving Economic Analysis Problems

Key Assumptions

• End-of-Year Convention: All cash flows are assumed to occur at the end of each year unless otherwise specified.

• Viewpoint of the Firm: Analysis is conducted from the perspective of the firm making the investment.

• Sunk Costs: Costs that have already been incurred and cannot be recovered are ignored in decision-making.

• Project Alternatives: Each alternative requires separate decisions regarding financing and investment.

• Financing: Money is obtained at an interest rate, typically through borrowing from a bank or the firm itself.

• Investment: Money is spent considering the lifecycle costs and benefits of the project.

• Inflation & Deflation: Prices are assumed stable unless otherwise noted (inflation is considered in later chapters).

• Income Taxes: Taxes are introduced in more advanced analysis (see Chapter 12).

Economic Criteria for Decision Making

Input/Output Criteria Table

Economic criteria help determine the best alternative based on the nature of inputs and outputs.

Present Worth Analysis: All alternatives are valued in terms of their equivalent present consequences. The terms 'present worth' and 'net present worth' are often used interchangeably, except in spreadsheet function names.

Applying Present Worth Analysis

When Useful Lives are Equal

When comparing alternatives with equal useful lives, the present worth of each is calculated and compared directly.

• Formula for Present Worth:

• Example 5-1: Device A: Device B:

Spreadsheet Solutions

Spreadsheet functions such as PV (Present Value), FV (Future Value), and PMT (Payment) are used to automate calculations.

Example 5-2: Facility Construction

• Single-stage construction: million$

• Two-stage construction: million million million million million$

Comparing Alternatives with Different Useful Lives

Study Period Selection

When alternatives have different useful lives, comparisons must be made over a common study period, typically the least common multiple of the lives.

• If A's life is 3 years and B's is 6 years, use a 6-year study period.

• Estimate salvage values for alternatives at the end of the study period.

Example 5-4: Pump Replacement

• Pump A:

• Pump B:

Present Worth with Infinite Analysis Period (Capitalized Cost)

Capitalized Cost

Capitalized cost is the present worth of a perpetual series of uniform annual costs.

• Formula: where is the annual cost and is the interest rate.

• Example: How much must be set aside now to pay P = \frac{5000}{0.04} = 125,000$

Multiple Alternatives and Spreadsheet Analysis

Comparing Multiple Pipe Sizes

• Calculate total cost for each alternative using:

Bond Pricing

Principles of Bond Pricing

Bond pricing is a time value of money problem involving the present worth of future interest payments and the face value at maturity.

• Face Value: The amount repaid at maturity.

• Interest Payments: Usually paid semi-annually.

• Market Interest Rate: Determines the present value of future payments.

Example 5-14: Municipal Bond

• 5-year municipal bond, 4% coupon rate, paid semi-annually, face value $1,000, market rate 6.09%.

• Semiannual interest rate:

• Present Worth:

Summary Table: Key Formulas

Additional info: Spreadsheet solutions and function names (e.g., PV, FV, PMT) are commonly used in financial accounting and engineering economics to automate present worth calculations. The examples provided are typical applications in capital budgeting and investment analysis.