Other Analysis Techniques

Introduction

This chapter introduces additional methods for evaluating financial alternatives in engineering and economic analysis. The focus is on Future Worth Analysis, Benefit-Cost Ratio Analysis, and the Payback Period. These techniques help decision-makers assess the financial viability and comparative value of projects or investments.

Future Worth Analysis

Definition and Purpose

Future Worth (FW) Analysis is a method for comparing alternatives by calculating the value of each option at a specified future time. This approach emphasizes the final outcome, such as a firm's ending wealth or retirement savings, and is easily convertible to/from Present Worth (PW), Equivalent Annual Worth (EAW), and Equivalent Annual Annuity (EAA) methods.

• Key Point: FW analysis is useful when the final value at a future date is of primary interest.

• Key Point: It is commonly applied in scenarios like retirement planning or evaluating long-term investments.

Formula

The general formula for future worth using a uniform series is:

Where:

• PMT: Regular payment or savings amount

• i: Interest rate per period

• n: Number of periods

• (F/A, i, n): Uniform series compound amount factor

Example

Example 9-1: Future Worth Calculation

• A 30-year-old quits a $35/week lottery habit and deposits the money into a savings account paying 5% interest, compounded semiannually, until age 65.

• Semiannual saving:

• Future Worth:

• If a every 6 months.

• Future Worth:

Benefit-Cost Ratio Analysis

Definition and Purpose

Benefit-Cost Ratio (B/C Ratio) analysis is a method for evaluating the economic feasibility of projects by comparing the present worth of benefits to the present worth of costs. It is widely used in public sector projects, such as infrastructure investments, to determine if the benefits justify the costs.

• Key Point: An alternative is considered acceptable if its B/C ratio is greater than or equal to 1.

• Key Point: Incremental analysis is used when comparing multiple alternatives.

Formula

The basic formula for the benefit-cost ratio is:

Alternatively, when disbenefits are present:

Example

Example: Road Project

• Benefits (PW):

• Disbenefits (PW):

• Costs (PW):

• B/C Ratio:

Benefit-Cost Ratio Analysis Table

The following table summarizes the B/C ratio for several alternatives:

Additional info: Table entries inferred from context and typical B/C analysis structure.

Payback Period

Definition and Purpose

The Payback Period is the time required for the cumulative profits or benefits of a project to equal its initial cost. It is a simple and approximate method for economic analysis, often used in start-up enterprises or when capital is limited. However, it ignores the time value of money and all cash flows after the payback point.

• Key Point: Payback period is not always consistent with equivalent worth or rate of return methods.

• Key Point: Most projects with good payback periods also perform well on other measures, but not always.

Formula

For uniform annual savings:

For non-uniform cash flows, the payback period is calculated by summing annual savings until the initial investment is recovered.

Example

Example: Machine Purchase

• Machine A: Initial cost = $10,000, Annual savings = $4,000

• Payback Period: years

• Machine B: Initial cost = $15,000, Annual savings = $4,000

• Payback Period: years

Example: Computer System

• Initial cost: $20,000

• Savings: Year 1 = $8,000, Year 2 = $4,000, Year 3 = $6,000

• After 3 years, cumulative savings = $18,000

• Remaining to payback: $2,000 out of $4,000 received in year 4

• Payback Period: years

Summary Table: Analysis Techniques

Additional info: Table synthesized for clarity and completeness.