Cost-Benefit Analysis (CBA) is a systematic approach to estimating the strengths and weaknesses of alternatives. It is used to determine options that provide the best approach to achieve benefits while preserving savings. This method is widely used in business, project management, and public policy to evaluate the total expected cost of a project compared to the total expected benefits.

Cost-Benefit Analysis is a financial decision-making tool that helps to evaluate the economic worth of a project or decision by comparing the costs and benefits.

• Informed Decision Making: Helps in making informed decisions by quantifying the costs and benefits.
• Resource Allocation: Assists in the optimal allocation of resources.
• Risk Management: Identifies potential risks and benefits, aiding in risk management.
• Transparency: Provides a transparent and systematic approach to decision making.

1. Identify the Project or Decision: Clearly define the project or decision to be analyzed.
2. List All Costs and Benefits: Identify and list all the costs and benefits associated with the project.
3. Assign a Monetary Value to Costs and Benefits: Quantify the costs and benefits in monetary terms.
4. Calculate Net Present Value (NPV): Discount future costs and benefits to their present value.
5. Compare Costs and Benefits: Compare the total costs and benefits to determine the net benefit.
6. Make a Decision: Based on the comparison, decide whether to proceed with the project or decision.

A company is considering investing in a new software system to improve productivity. The initial cost of the software is $100,000, and it is expected to save $30,000 annually in labor costs over five years.

1. Identify the Project: Investment in a new software system.
2. List All Costs and Benefits:
   • Costs: Initial cost of $100,000.
   • Benefits: Annual savings of $30,000 for five years.
3. Assign a Monetary Value:
   • Costs: $100,000.
   • Benefits: $30,000 per year for five years.
4. Calculate Net Present Value (NPV):
   • Assuming a discount rate of 5%, the NPV of the benefits is calculated as follows: \[ NPV = \sum \frac{Benefit_t}{(1 + r)^t} - Cost \] Where \( t \) is the year, and \( r \) is the discount rate. \[ NPV = \frac{30,000}{(1 + 0.05)^1} + \frac{30,000}{(1 + 0.05)^2} + \frac{30,000}{(1 + 0.05)^3} + \frac{30,000}{(1 + 0.05)^4} + \frac{30,000}{(1 + 0.05)^5} - 100,000 \] \[ NPV = 28,571.43 + 27,210.88 + 25,915.12 + 24,681.07 + 23,505.78 - 100,000 \] \[ NPV = 129,884.28 - 100,000 = 29,884.28 \]
5. Compare Costs and Benefits:
   • Total Costs: $100,000
   • Total Benefits (NPV): $129,884.28
   • Net Benefit: $29,884.28
6. Make a Decision:
   • Since the NPV is positive ($29,884.28), the investment in the new software system is financially beneficial.

A company is considering launching a new product. The initial investment is $200,000, and the expected annual profit is $50,000 for six years. Calculate the NPV assuming a discount rate of 4%.

Solution:

1. Identify the Project: Launching a new product.
2. List All Costs and Benefits:
   • Costs: $200,000.
   • Benefits: $50,000 per year for six years.
3. Assign a Monetary Value:
   • Costs: $200,000.
   • Benefits: $50,000 per year for six years.
4. Calculate NPV: \[ NPV = \sum \frac{Benefit_t}{(1 + r)^t} - Cost \] \[ NPV = \frac{50,000}{(1 + 0.04)^1} + \frac{50,000}{(1 + 0.04)^2} + \frac{50,000}{(1 + 0.04)^3} + \frac{50,000}{(1 + 0.04)^4} + \frac{50,000}{(1 + 0.04)^5} + \frac{50,000}{(1 + 0.04)^6} - 200,000 \] \[ NPV = 48,076.92 + 46,230.70 + 44,452.60 + 42,740.96 + 41,094.19 + 39,510.76 - 200,000 \] \[ NPV = 262,106.13 - 200,000 = 62,106.13 \]
5. Compare Costs and Benefits:
   • Total Costs: $200,000
   • Total Benefits (NPV): $262,106.13
   • Net Benefit: $62,106.13
6. Make a Decision:
   • Since the NPV is positive ($62,106.13), the new product launch is financially beneficial.

A city is planning to build a new park. The initial cost is $500,000, and the annual maintenance cost is $20,000. The expected annual benefit from increased tourism and community health is $70,000 for ten years. Calculate the NPV assuming a discount rate of 3%.

Solution:

1. Identify the Project: Building a new park.
2. List All Costs and Benefits:
   • Costs: $500,000 initial cost + $20,000 annual maintenance.
   • Benefits: $70,000 annual benefit for ten years.
3. Assign a Monetary Value:
   • Costs: $500,000 + $20,000 per year for ten years.
   • Benefits: $70,000 per year for ten years.
4. Calculate NPV: \[ NPV = \sum \frac{Benefit_t - Maintenance_t}{(1 + r)^t} - Initial\ Cost \] \[ NPV = \sum \frac{70,000 - 20,000}{(1 + 0.03)^t} - 500,000 \] \[ NPV = \sum \frac{50,000}{(1 + 0.03)^t} - 500,000 \] \[ NPV = \frac{50,000}{(1 + 0.03)^1} + \frac{50,000}{(1 + 0.03)^2} + \cdots + \frac{50,000}{(1 + 0.03)^{10}} - 500,000 \] \[ NPV = 48,543.69 + 47,124.94 + 45,742.66 + 44,396.75 + 43,086.17 + 41,810.84 + 40,569.74 + 39,362.85 + 38,189.17 + 37,047.73 - 500,000 \] \[ NPV = 426,874.50 - 500,000 = -73,125.50 \]
5. Compare Costs and Benefits:
   • Total Costs: $500,000 initial + $20,000 annual maintenance.
   • Total Benefits (NPV): $426,874.50
   • Net Benefit: -$73,125.50
6. Make a Decision:
   • Since the NPV is negative (-$73,125.50), the project is not financially beneficial.

• Ignoring Time Value of Money: Not discounting future costs and benefits to their present value.
• Incomplete Cost and Benefit Listing: Missing out on some costs or benefits.
• Incorrect Discount Rate: Using an inappropriate discount rate can skew the results.

• Comprehensive Listing: Ensure all costs and benefits are listed and quantified.
• Appropriate Discount Rate: Use a discount rate that reflects the risk and time value of money.
• Sensitivity Analysis: Conduct sensitivity analysis to understand the impact of changes in key assumptions.

Cost-Benefit Analysis is a powerful tool for making informed decisions by comparing the costs and benefits of different options. By following a systematic approach, decision-makers can ensure that resources are allocated efficiently and effectively. Understanding and applying CBA can significantly enhance the quality of decision-making in both professional and personal contexts.