Two projects are under evaluation. Project A will cost $200,000 to build and $20,000
per year to operate. Project B will cost $300,000 to build and $10,000 a year to operate. The useful economic life of both projects is 40 years. Money costs 6 percent.

Based on this information, you will recommend Project  because its life cycle cost is  than that of Project  by $ .

To determine which project is more cost-effective over its lifetime, we calculate the **Life Cycle Cost (LCC)** for both projects. The LCC includes the initial cost, annual operating costs, and the present value of those operating costs over the project's lifespan.

### Given:
- **Project A:**
  - Initial cost: $200,000
  - Annual operating cost: $20,000
  - Life span: 40 years
  - Discount rate: 6%

- **Project B:**
  - Initial cost: $300,000
  - Annual operating cost: $10,000
  - Life span: 40 years
  - Discount rate: 6%

### Formula for Life Cycle Cost (LCC):
\[ \text{LCC} = \text{Initial Cost} + \text{Present Value of Operating Costs} \]

### Present Value of Operating Costs (PV):
The present value of the annual operating costs over the life of the project can be calculated using the formula for the present value of an annuity:
\[ \text{PV} = C \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \]
Where:
- $ C $ is the annual operating cost
- $ r $ is the discount rate (6% or 0.06)
- $ n $ is the number of years

Let's calculate the LCC for both projects.

#### For Project A:
- Initial Cost: $200,000
- $ C = 20,000 $, $ r = 0.06 $, $ n = 40 $

\[ \text{PV}_{A} = 20,000 \times \left(\frac{1 - (1 + 0.06)^{-40}}{0.06}\right) \]

#### For Project B:
- Initial Cost: $300,000
- $ C = 10,000 $, $ r = 0.06 $, $ n = 40 $

\[ \text{PV}_{B} = 10,000 \times \left(\frac{1 - (1 + 0.06)^{-40}}{0.06}\right) \]

Now, let's compute these values.Based on the calculations:

- **Life Cycle Cost (LCC) for Project A**: $500,925.94
- **Life Cycle Cost (LCC) for Project B**: $450,462.97

Project B has a lower life cycle cost. Therefore, **Project B** is recommended because its life cycle cost is **$50,462.97** less than that of **Project A**.

Would you like more details on these calculations or have any other questions?

Here are five related questions to consider:
1. How would changes in the discount rate affect the LCC of each project?
2. What would happen if the useful economic life was reduced to 30 years?
3. How does the choice of project affect long-term financial planning?
4. Can the operating cost fluctuate annually, and how would that impact the analysis?
5. What are other factors to consider beyond the life cycle cost in choosing between these projects?

**Tip:** When comparing projects, always consider both initial costs and long-term operational costs to determine the most cost-effective option over the project's lifespan.

Learn how to compare the life cycle costs of projects using financial analysis techniques. This problem involves calculating the life cycle costs of two projects, considering initial costs, annual operating costs, and discount rates. Project B is recommended due to its lower life cycle cost, saving $50,462.97 compared to Project A.

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