Juan is considering two independent projects. Project A costs $74,600 and cash flows of $18,700, $46,300, and $12,200 for Years 1 to 3, respectively. Project B costs $70,000 and has cash flows of $10,600, $15,800, and $67,900 for Years 1 to 3, respectively. Juan assigns a discount rate of 10 percent to Project A and 11 percent to Project B. Which project or projects, if either, should he accept based on the profitability index rule? 

  accept both projects 
  accept Project A and reject Project B 
  accept either A or B, but not both 
  reject both projects 
  accept Project B and reject Project A 

To determine which project(s) Juan should accept based on the **profitability index (PI) rule**, we need to calculate the **PI** for each project. The profitability index is calculated as follows:

\[
PI = \frac{ \text{Present Value of Future Cash Flows}}{\text{Initial Investment}}
\]

The general rule is:
- If **PI > 1**, the project is acceptable (since the present value of cash flows exceeds the cost).
- If **PI < 1**, the project should be rejected.

### **Project A**:
- **Initial cost** = \$74,600
- **Cash flows**: \$18,700 in Year 1, \$46,300 in Year 2, and \$12,200 in Year 3.
- **Discount rate** = 10%

The present value of cash flows is calculated as:

\[
PV = \frac{18,700}{(1 + 0.10)^1} + \frac{46,300}{(1 + 0.10)^2} + \frac{12,200}{(1 + 0.10)^3}
\]

### **Project B**:
- **Initial cost** = \$70,000
- **Cash flows**: \$10,600 in Year 1, \$15,800 in Year 2, and \$67,900 in Year 3.
- **Discount rate** = 11%

Similarly, the present value of cash flows is:

\[
PV = \frac{10,600}{(1 + 0.11)^1} + \frac{15,800}{(1 + 0.11)^2} + \frac{67,900}{(1 + 0.11)^3}
\]

Let's calculate these values.The profitability index (PI) for each project is:

- **Project A**: PI = 0.864
- **Project B**: PI = 1.029

According to the **profitability index rule**:
- Since **PI < 1** for **Project A**, Juan should **reject Project A**.
- Since **PI > 1** for **Project B**, Juan should **accept Project B**.

Thus, the correct choice is to **accept Project B and reject Project A**.

Would you like to go over more details or any specific part of the calculations?

Here are 5 related questions for deeper understanding:
1. What factors influence the profitability index of a project?
2. How does changing the discount rate affect the PI of a project?
3. Can a project with a negative NPV ever have a PI greater than 1?
4. How do independent and mutually exclusive projects differ in decision-making?
5. What other criteria besides PI might Juan use to evaluate these projects?

**Tip:** When choosing projects, it's important to balance profitability with risk.

Juan is considering two independent projects. Project A costs $74,600 and cash flows of $18,700, $46,300, and $12,200 for Years 1 to 3, respectively. Project B costs $70,000 and has cash flows of $10,600, $15,800, and $67,900 for Years 1 to 3, respectively. Juan assigns a discount rate of 10 percent to Project A and 11 percent to Project B. Which project or projects, if either, should he accept based on the profitability index rule?

Learn how to evaluate two independent projects, Project A and Project B, using the profitability index (PI) rule. This example covers key finance concepts like present value, discounting cash flows, and calculating PI. Project A has an initial cost of $74,600 and Project B has an initial cost of $70,000, with different cash flows and discount rates for both. Find out which project Juan should accept based on the PI calculations.

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