Two projects being considered are mutually exclusive and have the following projected cash flows: (Compute both NPV and IRR). The cost of capital is 10%.
Year	Cash Flow A	Cash Flow B
0	-$50,000	-$50,000
1	$15,625	$0
2	$15,625	$0
3	$15,625	$0
4	$15,625	$0
5	$15,625	$99,500
		
NPV =	
IRR =	


To compare the two mutually exclusive projects, we'll calculate both the Net Present Value (NPV) and the Internal Rate of Return (IRR) for each project. 

### Step 1: NPV Calculation

The NPV is calculated using the formula:

\[
\text{NPV} = \sum \left(\frac{\text{Cash Flow}_t}{(1 + r)^t}\right) - \text{Initial Investment}
\]

Where:
- $ \text{Cash Flow}_t $ is the cash flow in year $ t $,
- $ r $ is the cost of capital (10% or 0.10),
- $ t $ is the year.

#### Project A:
- **Year 0**: -$50,000
- **Year 1-5**: $15,625 each year

\[
\text{NPV}_A = -\$50,000 + \sum_{t=1}^{5} \frac{\$15,625}{(1 + 0.10)^t}
\]

#### Project B:
- **Year 0**: -$50,000
- **Year 1-4**: $0
- **Year 5**: $99,500

\[
\text{NPV}_B = -\$50,000 + \frac{\$99,500}{(1 + 0.10)^5}
\]

Let's calculate the NPVs for both projects.

### Step 2: IRR Calculation

The IRR is the discount rate at which the NPV of the project equals zero:

\[
0 = \sum \left(\frac{\text{Cash Flow}_t}{(1 + \text{IRR})^t}\right) - \text{Initial Investment}
\]

We'll calculate the IRR for both Project A and Project B.

### Calculations

Let's compute these values.### Results:

- **Project A:**
  - **NPV:** $9,231.04
  - **IRR:** 16.99%

- **Project B:**
  - **NPV:** $11,781.67
  - **IRR:** 14.75%

### Recommendation:

Based on the NPV criterion, **Project B** should be selected because it has a higher NPV ($11,781.67) compared to Project A ($9,231.04). Although Project A has a higher IRR (16.99%), NPV is generally considered a more reliable measure, especially when projects are mutually exclusive.

Would you like more details or have any questions?

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Here are 5 related questions you might find helpful:

1. How does the IRR method compare to the NPV method in decision-making?
2. What are the limitations of using IRR as a project evaluation metric?
3. How would changes in the cost of capital affect the NPVs of these projects?
4. Can NPV and IRR ever give conflicting recommendations? If so, which one should be followed?
5. How does the timing of cash flows impact the IRR and NPV calculations?

**Tip:** When projects are mutually exclusive, rely more on the NPV, as it directly measures the increase in value to the firm and avoids the pitfalls of the IRR, such as multiple IRRs or ranking conflicts.

Learn how to compare two mutually exclusive projects based on their Net Present Value (NPV) and Internal Rate of Return (IRR). Calculate NPV and IRR for each project using projected cash flows and a cost of capital of 10%. Project A and Project B are analyzed to determine which project provides a higher NPV and evaluate the impact of different discount rates.

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