To determine which project should be accepted, we analyze the Net Present Value (NPV) and the Profitability Index (PI) for each project, as they help assess the value a project generates relative to its cost. Since the question explicitly asks for the best reasoning, we prioritize NPV for decision-making unless the profitability index (PI) conflicts or adds insight.

Calculations:

The formula for NPV is:

$NPV = \sum \frac{C_t}{(1 + r)^t} - C_0$

Where:

• $C_t$: Cash flow at time $t$,
• $C_0$: Initial investment,
• $r$: Discount rate (14% = 0.14),
• $t$: Year.

The formula for Profitability Index (PI) is:

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

Project A:

NPV of Project A:

$NPV_A = \frac{9500}{(1+0.14)^1} + \frac{16200}{(1+0.14)^2} + \frac{8700}{(1+0.14)^3} - 24000$

Breaking it down:

• Year 1: $\frac{9500}{1.14} = 8333.33$,
• Year 2: $\frac{16200}{(1.14)^2} = 12461.57$,
• Year 3: $\frac{8700}{(1.14)^3} = 5778.45$.

$NPV_A = 8333.33 + 12461.57 + 5778.45 - 24000 = 2605.35$

PI of Project A:

$PI_A = \frac{8333.33 + 12461.57 + 5778.45}{24000} = 1.11$

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Project B:

NPV of Project B:

$NPV_B = \frac{6500}{(1+0.14)^1} + \frac{9800}{(1+0.14)^2} + \frac{15200}{(1+0.14)^3} - 21000$

Breaking it down:

• Year 1: $\frac{6500}{1.14} = 5701.75$,
• Year 2: $\frac{9800}{(1.14)^2} = 7515.30$,
• Year 3: $\frac{15200}{(1.14)^3} = 10095.55$.

$NPV_B = 5701.75 + 7515.30 + 10095.55 - 21000 = 1312.60$

PI of Project B:

$PI_B = \frac{5701.75 + 7515.30 + 10095.55}{21000} = 1.06$

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Decision:

• NPV Comparison: Project A ($2605.35$) > Project B ($1312.60$).
• PI Comparison: Project A ($1.11$) > Project B ($1.06$).

Since NPV and PI agree, the best decision is Project A because it has the higher Net Present Value.

Correct Answer:

Project A; because it has the higher net present value.

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Let me know if you'd like detailed steps for calculations or further insights!

Follow-up questions:

1. What is the significance of the Net Present Value in investment decision-making?
2. How does the Profitability Index relate to NPV, and why might one be preferred in some situations?
3. Could the payback period ever influence the choice between two mutually exclusive projects?
4. How would a change in the required return rate (e.g., from 14% to 12%) affect the analysis?
5. What are other key factors to consider when comparing two mutually exclusive projects?

Tip: Always prioritize NPV for mutually exclusive projects as it measures the absolute value added, while PI is more useful for resource-constrained scenarios.