Step-by-Step Solution

Given Data:

• Estimated annual net cash flows: $13,750
• Number of years: 3
• Cost of the project: $30,000
• Minimum acceptable rate of return: 10%
• Present value factor for 3 years at 10%: 2.487 (from the table)

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(a) Net Present Value (NPV)

Formula:
$NPV = (Annual\ Net\ Cash\ Flow \times Present\ Value\ Factor) - Initial\ Investment$

Substituting the values: $NPV = (13,750 \times 2.487) - 30,000$

$NPV = 34,186.25 - 30,000 = 4,186.25$

The Net Present Value (NPV) is $4,186 (rounded to the nearest dollar).

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(b) Present Value Index (PVI)

Formula:
$PVI = \frac{\text{Total Present Value of Net Cash Flows}}{\text{Initial Investment}}$

Substituting the values: $PVI = \frac{13,750 \times 2.487}{30,000}$

$PVI = \frac{34,186.25}{30,000} = 1.14$

The Present Value Index (PVI) is 1.14 (rounded to two decimal places).

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Final Answers:

1. Net Present Value (NPV): $4,186
2. Present Value Index (PVI): 1.14

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Let me know if you need further explanation or calculations!

Related Questions:

1. What does a positive NPV indicate about a project’s viability?
2. How does changing the discount rate affect the NPV of a project?
3. Can a project with an NPV of 0 still be considered viable? Why?
4. What is the significance of the Present Value Index in decision-making?
5. How do you calculate the break-even discount rate for a project?

Tip:

Always cross-check values from financial tables and use consistent rounding rules to ensure precision in financial decision-making.