MT480 CORPORATE FINANCE

Assignment: Time Value of Money and Multiple Cash Flow Valuation

This assignment evaluates your mastery of time value of money (TVM) concepts from Chapter 5 and multiple cash flow valuation techniques from Chapter 6. You will demonstrate your understanding through calculations, analysis, and real-world applications while leveraging Gemini AI as an analytical assistant.

AI Documentation Requirements

For every interaction with Gemini AI, include a brief note that summarizes:

• The specific question or request you made
• A summary of Gemini AIs response
• How the AI improved or clarified your analysis
• Any limitations or where you relied on your own understanding

Part 1: Single Cash Flow Analysis (Chapter 5) 14 Points

Task 1A: Present and Future Value Fundamentals (8 Points)

Problem Set:

1. Future Value: What will a $12,000 investment at 8% annual interest be worth in 15 years?
2. Present Value: What is the present value of $85,000 received in 7 years at a 10% discount rate?
3. Interest Rate: What annual rate is required for $20,000 to grow to $35,000 in 6 years?
4. Time Period: How long will it take for $8,000 to double at 9% annual interest?

AI Integration:

• Use Gemini AI to verify each calculation.
• Ask it to model how outcomes change by adjusting one variable (rate, time, or amount) by 20%.
• Create a table with Gemini AI showing how each variable affects results when increased and decreased by 20%.

Task 1B: Investment Evaluation Application (6 Points)

Scenario: Equipment costs $75,000 and is expected to return:

• Year 3: $25,000
• Year 5: $35,000
• Year 8: $40,000

Instructions:

1. Calculate the present value of each cash inflow using a 12% discount rate.
2. Calculate the total present value of all inflows.
3. Determine whether the investment should be accepted based on the initial cost.
4. Compute the projects net present value (NPV).

AI Integration:

• Ask Gemini AI to identify the break-even discount rate at which the NPV = $0.
• Create a chart showing NPV values at discount rates from 6% to 18% (in 2% increments).

Part 2: Multiple Cash Flows and Annuities (Chapter 6) 18 Points

Task 2A: Annuity Calculations (10 Points)

Problem Set:

1. Present Value of an Ordinary Annuity: $5,500/year for 8 years at 7%
2. Present Value of an Annuity Due: Same cash flow, but received at the beginning of each year
3. Future Value of Annuity: $2,400/year for 12 years at 6% interest
4. Payment Calculation: What annual payment is required to accumulate $50,000 in 10 years at 8%?

AI Integration:

• Use Gemini AI to create a table comparing present values at discount rates ranging from 5% to 15% (in 2% increments).
• Ask AI to explain the differences between ordinary annuities and annuities due based on timing of payments.

Task 2B: Perpetuities and Growing Cash Flows (8 Points)

Problem Set:

1. Perpetuity: $8,000 annually, starting in one year, at 9%
2. Growing Perpetuity: Starts at $6,000, grows at 3% annually, discounted at 10%
3. Growing Annuity: Starts at $4,000, grows 4% annually for 15 years, at 11% discount rate

AI Integration:

• Ask Gemini AI to model how changing the growth rate (1% to 6%) affects the present value of the growing perpetuity.
• Create a chart showing the sensitivity of the present value to each growth rate.
• Reflect on how small growth rate changes impact long-term value.

Part 3: Interest Rate Applications and Real-World Analysis 8 Points

Task 3A: Effective Annual Rate vs. APR (4 Points)

Problem:

A credit card advertises an APR of 18% compounded monthly.

1. Calculate the effective annual rate (EAR)
   
2. How much will you owe after one year on a $5,000 balance, assuming no payments?
3. Compare this to an 18% simple interest calculation
4. Explain the implications of compounding for business finance

AI Integration:

• Use Gemini AI to model how EAR changes with monthly, quarterly, and daily
• Create a table comparing EAR across different compounding frequencies.

Task 3B: Long-Term Investment Facility Decision (4 Points)

Scenario: A new manufacturing facility requires a $450,000 investment. Projected returns are:

• Years 13: $75,000/year
• Years 48: $95,000/year
• Years 912: $110,000/year
• Terminal value at Year 12: $125,000

Required return: 13%

Instructions:

1. Calculate the present value of each cash flow stream
2. Determine total present value and NPV
3. Make a recommendation based on your findings
4. Identify key variables that could influence the decision

AI Integration:

• Ask Gemini AI to run a sensitivity analysis by adjusting:
  • Cash flows 10%
  • Discount rate 2%
• Create a chart or table summarizing how changes in these variables affect the NPV and your decision.

Submission Requirements

Format: Submit as a single Word or PDF file with:

• Clear headers for each task
• Step-by-step calculations
• Complete sentences and professional formatting
• AI documentation integrated in each relevant section

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