Assignment 1: Six Problems Listed With Point Values ✓ Solved

Assignment 1there Are 6 Problems Listed Below With Point Values Assign

There are 6 problems listed below with point values assigned for each. Each problem corresponds to material from Chapters 1, 2, 3, 4, 7. Complete each problem in Excel. Submit your Excel worksheet in EXCEL format so I can see how you solved the problems. Please MARK or Outline your answers so I can tell where they are. See questions below.

Sample Paper For Above instruction

Problem 1 (4 Points): You need money for new equipment. You will take out a loan of $21,500 for a term of 4 years at 3.8% (PYCY) interest. You and the lender have agreed that this loan will be paid back in one payment at the end of 4 years. How much will you pay if the lender charges simple interest? How much will you pay if the lender charges compound interest?

Problem 2 (8 Points): You are looking at loans and considering a loan of $41,620 from a lender at 5.1% interest over a 5-year period. Show two different ways and calculate the results that demonstrate financial equivalence for this problem. I am looking for two different methods using compound interest. How much will you pay over the life of the loan in each way? Briefly explain the concept of financial equivalence. What is the book definition? Explain what that means in your own words.

Problem 3 (8 Points): You want to buy a boat when you retire. It's a big one and you will need $375,000 in the bank when you retire in 15 years to buy it. You have $21,000 to open the account and you will deposit $900 at the end of each month. What yearly rate will you need in the market for this to work?

Problem 4 (8 Points): You have the plan locked in for the dream boat account. Now you are working on the FUEL Account (it's a big boat). You need $102,000 in that account in 15 years. You are able to place $4,050 into the account at the end of each year. No balance on year 0. First deposit is on year 1. But, you know that won't get you there. You are expecting an inheritance from your late aunt in 5 years. (start the savings account now.. 5 years from now, you will have $$ from aunt). If you can get a 3.6% rate on your account (PYCY)… how much do you need from your Aunt to make this work?

Problem 5 (12 Points): Your company is preparing to launch a new product over the next 10 years. The equipment to make this new product will have an initial cost of $154,000 to the company. At the end of the project, you believe you can get $26,000 for the equipment as salvage. Supplies will cost $1,800 the first year and go up by $750 each year. Maintenance costs start at $1,510 the first year and will increase by 1.9% each year. The company expects to make $18,500 the first year and this will increase by 2.1% each year. Create the cash flow table showing these costs and profits and the net cash flow. If the interest rate is 3.8%, what will be the NPV of the project? What is the book definition of NPV? Put that definition in your own words.

Problem 6 (10 Points): Please examine the provided cash flow table:

  • Year 0: -9P
  • Year 1: -3P
  • Year 2: 0.5P
  • Year 3: 4P
  • Year 4: P
  • Year 5: P

The interest rate is 3.9%. Use the goal seek function to answer these questions:

  1. 6a. What is the value of P at 3.9% to make all of the cash flow transactions balance out?
  2. 6b. If P is $5,500, what rate do we need?

Sample Paper For Above instruction

Problem 1: Calculating Loan Payments with Simple and Compound Interest

In financial decision-making, understanding how different interest calculations impact loan repayment amounts is essential. Given a loan of $21,500 for four years at an annual interest rate of 3.8%, the first step is to determine the total payment under simple interest. Simple interest is calculated using the formula: Interest = Principal x Rate x Time. Therefore, for simple interest, the total interest accrued over four years is:

Interest = $21,500 x 0.038 x 4 = $3,268

Thus, the total amount payable at the end of four years is:

Total = Principal + Interest = $21,500 + $3,268 = $24,768

In contrast, compound interest considers interest on accumulated interest. The formula for future value with compound interest is:

FV = Principal x (1 + r/n)^{nt}

Assuming compounded annually, n=1, the calculation becomes:

FV = $21,500 x (1 + 0.038)^4 ≈ $21,500 x 1.1614 ≈ $24,977.10

Therefore, under compound interest, the total payment at the end of 4 years is approximately $24,977.10. This comparison illustrates the impact of interest calculation methods on loan repayment amounts, highlighting the importance of understanding underlying financial concepts in borrowing decisions.

Problem 2: Demonstrating Financial Equivalence with Compound Interest in Loans

Financial equivalence refers to different financial arrangements yielding the same future value or present value, enabling comparison of different loan options. Here, a loan of $41,620 at 5.1% interest over five years can be analyzed using two different compounded interest methods to demonstrate equivalence.

Method 1: Using Future Value (FV) formula:

FV = PV x (1 + r)^n = $41,620 x (1 + 0.051)^5 ≈ $41,620 x 1.2834 ≈ $53,448.48

Method 2: Using Present Value (PV) with the same interest rate, considering the scheduled payments, yields the same FV if computed accordingly. Both methods demonstrate how variations in calculation approach still lead to equivalent financial outcomes, emphasizing the importance of understanding compounding in financial products.

Financial equivalence essentially means that different interest calculation methods or payment schedules, when properly understood, result in comparable financial obligation or benefit, allowing investors and borrowers to make informed choices.

Problem 3: Calculating Required Interest Rate for Saving Goals

Future value, present deposits, and periodic contributions determine the necessary annual interest rate. Using the future value of an investment with regular deposits (ordinary annuity) plus a lump sum initial deposit:

FV = P [(1 + r)^t - 1]/r + PV (1 + r)^t

Given: FV = $375,000, PV = $21,000, PMT = $900/month ($10,800/year), t = 15 years

Solving for r involves iterative calculation or financial calculator use. Approximate solutions suggest the required annual rate is approximately 8.5% to 9.0% to reach the goal, considering the contributions and initial deposit.

Problem 4: Determining Additional Funds from Aunt for Future Savings

Target: $102,000 in 15 years, with annual deposits of $4,050, and a 3.6% interest rate. First, calculate the future value of the series of deposits starting in 5 years, then determine the lump sum needed at the beginning to reach the goal.

The future value of an ordinary annuity:

FV = PMT * [(1 + r)^n - 1]/r

Calculate FV of deposits made over 10 years starting from year 5 to year 15, then find the present value of this amount at year 0, subtracting initial deposits and accumulated interest, to find the plus amount required from the aunt.

Problem 5: Cash Flows and NPV of a New Product Launch

The project involves initial investment, salvage, variable costs, and revenues over 10 years. Building the cash flow table involves calculating each year's costs and revenues, adjusting for inflation, and discounting at 3.8%. The NPV is the sum of the discounted cash flows minus initial investment. This metric evaluates the profitability of the project, guiding investment decisions. In my own words, NPV is the total value of net cash inflows and outflows over the project's life, discounted at the required rate, indicating whether the project adds value to the company.

Problem 6: Goal Seek to Find P and Required Rate

This problem involves balancing cash flows with goal seek. To find P that makes total cash flows zero at a 3.9% rate, use Excel's goal seek function to set the net present value to zero, changing P. To find the rate when P = $5,500, use goal seek to set the net present value to zero by varying the interest rate. These functions facilitate finding unknown variables in financial equations efficiently.

References

  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley Finance.
  • Ross, S. A., Westerfield, R., & Jaffe, J. (2018). Corporate Finance (12th ed.). McGraw-Hill Education.
  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Bernstein, P. L. (2019). Capital Ideas: The Improbable Origins of Modern Wall Street. Wiley.
  • Clark, E. (2014). Principles of Financial Engineering. Cambridge University Press.
  • Fabozzi, F. J., & Modigliani, F. (2003). Capital Markets: Institutions, Risks, and Rewards. Prentice Hall.
  • Higgins, R. C. (2012). Analysis for Financial Management (10th ed.). McGraw-Hill Education.
  • Kaplan, R. S., & Norton, D. P. (2004). Strategy Maps: Converting Intangible Assets into Tangible Outcomes. Harvard Business Review Press.
  • Van Horne, J. C., & Wachowicz, J. M. (2008). Fundamentals of Financial Management (13th ed.). Pearson Education.

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