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FIN 4453 – PROJECT 1 (10 Questions)
Fall 2024
1. (15 Points) A rapidly growing firm is currently paying a dividend of $3.60. The dividend growth rate is expected to be 6% for the next 2 years, 5% for the following 4 years, 4% for the next 3 years, and 3% annually thereafter. The expected return on the market is 8%, the risk-free rate is 4% and the firm’s Beta is 0.88.
a. Calculate the estimated price (intrinsic value) for a share of this firm’s stock.
b. If an analyst uses a 6% rule, at what price range would this stock be fairly priced?
c. Using EXCEL’s Data Table feature create a two-way data table to determine the cost of equity by varying both Beta and the risk-free rate of interest. Use Beta values of 0.55 to 1.45 in increments of 0.15, and risk-free interest rate values of 2%, 3%, 4%, 5%, and 6%.
d. Using EXCEL’S Text Box Feature explain how the cost of equity is impacted by:
i. A change in Beta
ii. A change in the risk-free interest rate.
2. (15 Points) The Excel file Stock Data contains monthly data for several stocks and the S&P 500 Index (i.e., the market).
a. Compute the equation of the Characteristic Line for MSFT.
b. Explain what the intercept term in this equation measures relative to the market return.
c. Explain what the slope term in this equation measures relative to the market return.
d. Conduct a complete hypothesis test to determine if a is Significant.
e. Conduct a complete hypothesis test to determine if β is Significant.
f. Compute the R2 value associated with this equation.
g. Explain what R2 measures for this equation.
h. Construct a graph of the Characteristic Line for MSFT.
i. On this graph (using EXCEL’s graphing features) include a trendline, the computed equation, and the R2 value.
ii. Label the axes and include a title for the graph.
3. (10 Points) An investment has the following cash flows:
July 12, 2008 $ -750
September 22, 2009 $ +700
March 5, 2010 $ +400
August 25, 2011 $ +500
July 18, 2012 $ +800
December 19, 2013 $ -1800
a. Create a data table and graph illustrating the impact of the discount rate on the Net Present Value of this investment. Include a title and label the axes for the graph.
b. Use Solver to determine the Internal Rate of Return(s) associated with this investment.
4. (10 Points) You are considering buying a risky bond. The bond has a $1,000 face value, a 1-year maturity, and a coupon rate of 8%. Coupon payments are made annually. You believe the probability the company will survive to pay off the bond is 88%. You also believe there is a 12% probability the company will default within the first 3 months, in which case you will be able to recover 32% of the bond’s face value at the end of year 1. The bond is selling for $880.
a. Calculate the expected return on this bond on an annual basis.
b. Use Goal Seek or Solver to determine the probability of survival that would yield an expected annual return of 6%.
5. (10 Points) An employee plans to invest in a retirement fund at the beginning of each of the next 14 years. The employee will initially invest $40,000 in the first year and increase the annual investment amount by 6% in each subsequent year. The employee believes she will earn 8% annually on her investments in the first 2 years, then 6% annually in the next 3 years, then 5% annually in the next 4 years, and then 4% annually in each of the final 5 years before she retires.
a. How much money will the employee have in the retirement fund when she retires?
b. What would be the internal rate of return associated with her investments and her final retirement position?
6. (8 Points) A college savings education plan claims that had you invested $600 semi-annually in the plan for the last 16 years you would have accumulated $100,000. Assuming the investments were made at the beginning of each semi-annual period, calculate the effective compound annual rate of return an investor would have received using either Goal Seek or Solver.
7. (8 Points) This question relates to the computation of a firm’s cost of equity.
a. Assume the current selling price of a firm’s stock is: $50. Using the Excel file Dividend Data, compute the firm’s annualized cost of equity using the Gordon dividend model.
8. (8 Points) This question addresses issues related to interest rates and rates of return.
a. Compute the Present Value of the following cash flows using a continuously compounded annual interest rate of 6.5%.
Year Cash Flows
0.60 500
1.20 675
2.20 800
3.50 855
4.30 930
5.50 600
6.75 750
b. Suppose at time 0 you had $1500 in the bank and 10 years later you had $9500. Calculate the effective annual rate of return if the bank pays interest continuously.
c. Suppose at time 0 you had $700 in the bank and 8 years later you had $2000. Calculate the effective annual rate of return if the bank pays compound interest weekly.
9. (8 Points) The following problem addresses issues related to present value.
a. If today is May 10, 2024, and the cost of capital r = 7%, what is the net present value of the following cash flows as of May 10, 2024:
03/07/2025 $ +800
07/25/2026 $ +300
04/12/2027 $ +750
09/18/2028 $ +475
02/05/2029 $ +625
10/27/2030 $ +950
11/02/2031 $ +550
b. A customer will pay $75 per quarter at the beginning of each quarter to her Internet provider for the next 4 years. Determine the net present value of these payments if the annual discount rate is 8%.
10. (8 Points) I have $700,000 in the bank now. I plan to withdraw $25,000 at the end of this year. Each subsequent end of year withdrawal will increase by 5%. If I earn 10% per year on my bank funds in the first 2 years, then 5% per year in the next 3 years, and 3% per year in the following 4 years,
a. Determine how much money I will have at the end of 9 years.
b. Determine the initial withdrawal amount at the end of this year that will leave me with no money at the end of 9 years using either Solver or Goal Seek.