Fin 534 Homework Set 2 2014 Strayer University All Rights Re

Fin 534 Homework Set 2 2014 Strayer University All Rights Reserve

Answer the following questions on a separate document. Explain how you reached the answer or show your work if a mathematical calculation is needed, or both. Submit your assignment using the assignment link in the course shell. This homework assignment is worth 100 points. Use the following information for Questions 1 through 5: Assume that you are nearing graduation and have applied for a job with a local bank. The bank’s evaluation process requires you to take an examination that covers several financial analysis techniques. The first section of the test asks you to address these discounted cash flow analysis problems:

Paper For Above instruction

Question 1: Present Value of Uneven Cash Flows

Calculate the present value (PV) of an uneven cash flow stream occurring at the end of Years 0 through 3, with cash flows of -$50, $100, $75, and $50 respectively, using a discount rate of 10% compounded annually. To find the PV, each cash flow must be discounted back to the present using the formula PV = CF / (1+r)^n, where CF is the cash flow, r is the interest rate, and n is the year. Specifically, PV = -50 / (1+0.10)^0 + 100 / (1+0.10)^1 + 75 / (1+0.10)^2 + 50 / (1+0.10)^3.

Question 2: Time to Double Investment

Determine how long it takes an investment growing at 20% annually to double in value. Using the rule of 72, which is a simple approximation, divide 72 by the growth rate: 72 / 20 = 3.6 years. For a exact calculation, solve the equation (1 + 0.20)^t = 2 for t, which yields t = log(2) / log(1.20) ≈ 3.80 years.

Question 3: Impact of Compounding Frequency on Future Value

When interest is compounded more frequently than annually, the future value (FV) of an initial amount increases when holding the nominal rate constant. This occurs because more frequent compounding means interest is calculated and added to the principal more often, leading to interest-on-interest effects. Mathematically, FV = PV (1 + r/m)^(mt), where m is the number of compounding periods per year. As m increases, FV increases if r, PV, and t are constant. Therefore, compounding semiannually, quarterly, or daily results in higher FV compared to annual compounding due to more frequent interest application.

Question 4: Effective Annual Rate (EAR) Calculations

Given a nominal rate of 12%, compounded semiannually (m=2), quarterly (m=4), monthly (m=12), and daily (m=365), the EAR is calculated by:

  • Semiannual: EAR = (1 + 0.12/2)^2 - 1 = (1 + 0.06)^2 - 1 ≈ 12.36%
  • Quarterly: EAR = (1 + 0.12/4)^4 - 1 = (1 + 0.03)^4 - 1 ≈ 12.55%
  • Monthly: EAR = (1 + 0.12/12)^12 - 1 = (1 + 0.01)^12 - 1 ≈ 12.68%
  • Daily: EAR = (1 + 0.12/365)^365 - 1 ≈ 12.75%

These calculations illustrate that higher compounding frequencies result in a higher EAR due to the effects of interest accumulation on interest more frequently within a year.

Question 5: Growth of Deposits with Daily Compounding

You deposit $100 at a nominal rate of 11.33463%, compounded daily, for 9 months (which is about 273 days). Using the formula FV = PV (1 + r/n)^(nt), where r = 0.1133463, n=365, t=273/365 ≈ 0.75 years:

FV = 100 (1 + 0.1133463/365)^(3650.75) ≈ 100 (1 + 0.0003104)^273 ≈ 100 e^{0.0003104 273} ≈ 100 e^{0.0848} ≈ 100 * 1.0885 ≈ $108.85.

Additional Questions

Use the above understanding of time value of money and interest calculations to address questions 6 through 9:

Question 6: Bond Valuation with Increased Inflation Expectation

A 10-year, $1,000 par value bond with a 10% annual coupon and a required return (rd) of 10% is issued. If inflation rises, causing the required return to increase to 13%, the bond’s value declines. The bond’s value is determined by discounting future coupon payments and face value at the new rd of 13%. Since rd > coupon rate, the bond price will fall below $1,000, indicating it is now trading at a discount.

Question 7: Bond Valuation with Lower Inflation

If inflation decreases, and the required rate decreases to 7%, the bond’s value increases above $1,000, indicating a premium bond. The lower discount rate results in higher present values of future cash flows, thus increasing the bond’s price.

Question 8: Yield to Maturity (YTM)

For a bond with a 9% coupon rate, 10-year maturity, and face value of $1,000, selling at $887, the YTM is found by solving the present value of the bond's cash flows equal to its current price. When the bond sells at a discount, the YTM exceeds the coupon rate; conversely, if it sells at a premium ($1,134.20), the YTM is less than the coupon rate. Approximate YTM calculations can be performed using iterative methods or financial calculators.

Question 9: Total Return, Current Yield, and Capital Gains Yield

The total return considers all earnings from holding the bond to maturity, including the coupon payments and capital gains or losses due to price changes. Current yield is calculated as annual coupon payment divided by current price: for the discount bond at $887, current yield = $90 / $887 ≈ 10.14%; for the premium bond at $1,134.20, current yield = $90 / $1,134.20 ≈ 7.93%. Capital gains yield is derived from the change in bond price over the period, assuming the bondholder holds it to maturity with no default risk, and influences the total return accordingly.

References

  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Fabozzi, F. J. (2013). Bond Markets, Analysis, and Strategies. Pearson.
  • Ross, S. A., Westerfield, R. W., & Jaffe, J. (2013). Corporate Finance. McGraw-Hill Education.
  • Brealy, R. A., Myers, S. C., & Allen, F. (2016). Principles of Corporate Finance. McGraw-Hill Education.
  • Higgins, R. C. (2012). Analysis for Financial Management. McGraw-Hill Education.
  • Glen, J. (2018). "Understanding the Effect of Compounding Frequencies." Journal of Finance and Financial Analysis.
  • Investopedia (2023). "Effective Annual Rate (EAR) Definition." https://www.investopedia.com/terms/e/ear.asp
  • Chen, L., & Wang, D. (2019). "Impact of Inflation on Bond Prices." Financial Review
  • Hull, J. C. (2017). Options, Futures, and Other Derivatives. Pearson.
  • Mishkin, F. S., & Eakins, S. G. (2016). Financial Markets and Institutions. Pearson.

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