Fin 534 Homework Set 2 2015 Strayer University All Rights Re

Fin 534 Homework Set 2 2015 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. 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. Use the following information for Questions 1 through 2:

Questions and Calculations

Question 1:

What is the present value of the following uneven cash flow stream: -$50, $100, $75, and $50 at the end of Years 0 through 3? The appropriate interest rate is 10%, compounded annually.

To calculate the present value (PV), each cash flow is discounted at the given interest rate: PV = Σ (Cash Flow / (1 + r)^t). Using r = 10% or 0.10:

  • Year 0: -$50 / (1 + 0.10)^0 = -$50 / 1 = -$50
  • Year 1: $100 / (1 + 0.10)^1 = $100 / 1.10 ≈ $90.91
  • Year 2: $75 / (1 + 0.10)^2 = $75 / 1.21 ≈ $61.98
  • Year 3: $50 / (1 + 0.10)^3 = $50 / 1.331 ≈ $37.56

Summing these: PV ≈ -$50 + $90.91 + $61.98 + $37.56 ≈ $140.45

Question 2:

Suppose that on January 1 you deposit $100 in an account that pays a nominal (or quoted) interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months later?

Assuming 365 days in a year, the daily interest rate is: 0.1133463 / 365 ≈ 0.0003104. The number of days from January 1 to October 1 is approximately 273 days.

Future value (FV) = Principal × (1 + daily interest rate)^{number of days} = $100 × (1 + 0.0003104)^{273}.

Calculating: FV ≈ $100 × e^{273 × ln(1.0003104)}. Since ln(1 + x) ≈ x for small x, approximate as:

FV ≈ $100 × e^{273 × 0.0003104} ≈ $100 × e^{0.0849} ≈ $100 × 1.0896 ≈ $108.96

Question 3:

A firm issues a 10-year, $1,000 par value bond with a 10% annual coupon and a required rate of return of 10%. What is the yield to maturity (YTM) on:

  • A 10-year, 9% annual coupon, $1,000 par value bond that sells for $887.00?
  • A bond that sells for $1,134.20?

Since the bond's coupon rate is below or above the required rate, the bond sells at a discount or premium respectively. Calculating YTM involves solving the bond pricing equation:

P = Σ (C / (1 + YTM)^t) + face value / (1 + YTM)^t, where C = Coupon payment, P = Price, t = year.

For the 9% coupon bond:

  • Coupon payment C = 0.09 × $1,000 = $90
  • Price P = $887

Since the bond trades below face value, the YTM exceeds 9%. Using iterative approximation or a financial calculator, the YTM is approximately 10.5%.

Similarly, for the bond selling at $1,134.20, which is above face value, the YTM will be less than 10%. Approximate YTM ≈ 9.0%.

The relationship indicates that when a bond trades at a discount, the YTM > coupon rate; at a premium, the YTM

Question 4:

What are the total return, the current yield, and the capital gains yield for the discount bond ($887) and premium bond ($1,134.20) in Question 3, assuming the bonds are held to maturity and there is no default?

Definitions:

  • Total Return: (Income + Capital Gain) / Initial Price
  • Current Yield: Coupon Payment / Purchase Price
  • Capital Gains Yield: (Sell Price - Purchase Price) / Purchase Price

For the $887 bond:

  • Coupon payment = $90
  • Capital gain = $1,000 - $887 = $113
  • Total return = ($90 + $113) / $887 ≈ 0.2138 or 21.38%
  • Current yield = $90 / $887 ≈ 0.1014 or 10.14%
  • Capital gains yield = $113 / $887 ≈ 0.1273 or 12.73%

For the $1,134.20 bond:

  • Coupon payment = $90
  • Capital loss = $1,134.20 - $1,000 = -$134.20
  • Total return = ($90 - $134.20) / $1,134.20 ≈ -0.0419 or -4.19%
  • Current yield = $90 / $1,134.20 ≈ 0.0792 or 7.92%
  • Capital gains yield = -$134.20 / $1,134.20 ≈ -0.1182 or -11.82%

These yields illustrate how bond prices influence returns, with discounts typically offering higher total yields due to capital gains, and premiums often resulting in capital losses over the holding period.

References

  • Fabozzi, F. J. (2016). Bond Markets, Analysis and Strategies. Pearson.
  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
  • Ross, S. A., Westerfield, R., & Jaffe, J. (2019). Corporate Finance. McGraw-Hill Education.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Intrinsic Value of Any Asset. John Wiley & Sons.
  • Steven, A. (2017). Fundamentals of Investments. McGraw-Hill Education.
  • Investopedia. (2020). Present Value. https://www.investopedia.com/terms/p/presentvalue.asp
  • Investopedia. (2020). Yield to Maturity (YTM). https://www.investopedia.com/terms/y/yieldtomaturity.asp
  • Fabozzi, F. J. (2013). The Handbook of Fixed Income Securities. McGraw-Hill.
  • Reilly, F. K., & Brown, K. C. (2012). Investment Analysis and Portfolio Management. Cengage Learning.
  • Michel, A., & Ennew, C. (2017). Financial Markets and Institutions. Oxford University Press.

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