Sheet1 Directions: Answer The Following Questions On A Separ

Sheet1directions Answer The Following Questions On a Separate Documen

Sheet1directions Answer The Following Questions On a Separate Documen

Sheet1 Directions: 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: 1 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. The PV of uneven cash flow stream of ($50) at a 10% interest rate compounded annually at the end of Years 0 through 3 is $37.57 PV=FV/1...

The PV of uneven cash flow stream of $100 at a 10% interest rate compounded annually at the end of Years 0 through 3 is $75.13 The PV of uneven cash flow stream of $75 at a 10% interest rate compounded annually at the end of Years 0 through 3 is $56.35 The PV of uneven cash flow stream of $50 at a 10% interest rate compounded annually at the end of Years 0 through 3 is ($37.. 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? Use the following information for Questions 3 and 4: A firm issues a 10-year, $1,000 par value bond with a 10% annual coupon and a required rate of return is 10%.

3. What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does a bond selling at a discount or at a premium tell you about the relationship between rd and the bond’s coupon rate?

4. What are the total return, the current yield, and the capital gains yield for the discount bond in Question #3 at $887.00? At $1,134.20? (Assume the bond is held to maturity and the company does not default on the bond.)

Paper For Above instruction

In the realm of financial analysis, understanding the core concepts of present value, bond valuation, and yield calculations is pivotal for making informed investment decisions. This paper addresses key questions revolving around these themes, applying foundational financial principles to real-world scenarios involving uneven cash flows, compound interest, and bond market dynamics.

Calculating Present Value of Uneven Cash Flows

The first scenario involves calculating the present value (PV) of an uneven cash flow stream of -$50, $100, $75, and $50 across four years, with an annual interest rate of 10%. The PV formula for each cash flow is:

PV = Cash Flow / (1 + r)^t

where r is the interest rate and t is the year. Applying this to each cash flow:

  • Year 0: PV = -50 / (1.10)^0 = -50
  • Year 1: PV = 100 / (1.10)^1 ≈ 90.91
  • Year 2: PV = 75 / (1.10)^2 ≈ 61.98
  • Year 3: PV = 50 / (1.10)^3 ≈ 37.57

The total PV of the stream is the sum: -50 + 90.91 + 61.98 + 37.57 ≈ 140.03. Note that the initial cash flow was negative, indicating an outflow, while the remaining are inflows, leading to a net present value (NPV) of approximately $140.03. This calculation demonstrates how uneven cash flows are discounted to their present value using the appropriate rate, crucial for investment evaluations.

Future Value of a Daily Compounded Account

Next, consider a deposit of $100 on January 1 into an account with an annual nominal interest rate of 11.33463%, compounded daily. To compute the future value (FV) after 9 months (October 1), the following formula applies:

FV = PV × (1 + i/n)^(n×t)

where i is the annual interest rate, n is the number of compounding periods per year (365 for daily), and t is time in years.

Substituting values:

FV = 100 × (1 + 0.1133463/365)^(365×(9/12))

Calculating the exponent:

FV ≈ 100 × (1 + 0.0003106)^273 ≈ 100 × e^(0.0003106×273) ≈ 100 × e^0.0848 ≈ 100 × 1.0884 ≈ 108.84

Thus, approximately $108.84 will be in the account after 9 months, reflecting the effect of daily compounding on growth over this period.

Bond Valuation and Yield to Maturity

The third question pertains to a 10-year, $1,000 par value bond with a 10% coupon rate, which corresponds to annual coupon payments of $100. The yield to maturity (YTM) is the internal rate of return (IRR) of the bond’s cash flows, given its current market price.

For bonds trading below par ($887), the YTM exceeds the coupon rate, indicating it's sold at a discount, which implies a higher return to compensate for the lower purchase price.

Using the bond pricing formula:

P = \sum_{t=1}^{n} \frac{C}{(1 + y)^t} + \frac{F}{(1 + y)^n}

where P is price, C is annual coupon, F is face value, n is years to maturity, and y is YTM.

Applying numerical methods or a financial calculator, the YTM for the bond selling at $887 is approximately 11.93%, whereas at $1,134.20, it is approximately 8.35%. The difference signifies that bonds trading at a discount have yields above their coupon rate, while those at a premium have yields below the coupon rate.

Total Return, Current Yield, and Capital Gains Yield

These metrics evaluate the return on bond investments under the assumption of holding to maturity without default:

  • Current Yield: C / P
  • Capital Gains Yield: (P_{end} - P_{initial}) / P_{initial}
  • Total Return: Sum of income (coupons) plus capital gains, expressed as a percentage of initial price.

At the purchase price of $887, the current yield is:

100 / 887 ≈ 11.27%

At the sale price of $1,134.20, the current yield drops to:

100 / 1134.20 ≈ 8.82%

The capital gains yield for holding from initial purchase to maturity can be approximated by:

(1000 - 887) / 887 ≈ 12.78%

and correspondingly at the premium price, the capital loss or gain can be calculated depending on the future sale or redemption price.

The total return combines annual coupon income and the capital gains/losses over the holding period, essential for assessing investment performance.

Conclusion

Understanding how to compute present values, future values, bond yields, and associated returns equips financial analysts and investors with critical tools for evaluating investment opportunities. These calculations not only reveal the valuation dynamics but also help interpret market signals, such as bond premiums and discounts, that influence decision-making and strategic planning in finance.

References

  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance. McGraw-Hill Education.
  • Fabozzi, F. J. (2017). Bond Markets, Analysis and Strategies. Pearson.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance. McGraw-Hill Education.
  • Hull, J. C. (2018). Options, Futures, and Other Derivatives. Pearson.
  • Kolb, R. W., & Overdahl, J. A. (2018). Financial Economics. Wiley.
  • Modigliani, F., & Miller, M. H. (1958). The Cost of Capital, Corporation Finance and the Theory of Investment. American Economic Review.
  • Elton, E. J., & Gruber, M. J. (2018). Modern Portfolio Theory and Investment Analysis. Wiley.
  • Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. The Review of Economics and Statistics.

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