Introduction To Finance FIN2030 Week 3 Assignment 2 Part 1

Introduction To Finance FIN2030 Week 3 Assignment 2 Part One: Quantitative Exercises Stocks Answers

Calculate the value of stocks given dividend payments, required returns, and growth rates; determine the required rate of return based on dividends, prices, and growth; find the stock's growth rate from dividends, prices, and required returns; and evaluate bond values and yields considering coupon payments, maturities, and market prices.

Paper For Above instruction

Introduction

The fundamental principles of finance hinge on understanding the valuation of stocks and bonds. These financial instruments serve as critical components for investors aiming to maximize returns while managing risks. The valuation of stocks involves evaluating dividends, growth rates, and required rates of return, often utilizing the Gordon Growth Model or other models. Bonds, on the other hand, require assessment of coupon payments, maturities, and yields to maturity (YTM). Accurate valuation processes facilitate informed investment decisions, risk assessment, and portfolio optimization.

Stock Valuation

The process of stock valuation typically employs the Gordon Growth Model (also known as the Dividend Discount Model), which assumes dividends grow at a constant rate. The model's formula is:

Price (P) = Dividend (D1) / (Required Return (r) - Growth Rate (g))

where D1 is the dividend expected in the next period. Based on this model, we analyze specific questions provided in the assignment.

Part One: Stock Valuation Calculations

  1. What is the value of a stock with a $2.50 dividend just paid, an 8% required return, and 0% growth?
  2. Given that dividend just paid (D0) is $2.50, with no growth, the dividend in the next period (D1) remains $2.50. Using the Gordon Growth Model:
  3. P = D1 / r = 2.50 / 0.08 = $31.25
  4. What is the value of a stock with a $3 dividend just paid, an 8% required return, and 2% growth?
  5. D0 = $3, g = 2%, r = 8%, D1 = D0 (1 + g) = 3 1.02 = $3.06
  6. Price: P = D1 / (r - g) = 3.06 / (0.08 - 0.02) = 3.06 / 0.06 = $51.00
  7. What is the value of a stock with a $7 dividend to be paid, a 10% required return, and 2% growth?
  8. D1 = $7 (since it's to be paid immediately, assuming it's the next dividend)
  9. Price: P = D1 / (r - g) = 7 / (0.10 - 0.02) = 7 / 0.08 = $87.50
  10. Alternatively, if D1 is projected based on last dividend D0 and given the growth rate, adjustments may be needed. But for straightforward calculation, assuming D1 is $7.
  11. Part Two: Required Rate of Return
  13. What is the required rate of return for a stock with an expected dividend of $2.50, a price of $19, and 6% growth?

    14. Using the Gordon model rearranged to find r:

    r = (D1 / P) + g = (2.50 / 19) + 0.06 ≈ 0.1316 + 0.06 = 0.1916 or 19.16%

  14. Expected dividend $2.75, price $20, growth 8%:

    15. D1 = 2.75 * 1.08 = 2.97

    r = (2.97 / 20) + 0.08 = 0.1485 + 0.08 = 0.2285 or 22.85%

  15. Expected dividend $2.50, price $19, growth 9%:

    16. D1 = 2.50 * 1.09 = 2.725

    r = (2.725 / 19) + 0.09 ≈ 0.1434 + 0.09 = 0.2334 or 23.34%

    Growth Rate Assessment

    1. Growth rate of stock with expected dividend $3.00, price $20.60, required return 15%:
    2. g = r - (D1 / P) = 0.15 - (3 / 20.60) ≈ 0.15 - 0.1456 = 0.0044 or 0.44%
    3. Expected dividend $2.40, price $25.35, required return 10%:
    4. D1 = 2.40 * 1.10 = 2.64
    5. g = (P r - D1) / P = (25.35 0.10 - 2.64) / 25.35 ≈ (2.535 - 2.64) / 25.35 ≈ -0.105 / 25.35 ≈ -0.0041 or -0.41%
    6. Expected dividend $2, price $8.30, required return 11%:
    7. D1 = 2 * 1.11 = 2.22
    8. g = (D1 / P) - r = (2.22 / 8.30) - 0.11 ≈ 0.2675 - 0.11 = 0.1575 or 15.75%
    9. Bond Valuation
    10. The value of a bond is determined by the present value of its future cash flows — coupons and face value — discounted at the bond's yield to maturity (YTM). The general formula is:
    11. Bond Price = Σ (Coupon Payment / (1 + YTM)^t) + Face Value / (1 + YTM)^n
    12. Part One: Bond Price Calculations
    14. Bond with a par value of $1,000, 10% annual coupon, 10-year maturity, and 15% required return:

      15. Coupon = $1,000 * 10% = $100

      Bond price = PV of coupons + PV of face value

      PV of coupons = $100 [(1 - (1 + 0.15)^-10) / 0.15] ≈ $100 5.0188 = $501.88

      PV of face value = $1,000 / (1 + 0.15)^10 ≈ $1,000 / 4.0456 ≈ $247.19

      Total: $501.88 + $247.19 ≈ $749.07

    15. Bond with an 8% coupon, 10-year maturity, 8% required return:

      16. Coupon = $80

      PV coupons = $80 [(1 - (1 + 0.08)^-10) / 0.08] ≈ $80 6.7101 ≈ $536.81

      PV face value = $1,000 / (1 + 0.08)^10 ≈ $1,000 / 2.1589 ≈ $463.19

      Total: $536.81 + $463.19 ≈ $1,000

    16. Bond with an 11% semiannual coupon, 20-year maturity, 11% required return:

      17. Coupon per period = $1,000 * 11% / 2 = $55

      Total periods = 20 * 2 = 40

      PV of coupons = $55 [(1 - (1 + 0.055)^-40) / 0.055] ≈ $55 22.37 ≈ $1,229.35

      PV of face value = $1,000 / (1 + 0.055)^40 ≈ $1,000 / 7.099 ≈ $140.83

      Total: $1,229.35 + $140.83 ≈ $1,370.18

    17. Bond with an 8% semiannual coupon, 20-year maturity, 9% required return:

      18. Coupon per period = $1,000 * 8% / 2 = $40

      PV of coupons = $40 [(1 - (1 + 0.045)^-40) / 0.045] ≈ $40 23.57 ≈ $942.80

      PV of face value = $1,000 / (1 + 0.045)^40 ≈ $1,000 / 5.254 ≈ $190.18

      Total: $942.80 + $190.18 ≈ $1,132.98

      Part Two: Yield to Maturity Calculations

      1. YTM of a $1,000 par value bond with 10% annual coupon, 10 years to maturity, and market price $1,000:
      2. Since the bond price equals the face value, YTM ≈ coupon rate = 10%.
      3. YTM with a $1,000 par, 9.5% coupon, 20 years to maturity, price $788:
      4. This requires iterative calculation or financial calculator; approximated using Excel or financial calculator, the YTM ≈ 12.4%.
      5. YTM with a 5% coupon rate, 8-year maturity, price $800:
      6. Again, iterative approximation gives YTM ≈ 6.5%.

      Conclusion

      The valuation of stocks and bonds requires careful analysis of dividends, growth rates, maturities, coupons, and market conditions. Employing models such as the Gordon Growth Model for stocks and present value calculations for bonds provides essential insights for investors. The calculations above demonstrate fundamental financial principles and emphasize the importance of precise computation in investment decision-making.

      References

  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Fabozzi, F. J. (2018). Bond Markets, Analysis, and Strategies (10th ed.). Pearson.
  • Brigham, E. F., & Ehrhardt, M. C. (2019). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
  • Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance (12th ed.). McGraw-Hill Education.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley.
  • Gordon, M. J. (1959). Dividends, Earnings, and Stock Prices. The Review of Economics and Statistics, 41(2), 99-105.
  • Investopedia. (2023). Bond Valuation. https://www.investopedia.com/terms/b/bondvaluation.asp
  • Helwege, J., & Turner, P. (2020). The Yield Curve and Economic Activity. Financial Analysts Journal, 76(2), 12-30.
  • Shapiro, A. C. (2020). Multinational Financial Management (11th ed.). Wiley.
  • Mun, J. (2019). Financial Institutions, Instruments, and Markets (8th ed.). Routledge.

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