You Are Considering Three Investments The First Is A Bond ✓ Solved

You Are Considering Three Investments The First Is A Bond That Is Sel

You are considering three investments. The first is a bond that is selling in the market at RM1,200. The bond has an RM1,000 par value, pays interest at 14 percent, and is scheduled to mature in 12 years. For bonds of this risk class, you believe that a 12 percent rate of return should be required. The second investment is a preferred stock (RM100 par value) that sells for RM80 and pays an annual dividend of RM12. Your required rate of return for this stock is 14 percent. The third investment is a common stock (RM25 par value) that recently paid an RM3 dividend. The firm’s earnings per share have increased from RM4 to RM8 in 10 years, which also reflects the expected growth in dividends per share for the indefinite future. The stock is selling for RM25, and you think a reasonable required rate of return for the stock is 20 percent.

(a) Calculate the value of each security based on your required rate of return.

(b) Which investment(s) should you accept? Why?

(c) If your required rate of return changed to 14 percent for the bond, 16 percent for the preferred stock, and 18 percent for the common stock, how would your answer to (a) and (b) change?

(d) Assuming again your required rate of return for the common stock is 20 percent, but the anticipated constant growth rate changes to 12 percent, how would your answers to questions (a) and (b) change?

Sample Paper For Above instruction

Introduction

Investing in securities requires thorough valuation to determine their intrinsic worth and make informed decisions. This paper evaluates three types of securities—a bond, preferred stock, and common stock—using the investor's required rate of return assumptions. The analysis includes calculating their intrinsic values under different scenarios and provides investment recommendations based on these valuations.

Part (a): Valuation of Securities Based on Required Rate of Return

1. Bond Valuation

The bond's characteristics include a market price of RM1,200, a par value of RM1,000, a coupon rate of 14%, and a maturity of 12 years. The required rate of return for bonds with similar risk is 12%. The bond pays annual interest, which calculates to:

  • Annual coupon payment = 14% of RM1,000 = RM140

The current market value of a bond (present value) is the sum of the present value of its future coupon payments and the present value of its face value at maturity:

The formula for bond valuation:

PV = (C × [1 - (1 + r)^-n] / r) + (FV / (1 + r)^n)

Where:

  • C = Annual coupon payment = RM140
  • r = Required rate of return = 12% or 0.12
  • n = Number of years = 12
  • FV = Face value = RM1,000

Calculations:

PV of coupons = RM140 × [1 - (1 + 0.12)^-12] / 0.12 ≈ RM140 × 6.8137 ≈ RM953.92


PV of face value = RM1,000 / (1 + 0.12)^12 ≈ RM1,000 / 3.8959 ≈ RM256.72


Total value ≈ RM953.92 + RM256.72 ≈ RM1,210.64

Since the calculated value (~RM1,210.64) aligns closely with the market price of RM1,200, the bond appears fairly valued under the required rate of return.

2. Preferred Stock Valuation

The preferred stock pays an annual dividend of RM12, sells for RM80, and has a required return of 14%. The valuation formula for preferred stock with a fixed dividend is:

Value = D / r

Where:

  • D = RM12
  • r = 14% or 0.14

Calculations:

Value = RM12 / 0.14 ≈ RM85.71

Compared to the current market price (RM80), the stock appears slightly undervalued, suggesting a potential investment opportunity.

3. Common Stock Valuation

The current dividend (D1) is RM3, the stock's current price is RM25, and the estimated growth rate (g) is derived from earnings growth.

Given the EPS increased from RM4 to RM8 over 10 years, the growth rate (g) can be calculated as:

g = (Final EPS / Initial EPS)^{1/Number of years} - 1


g = (8 / 4)^{1/10} - 1 ≈ (2)^{0.1} - 1 ≈ 1.07177 - 1 ≈ 0.07177 or 7.18%

Using the Gordon Growth Model for stock valuation:

Price = D1 / (r - g)

Where:

  • D1 = RM3
  • r = 20% or 0.20
  • g = 7.18% or 0.0718

Calculations:

Price = RM3 / (0.20 - 0.0718) ≈ RM3 / 0.1282 ≈ RM23.39

Since the current market price is RM25, the stock is slightly overvalued based on this valuation.

Part (b): Investment Recommendations

Comparing intrinsic values to current market prices:

  • Bond: The intrinsic value (~RM1,210.64) is close to the market price (RM1,200), indicating it’s fairly valued and acceptable for investment.
  • Preferred stock: Its intrinsic value (~RM85.71) exceeds the market price (RM80), suggesting it is undervalued and appealing for purchase.
  • Common stock: The calculated intrinsic value (~RM23.39) is slightly below the market price (RM25), indicating it is overvalued and perhaps less attractive.

Based on this analysis, the bond and preferred stock are recommended for investment, while the common stock might be less appealing under current conditions.

Part (c): Impact of Changed Required Rates of Return

Re-calculating Values with New Rates

1. Bond (New rate: 14%)

Re-using the bond valuation formula with r = 14% (0.14):

PV of coupons = RM140 × [1 - (1 + 0.14)^-12] / 0.14 ≈ RM140 × 5.898 ≈ RM825.72


PV of face value = RM1,000 / (1 + 0.14)^12 ≈ RM1,000 / 4.904 ≈ RM203.89


Total ≈ RM825.72 + RM203.89 ≈ RM1,029.61

This new value (~RM1,029.61) is below the market price of RM1,200, indicating the bond appears overvalued, and an investor might reconsider purchasing at current prices.

2. Preferred Stock (New rate: 16%)

Value = RM12 / 0.16 = RM75

Indicating undervaluation since RM75

3. Common Stock (New rate: 18%)

Price = RM3 / (0.18 - 0.0718) ≈ RM3 / 0.1082 ≈ RM27.72

Since this exceeds current price (RM25), the stock appears undervalued, favoring investment.

Investment Decision Changes

  • Bond: The bond's intrinsic value drops below market price, making it less attractive.
  • Preferred stock: Slight undervaluation suggests a decreased appeal.
  • Common stock: Now undervalued based on the new valuation, potentially making it a better buy.

Part (d): Changing Growth Rate to 12% with a 20% Required Return

Using the Gordon Growth Model:

Price = RM3 / (0.20 - 0.12) = RM3 / 0.08 = RM37.50

This is significantly higher than the current market price of RM25, implying undervaluation and attractiveness for investors.

Revised Investment Recommendation

  • The stock appears undervalued under the new growth rate assumption, making it a more appealing investment compared to the initial analysis.
  • Therefore, based on the revised valuation, choosing the common stock is more favorable, whereas previously it was overvalued.

Conclusion

This comprehensive valuation analysis demonstrates how changes in required rate of return and growth expectations influence investment decisions. It emphasizes the importance of dynamic valuation methods in active portfolio management. Investors should continuously reevaluate securities as market conditions and assumptions evolve to optimize investment outcomes.

References

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  • Brealey, R. A., Myers, S. C., & Allen, F. (2017). Principles of Corporate Finance. McGraw-Hill Education.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2018). Fundamentals of Corporate Finance. McGraw-Hill Education.
  • Graham, B., & Dodd, D. L. (2008). Security Analysis: Sixth Edition. McGraw-Hill Education.
  • Higgins, R. C. (2012). Analysis for Financial Management. McGraw-Hill Education.
  • Fabozzi, F. J. (2016). Bond Markets, Analysis, and Strategies. Pearson Education.
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  • Lavine, M. (2018). The Essential Guide to Wealth Management. Harvard Business Review Press.
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