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Question 1171817: You are considering three invest¬ments. The first is a bond that is selling in the market at RM1,200. The bond has a RM 1,000 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 that you are analyzing is a preferred stock (RM100 par value) that sells for RM80 and pays an annual dividend of RM 12. Your required rate of return for this stock is 14 percent. The last investment is a common stock (RM35 par value) that recently paid a 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. 1. If your required rates 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 answers change to parts (a) and (b)?
2. Assuming again that your required rate of return for the common stock is 20 percent, but the anticipated growth rate changes to 12 percent, would your answers to parts (a) and (b) be different
d. Explain the relationship between an investor’s required rate of return and the value of a security.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Absolutely! Let's break down each investment scenario step-by-step.
**a. Calculate the Value of Each Security Based on Your Required Rate of Return**
**1. Bond Valuation**
* **Par Value (FV):** RM 1,000
* **Coupon Rate:** 14% of RM 1,000 = RM 140 per year
* **Market Price:** RM 1,200
* **Years to Maturity (n):** 12
* **Required Rate of Return (r):** 12% = 0.12
We need to calculate the present value of the bond's cash flows (coupon payments and par value) using the required rate of return.
* **Present Value of Coupon Payments (Annuity):**
* PV = C * [1 - (1 + r)^-n] / r
* PV = 140 * [1 - (1 + 0.12)^-12] / 0.12
* PV = 140 * [1 - (1.12)^-12] / 0.12
* PV = 140 * [1 - 0.25596] / 0.12
* PV = 140 * 0.74404 / 0.12
* PV ≈ RM 868.05
* **Present Value of Par Value:**
* PV = FV / (1 + r)^n
* PV = 1000 / (1.12)^12
* PV = 1000 / 3.89597599
* PV ≈ RM 256.68
* **Total Bond Value:**
* Bond Value = PV of Coupon Payments + PV of Par Value
* Bond Value = 868.05 + 256.68
* Bond Value ≈ RM 1,124.73
**2. Preferred Stock Valuation**
* **Annual Dividend (D):** RM 12
* **Market Price:** RM 80
* **Required Rate of Return (r):** 14% = 0.14
* **Preferred Stock Value:**
* Value = D / r
* Value = 12 / 0.14
* Value ≈ RM 85.71
**3. Common Stock Valuation**
* **Current Dividend (D0):** RM 3
* **Current Stock Price:** RM 25
* **Required Rate of Return (r):** 20% = 0.20
* **Growth Rate (g):**
* Earnings per share increased from RM 4 to RM 8 in 10 years.
* 8 = 4(1+g)^10
* 2 = (1+g)^10
* 1.07177 = 1+g
* g = 0.07177 or 7.177%
* We will use the Gordon Growth model:
* Value = D1 / (r - g)
* D1 = D0 * (1 + g) = 3 * (1.07177) = 3.21531
* Value = 3.21531 / (0.20 - 0.07177)
* Value = 3.21531 / 0.12823
* Value ≈ RM 25.07
**b. Which Investment(s) Should You Accept? Why?**
* **Bond:**
* Calculated Value: RM 1,124.73
* Market Price: RM 1,200
* **Decision:** Do not accept. The market price is higher than your calculated value.
* **Preferred Stock:**
* Calculated Value: RM 85.71
* Market Price: RM 80
* **Decision:** Accept. The calculated value is higher than the market price.
* **Common Stock:**
* Calculated Value: RM 25.07
* Market Price: RM 25
* **Decision:** Accept. The calculated value is higher than or very close to the market price.
**c. Changes in Required Rates of Return and Growth Rate**
**1. Changed Required Rates of Return**
* **Bond (14%):**
* PV coupon = 140 * [1-(1.14^-12)]/0.14 = 721.28
* PV Par = 1000/1.14^12 = 207.56
* Bond Value = 721.28 + 207.56 = 928.84. Do not Accept.
* **Preferred Stock (16%):**
* Value = 12 / 0.16 = RM 75. Do not accept.
* **Common Stock (18%):**
* Value = 3.21531 / (0.18 - 0.07177) = 29.89. Accept.
**2. Changed Growth Rate (12% Common Stock)**
* **Growth Rate (g):** 12% = 0.12
* **D1:** 3 * 1.12 = 3.36
* Value = 3.36 / (0.20 - 0.12) = 3.36 / 0.08 = 42. Accept.
**d. Relationship Between Required Rate of Return and Security Value**
* There is an inverse relationship between an investor's required rate of return and the value of a security.
* When the required rate of return increases, the present value of future cash flows decreases, leading to a lower security value.
* Conversely, when the required rate of return decreases, the present value of future cash flows increases, resulting in a higher security value.
* Essentially, a higher required return means the investor demands a larger discount rate applied to future cash flows, reducing their present value.
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