To determine $X$, the expected return of Stock A, let's break down the problem and solve it step-by-step.

Step 1: Find the Present Value of Bond B

Since we know the total value of Stock A and Bond B combined, we first need to determine the current value of Bond B.

Given information about Bond B:

• Coupon rate = 12.30% (annual), so the semi-annual coupon payment is: $\text{Coupon payment} = \frac{1000 \times 0.123}{2} = 61.5$
• Yield to Maturity (YTM) = 8.58% (annual), or 4.29% per semi-annual period.
• Par value = $1,000
• Time to maturity = 17 years, or $17 \times 2 = 34$ semi-annual periods.

The present value (PV) of Bond B, given that it pays semi-annual coupons, can be calculated as the sum of the present values of the annuity (coupon payments) and the par value (face value) at maturity.

$\text{PV of coupons} = 61.5 \times \frac{1 - (1 + 0.0429)^{-34}}{0.0429}$ $\text{PV of face value} = 1000 \times (1 + 0.0429)^{-34}$

Calculating these values:

1. PV of coupons: $61.5 \times \frac{1 - (1 + 0.0429)^{-34}}{0.0429} \approx 1032.16$

2. PV of face value: $1000 \times (1 + 0.0429)^{-34} \approx 291.85$

Adding these gives the present value of Bond B: $\text{PV of Bond B} = 1032.16 + 291.85 = 1324.01$

Step 2: Find the Value of Stock A

The total value of the two holdings is given as $5,993.3, so the value of Stock A alone is: $\text{Value of Stock A} = 5993.3 - 1324.01 = 4669.29$

Step 3: Calculate $X$, the Expected Return on Stock A

Stock A is a perpetuity since it pays a dividend of $8.32 forever. The value of a perpetuity is given by: $\text{Value of Stock A} = \frac{\text{Dividend}}{X}$ Solving for $X$: $X = \frac{\text{Dividend}}{\text{Value of Stock A}}$ Substitute the values: X = \frac{8.32}{\frac{4669.29}{100}} \approx 8.32 \text{% per year}

Answer:

The expected return $X$ on Stock A is approximately 8.32% per year.

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Would you like details on any of the calculations or any questions about the process?

Additional Questions:

1. How would the expected return change if the dividend increased?
2. What impact would a decrease in Bond B’s YTM have on Stock A’s expected return?
3. How would semi-annual dividends affect Stock A’s expected return calculation?
4. What is the effect of a shorter time to maturity for Bond B on the overall portfolio value?
5. How could changes in interest rates influence the valuation of both Bond B and Stock A?

Tip:

In perpetuity calculations, always confirm the dividend frequency aligns with the expected return frequency (e.g., both annually).