To find the expected return $X$ of Stock A, we need to determine its current price using the given information and then solve for $X$.

First, let's calculate the price of Bond B using its given characteristics.

Bond B:

• Coupon rate ($C$): 14.40% of $\$1000$ par value = $0.144 \times 1000 = \$144$
• Number of coupon payments per year: 2
• Semi-annual coupon payment: $\frac{144}{2} = \$72$
• Yield to Maturity (YTM) ($r$): 18.26% per year, or 9.13% semi-annually (since it is a semi-annual coupon bond)
• Number of semi-annual periods ($n$): $21$ years $\times 2 = 42$ periods

The price of Bond B ($P_B$) is calculated using the present value of annuities (for the coupons) and the present value of a lump sum (for the par value):

$P_B = \sum_{i=1}^{42} \frac{72}{(1 + 0.0913)^i} + \frac{1000}{(1 + 0.0913)^{42}}$

To simplify, we use the formula for the present value of an annuity and the present value of a lump sum:

$P_B = 72 \times \left( \frac{1 - (1 + 0.0913)^{-42}}{0.0913} \right) + \frac{1000}{(1 + 0.0913)^{42}}$

Calculating this step by step:

1. Present value of coupons: $72 \times \left( \frac{1 - (1 + 0.0913)^{-42}}{0.0913} \right)$

2. Present value of the par value: $\frac{1000}{(1 + 0.0913)^{42}}$

Using a calculator or financial software to compute these values:

1. Present value of coupons: $72 \times 10.196 = 734.112$

2. Present value of the par value: $\frac{1000}{21.714} \approx 46.055$

Therefore, the price of Bond B: $P_B = 734.112 + 46.055 = 780.167$

Now, we know the value of Bond B is $780.167. The total value of the holdings is $4,359.67. Hence, the value of Stock A can be found by subtracting the value of Bond B from the total value:

$\text{Value of Stock A} = 4359.67 - 780.167 = 3579.503$

This is the total value of 100 shares of Stock A. Therefore, the price per share of Stock A ($P_A$) is:

$P_A = \frac{3579.503}{100} = 35.79503$

Stock A is expected to pay a dividend of $6.19 every year forever (a perpetuity). The price of a perpetuity is given by:

$P_A = \frac{D}{r}$

where $D$ is the dividend and $r$ is the expected return. Rearranging to solve for $r$:

$r = \frac{D}{P_A}$

Substituting the known values:

$r = \frac{6.19}{35.79503} \approx 0.1729$

Converting to percentage:

$X = 0.1729 \times 100 = 17.29\%$

So, the expected return $X$ of Stock A is approximately 17.29% per year.

Would you like more details or have any questions?

Here are five related questions you might find interesting:

1. How do you calculate the present value of an annuity?
2. What factors influence the yield to maturity of a bond?
3. How is the price of a perpetuity derived?
4. What is the significance of a bond's coupon rate compared to its YTM?
5. How does the dividend discount model help in valuing stocks?

Tip: Understanding the concept of present value is crucial in finance as it allows you to determine the value of future cash flows in today's terms.