You have 100 shares of stock A and 1 bond B. The total value of the two holdings is $5,229.24. Bond B has a coupon rate of 11.74 percent, par value of $1000, YTM of 15.22 percent, 18.0 years until maturity, and semi-annual coupons with the next coupon expected in 6 months. Stock A is expected to pay a dividend of $8.59 every year forever and has an expected return of X percent per year. The stock's next dividend is expected in 1 year. What is X?

please solve using TVM solver on a TI-83 calculator

To solve for $ X $ (the expected return on Stock A) using the Time Value of Money (TVM) solver on a TI-83 calculator, we need to follow these steps:

### Step 1: Determine the value of Bond B
Bond B's value can be calculated using the bond pricing formula, which is based on the present value of the bond's future coupon payments and the par value (face value) discounted at the bond's yield to maturity (YTM).

We are given the following information for Bond B:
- **Coupon Rate**: 11.74% (Annual)
- **Par Value**: \$1,000
- **YTM (Yield to Maturity)**: 15.22% (Annual)
- **Time to Maturity**: 18 years
- **Semi-annual Coupons**: Coupons are paid twice a year

From this, we can calculate:
- **Coupon Payment**: Since the bond pays semi-annual coupons, the annual coupon payment is:
  \[
  \text{Coupon Payment} = 1000 \times \frac{11.74}{100} = 117.40 \text{ annually}
  \]
  The semi-annual coupon payment is half of this:
  \[
  \text{Semi-annual Coupon Payment} = \frac{117.40}{2} = 58.70
  \]

- **Number of Periods (N)**: The bond pays coupons twice per year for 18 years, so the total number of periods is:
  \[
  N = 18 \times 2 = 36
  \]

- **Semi-annual Yield (I/Y)**: Since the bond's YTM is given as 15.22% annually, the semi-annual yield is half of this:
  \[
  \text{Semi-annual Yield} = \frac{15.22}{2} = 7.61\%
  \]

#### Bond Pricing Calculation
We now use the TVM solver to find the present value of the bond:
- $ N = 36 $ (number of periods)
- $ I/Y = 7.61 \% $ (semi-annual yield)
- $ PMT = 58.70 $ (semi-annual coupon payment)
- $ FV = 1000 $ (par value)

On the TI-83 calculator, use the TVM solver and plug in these values:

\[
\text{Bond Value (PV)} \approx -824.08
\]

So, the current value of Bond B is approximately \$824.08.

### Step 2: Determine the value of Stock A
The total value of the two holdings is given as \$5,229.24. The value of Bond B is \$824.08, so the value of Stock A can be found by subtracting the value of the bond from the total:

\[
\text{Value of Stock A} = 5,229.24 - 824.08 = 4,405.16
\]

Since you own 100 shares of Stock A, the value of each share is:

\[
\text{Price per Share} = \frac{4,405.16}{100} = 44.05
\]

### Step 3: Solve for $ X $ (Expected Return on Stock A)
Stock A is expected to pay a dividend of \$8.59 per share every year forever. We can use the Gordon Growth Model (also known as the Dividend Discount Model) to find the expected return $ X $. The formula is:

\[
\text{Price per Share} = \frac{D}{X}
\]

Where:
- $ D = 8.59 $ (annual dividend)
- $ X $ is the expected return
- $ \text{Price per Share} = 44.05 $

Rearranging the formula to solve for $ X $:

\[
X = \frac{D}{\text{Price per Share}} = \frac{8.59}{44.05} \approx 0.1949 = 19.49\%
\]

### Conclusion
The expected return $ X $ on Stock A is approximately **19.49%**.

Would you like further details or have any questions?

Here are 5 related questions you might want to explore:
1. How does the bond’s YTM affect its current price?
2. What factors influence the expected return on a stock?
3. How does the dividend discount model work for companies with growing dividends?
4. What are the implications of owning both stocks and bonds in a portfolio?
5. How would changes in interest rates affect the value of Bond B?

**Tip**: When solving financial problems involving bonds and stocks, always separate the components of the portfolio and solve for each separately before combining the results.

You have 100 shares of stock A and 1 bond B. The total value of the two holdings is $5,229.24. Bond B has a coupon rate of 11.74 percent, par value of $1000, YTM of 15.22 percent, 18.0 years until maturity, and semi-annual coupons with the next coupon expected in 6 months. Stock A is expected to pay a dividend of $8.59 every year forever and has an expected return of X percent per year. The stock's next dividend is expected in 1 year. What is X?

Learn how to calculate the expected return (X) on Stock A and the value of Bond B using the Time Value of Money (TVM) solver. This problem involves calculating bond pricing with semi-annual coupons and determining stock returns using the Dividend Discount Model. Suitable for college-level finance students.

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