To find the expected return $X \%$ of Investment B, we need to analyze the information given for each investment separately, then solve for $X$ based on the total value of the portfolio.

Step-by-Step Solution

1. Calculate the Present Value of Stock A:

   • The value of stock A (100 shares) is based on the expected future price and dividends.

   • Given:

     • Expected price in 2 years: $P_2 = 341.05$
     • Expected dividends: $D_1 = 10.95$ in 1 year and $D_2 = 11.67$ in 2 years
     • Expected return (discount rate) for stock A: $r_A = 12.54\%$

   • Find the present value (PV) of dividends and price in 2 years: $PV(\text{Stock A}) = \frac{D_1}{(1 + r_A)^1} + \frac{D_2}{(1 + r_A)^2} + \frac{P_2}{(1 + r_A)^2}$

   • Substitute the values: $PV(\text{Stock A}) = \frac{10.95}{(1 + 0.1254)^1} + \frac{11.67}{(1 + 0.1254)^2} + \frac{341.05}{(1 + 0.1254)^2}$

2. Calculate each component:

   • First dividend, $D_1$: $\frac{10.95}{1.1254} \approx 9.73$
   • Second dividend, $D_2$: $\frac{11.67}{(1.1254)^2} \approx 9.23$
   • Expected price, $P_2$: $\frac{341.05}{(1.1254)^2} \approx 269.70$
   • Summing these: $PV(\text{Stock A}) = 9.73 + 9.23 + 269.70 = 288.66$
   • For 100 shares, the total PV of Stock A is: $100 \times 288.66 = 28,866$

3. Calculate the Present Value of Investment B:

   • Let the present value of Investment B be $PV(\text{Investment B})$.
   • Since the total portfolio value is $35,654.17, we have: $PV(\text{Investment B}) = 35,654.17 - 28,866 = 6,788.17$

4. Determine the Expected Return (X) for Investment B:

   • Investment B pays $812$ annually for 17 years with the first payment in 1 year. We treat it as a 17-year annuity with payments $C = 812$ and present value $PV = 6,788.17$.
   • The formula for the present value of an annuity is: $PV = C \times \frac{1 - (1 + X)^{-n}}{X}$
   • Substituting $PV = 6788.17$, $C = 812$, and $n = 17$: $6788.17 = 812 \times \frac{1 - (1 + X)^{-17}}{X}$
   • Solving this equation numerically for $X$ yields approximately $X = 7.25\%$.

Answer:

The expected return $X \%$ for Investment B is approximately 7.25%.

Would you like further clarification on any part of this solution?

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Related Questions:

1. What is the formula for the present value of a growing annuity, and how does it differ from a standard annuity?
2. How do changes in expected dividends affect the present value of a stock?
3. What factors can influence the expected return of an investment?
4. How would the calculation change if dividends were paid quarterly rather than annually?
5. What is the impact of compounding frequency on the future value of an investment?

Tip:

When working with annuities, using financial calculators or software tools can simplify solving for unknown rates, especially for complex annuity structures or longer time frames.