Math Problem Statement

The expected return over the next quarter (from today to 3 months from today) for a stock is 15.61 percent. The stock’s price is $210.03 today, dividends of $12.76 are expected in 3 months, and dividends of $19.17 are expected in 6 months. What is the price of the stock expected to be in 3 months?

Input instructions: Round your answer to the nearest cent (so 2 decimal places).

Solution

To determine the expected price of the stock in 3 months, we can use the given expected return and the information about dividends. The expected return of the stock over the next quarter is 15.61%.

We calculate the expected price as follows:

  1. Step 1: Express the expected return as a decimal: Expected return=15.61100=0.1561\text{Expected return} = \frac{15.61}{100} = 0.1561

  2. Step 2: Use the expected return formula: Future Value (price after 3 months)=Price today×(1+Expected return)Dividends paid after 3 months\text{Future Value (price after 3 months)} = \text{Price today} \times (1 + \text{Expected return}) - \text{Dividends paid after 3 months} Substituting the values: Future Price=210.03×(1+0.1561)12.76\text{Future Price} = 210.03 \times (1 + 0.1561) - 12.76

  3. Step 3: Perform the calculations: Future Price=210.03×1.156112.76\text{Future Price} = 210.03 \times 1.1561 - 12.76 Future Price=242.8412.76\text{Future Price} = 242.84 - 12.76 Future Price=230.08\text{Future Price} = 230.08

Final Answer:

The expected price of the stock in 3 months is $230.08.


Would you like further details or clarification? Here are 5 related questions to expand your understanding:

  1. How is the expected return of a stock calculated?
  2. Why are dividends subtracted when calculating future stock prices?
  3. What is the significance of the quarterly return in stock price predictions?
  4. How does compounding affect multi-period expected returns?
  5. How might changing dividend payouts affect the expected future price?

Tip: Always check whether expected returns are expressed annually or for the specific period (quarterly, monthly) when solving financial problems.

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Math Problem Analysis

Mathematical Concepts

Finance
Expected Returns
Stock Valuation

Formulas

Future Price = Price Today × (1 + Expected Return) - Dividends

Theorems

Expected Return Formula

Suitable Grade Level

College Level (Finance or Economics courses)