A stock's ex-dividend price today is $125.00. The ex-dividend price a year from today (Year 1) is expected to be $130.00. The stock's expected return is 12%, and the dividend growth rate is 4% forever.

What dividend will the stock pay a year from today (Dividend at Year 1)?

Round to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.353

Question

A stock's ex-dividend price today is $125.00. The ex-dividend price a year from today (Year 1) is expected to be $130.00. The stock's expected return is 12%, and the dividend growth rate is 4% forever.

What dividend will the stock pay a year from today (Dividend at Year 1)?

Round to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.353

BlackTom AI · Accepted Answer

Using the relationship between expected return, current price, future price, and dividend, compute the dividend that makes the expected return equal to 12%.

1. Relevant knowledge points and concepts
- Total expected return r for a stock over one period equals (P1 + D1)/P0 - 1, where P0 is today’s ex-dividend price, P1 is the expected ex-dividend price next year, and D1 is the dividend paid during the year.
- The Gordon Growth Model (constant-growth dividend discount model) implies P1 = D2 / (r - g), where D2 = D1(1 + g) is the dividend one year after the payment and g is the perpetual dividend growth rate. Consistency between the return identity and Gordon model validates the dividend computed.

2. Step-by-step reasoning
- Start from the return identity: (P1 + D1)/P0 - 1 = r.
- Solve for D1: P1 + D1 = P0(1 + r) → D1 = P0(1 + r) - P1.

3. Calculation with intermediate steps
- Given P0 = 125.00, r = 0.12, P1 = 130.00.
- Compute P0(1 + r) = 125.00 × 1.12 = 140.00.
- Then D1 = 140.00 − 130.00 = 10.00.

Check with Gordon Growth consistency:
- g = 0.04 so D2 = D1(1 + g) = 10.00 × 1.04 = 10.40.
- Gordon price P1 = D2 / (r − g) = 10.40 / (0.12 − 0.04) = 10.40 / 0.08 = 130.00, which matches the given P1 and confirms internal consistency.

4. Why this answer is correct
- The computed D1 = $10.00 is the unique dividend that, when combined with the expected ex-dividend price of $130 and the required return of 12%, yields exactly the 12% expected return. The Gordon Growth check shows the perpetual growth assumption (g = 4%) is consistent with the given P1.

5. Other options
- Not applicable here (numerical answer). Any other dividend would either produce a different expected return or be inconsistent with the given perpetual growth and P1.

6. Conclusion
- The dividend at Year 1 is $10.00, which matches the provided answer 10.00.

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