Suppose you are willing to pay $30 today for a share of stock which you expect to sell at the end of one year for $32. If you require an annual rate of return of 12 percent, what must be the amount of the annual dividend which you expect to receive at the end of year 1? Select the closest answer.[Fill in the blank]

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BlackTom AI · Accepted Answer

To begin, consider the cash flows from holding the stock for one year: you receive a dividend D at the end of year 1 and you sell the stock for 32. The required return is 12%, so the present value of the combined cash flows must equal your initial price of 30.

Option a. $1.00: If the dividend were $1.00, the total cash received at year end would be 1.00 + 32 = 33.00. Discounting back at 12% gives a present value of 33.00 / 1.12 ≈ 29.46, which is less than 30. This would imply you’d pay less than 30 for the stock to achieve a 12% return, so $1.00 cannot be correct given the required return and end price.

Option b. $1.60: Here, dividends plus the sale price total 1.60 + 32 = 33.60. Discounting back at 12% gives 33.60 / 1.12 = 30.00, which exactly matches your willingness to pay. This aligns with the target return of 12%, so $1.60 is the correct dividend amount for the break-even with your 12% hurdle.

Option c. $1.95: The end-of-year payoff would be 1.95 + 32 = 33.95. Present value at 12% is 33.95 / 1.12 ≈ 30.29, which is higher than 30. Since you’d be paying more today than you’re willing to for a 12% return, this dividend would overstate the required return relative to your price point, making it inconsistent with the given $30 willingness to pay.

Option d. $2.25: With 2.25 dividend, total year-end payoff is 34.25. PV at 12% is 34.25 / 1.12 ≈ 30.59, still above your $30 willingness to pay. This similarly implies a return greater than 12% given the $30 price, so it’s not the correct amount that matches the stated investor requirement.

In summary, only $1.60 yields a year-end cash flow that, when discounted at 12%, equals your $30 upfront investment. The other options produce present values that are either below or above $30, which would correspond to returns different from the specified 12% requirement.

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