ALP’s most recent dividend was $2.00 per share and is selling today for $70. The dividend is expected to grow at 7% per year for the foreseeable future. Should you purchase the share if the market return is 10% on investments with comparable risk?

Question

ALP’s most recent dividend was​ $2.00 per share and is selling today for​ $70. The dividend is expected to grow at ​ 7% per year for the foreseeable future. Should you purchase the share if the market return is​ 10% on investments with comparable​ risk?

BlackTom AI · Accepted Answer

We start by identifying the key inputs: last dividend D0 = $2.00, growth g = 7% per year, required market return r = 10% for investments with comparable risk, and the stock price today P0 = $70.

Option a asks whether to buy if the share is under-priced by $3.33 and that you should buy if a is true. To check, compute the value from the dividend growth model.

Step 1: Compute the next dividend
D1 = D0 × (1 + g) = 2.00 × 1.07 = 2.14.

Step 2: Compute the intrinsic value using Gordon Growth Model
P0 (intrinsic) = D1 / (r − g) = 2.14 / (0.10 − 0.07) = 2.14 / 0.03 = 71.33 (approximately).

Step 3: Compare intrinsic value to market price
Intrinsic value ≈ $71.33, Market price = $70. The stock appears undervalued by about 71.33 − 70 ≈ $1.33 per share.

Option-by-option analysis:

Option a: “Yes, because the share is under-priced $3.33.” This asserts an underpricing of $3.33. Our calculation shows the mispricing is about $1.33, not $3.33, so this option overstates the amount of mispricing and is therefore incorrect.

Option b: “No, because the share is overpriced $1.33.” Here the claim is that the stock is overpriced by $1.33. Our valuation indicates the stock is undervalued, not overpriced, and the magnitude of mispricing is the opposite direction of what this option states. Thus this is incorrect.

Option c: “Yes, because the share is under-priced $1.33.” This aligns with the computed intrinsic value: the stock’s value is about $71.33, which is higher than the current price of $70, implying an underpricing of roughly $1.33. The reasoning is consistent with the Gordon growth framework and the provided inputs. This option is correct in direction and magnitude.

Option d: “No, because the share is overpriced $3.33.” This asserts the stock is overpriced by $3.33, which contradicts the calculated intrinsic value being higher than the market price and the implied undervaluation. The pricing conclusion here is incorrect on both the direction and the amount of mispricing.

In summary, the dividend discount model with constant growth yields an intrinsic value around $71.33, suggesting the stock is undervalued by about $1.33 relative to the current price. Among the choices, option c correctly states the buy recommendation and the correct magnitude of underpricing, while the other options either misstate the direction of mispricing or give an incorrect amount.

ALP’s most recent dividend was $2.00 per share and is selling today for $70. The dividend is expected to grow at 7% per year for the foreseeable future. Should you purchase the share if the market return is 10% on investments with comparable risk?单项选择题

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ALP’s most recent dividend was​ $2.00 per share and is selling today for​ $70. The dividend is expected to grow at ​ 7% per year for the foreseeable future. Should you purchase the share if the market return is​ 10% on investments with comparable​ risk?单项选择题