Is the following statement true or false? Déjà vu’ just paid a cash dividend of $0.20 per share. Investors require a 16% return from investments such as this. If the dividend is expected to grow at a steady 8% per year. The share will be worth $2.70 in five years?[Fill in the blank]

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BlackTom AI · Accepted Answer

To approach this statement, begin by identifying the given data and the model being used.
- The stock just paid a dividend of D0 = $0.20.
- The required return (cost of equity) is r = 16% = 0.16.
- The dividend is assumed to grow at a constant rate g = 8% = 0.08 per year.
- We are asked for the stock price at the end of year 5, i.e., the value five years from now.

Option A: True. This would mean the five-year price equals $2.70. To check this, compute the dividend at year 6 (the first dividend after year 5) under the Gordon growth framework, and use the perpetuity value from year 5 onward: P5 = D6 / (r − g).
- First, D1 = D0 × (1 + g) = 0.20 × 1.08 = 0.216.
- More generally, Dt = D0 × (1 + g)^t, so D6 = 0.20 × (1.08)^6.
- (1.08)^6 ≈ 1.5869, thus D6 ≈ 0.3174.
- Then P5 = D6 / (0.16 − 0.08) = 0.3174 / 0.08 ≈ 3.97.
Since 3.97 is not equal to 2.70, the statement that the share will be worth $2.70 in five years is incorrect.

Option B: False. The calculation above shows P5 ≈ $3.97 given the inputs. Therefore the claim of $2.70 is false.

In short, applying the dividend growth model with D0 = 0.20, g = 8%, and r = 16% yields a five-year price around $3.97, not $2.70. The correct assessment is that the statement is false.

Is the following statement true or false? Déjà vu’ just paid a cash dividend of $0.20 per share. Investors require a 16% return from investments such as this. If the dividend is expected to grow at a steady 8% per year. The share will be worth $2.70 in five years?[Fill in the blank]

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