The price of a stock at year 4 can be expressed as:

Question

BlackTom AI · Accepted Answer

Start by identifying the underlying model: in dividend discount models with constant growth, the stock price at year t is the next year's dividend D_{t+1} discounted by the required return minus the growth rate (R - g). With this in mind, evaluate each option.
Option 1: 'D0 / (R + G4).' This expression divides the initial dividend D0 by (R + G4). The denominator combines the required return with growth in an additive way, which does not reflect the standard Gordon growth form where growth is subtracted from return, and also uses D0 instead of the next-year dividend. Consequently, this is not consistent with the correct perpetuity pricing formula.
Option 2: 'D0 × (1 + R)5.' Here we multiply the initial dividend by (1 + R) to the fifth power. This resembles compounding a dividend by the cost of capital, rather than discounting future payments. It fails to represent a present value of future dividends and ignores growth rate in the correct manner, making it incorrect.
Option 3: 'D1 × (1 + R)5.' This option takes the Year 1 dividend and compounds it forward by (1 + R) for five periods. However, the stock price in a growing perpetuity framework is determined by the next year's dividend (not a compounded existing dividend) divided by (R - g). Therefore, this expression does not match the standard pricing formula.
Option 4: 'D4/(R-g).'
This form uses the Year 4 dividend D4 in the numerator divided by (R - g). While this resembles the correct structure, the dividend used should be D5 (the next year's dividend) in a price calculation at year 4, since P4 = D5/(R - g) under a constant growth assumption. Using D4 would imply using the current year's dividend rather than the next year’s, which is inconsistent with the standard perpetuity pricing derivation at year 4.
Option 5: 'D5/(R-g).'
This option matches the Gordon growth framework for a price observed at year 4: the price at year 4 equals the next year's dividend D5 discounted by (R - g). It correctly positions the numerator as the expected dividend next year and uses the appropriate discount minus growth in the denominator, aligning with the classic constant-growth dividend discount model for P4.
In summary, most options diverge from the standard dividend discount logic in different ways—either using the wrong year for the dividend, applying the growth/return terms incorrectly, or using compounding instead of discounting. The expression that adheres to the correct formula for price at year 4 under a constant growth assumption is D5/(R - g).

The price of a stock at year 4 can be expressed as:单项选择题

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