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]

Question

BlackTom AI · Accepted Answer

The prompt presents a true/false statement and two answer choices. Restating the content helps set up the analysis. The statement is: '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?'

Option analysis:
- True: This claim asserts that, given a $0.20 dividend, a required return of 16%, and a dividend growth rate of 8%, the stock price in five years will be $2.70. To evaluate this, one would typically use the Gordon growth model (or dividend discount model) for a stock with a constant growth rate, but that model provides the value today (or a present value) based on dividends expected at the next period, not a future price directly. The statement as written mixes a future price target with the dividend and growth assumptions without clearly aligning the timing of the dividend payments, the required return, and the growth. In addition, the standard approach would compute the present value or the terminal value at a given horizon using the appropriate discount rate and growth, which requires consistent cash flow timing. Depending on the exact interpretation (e.g., whether the $0.20 is the dividend just paid and the next expected dividend is $0.216, etc.), the conclusion may differ. As stated, the claim is oversimplified and potentially inconsistent with a straightforward application of the growth model, so labeling it as True would be misleading without additional calculation details.

- False: This option would be correct if, upon applying the correct dividend growth framework with the given parameters, the five-year terminal value is not exactly $2.70, or if the statement lacks consistent timing or uses the wrong metric (e.g., using price at five years without considering required return and growth in the right way). Since the question asks whether the stock will be worth $2.70 in five years given D0 = 0.20, g = 0.08, and r = 0.16, a precise calculation must be performed to determine the five-year forward price or the value implied by the dividend discount framework. Without performing that calculation and confirming the consistency of cash flows and discounting, the claim is risky to accept at face value. Therefore, the assertion is prone to being incorrect as stated.

Key conceptual points to consider when evaluating such statements:
- In a constant-growth dividend discount model, the current price is determined by the next dividend D1, the growth rate g, and the required return r: P0 = D1 / (r - g), assuming r > g. Here D1 would be D0*(1+g) if the dividend just paid is D0, but the equation yields the current price, not a future price in five years.
- To obtain a five-year price target, you would project dividends for years 1 through 5 and discount them back to today, or compute the terminal value at year 5 if you assume a perpetuity from year 6 onward, then discount back to present. The given numbers (D0 = 0.20, g = 8%, r = 16%) must be aligned with a clearly defined cash-flow timeline to deduce whether P5 equals 2.70. Without that, asserting P5 = 2.70 is not guaranteed to be correct.
- The statement also depends on whether the dividend growth rate remains at 8% indefinitely and whether the 16% required return is the appropriate discount rate for each future cash flow. If any of these conditions are misapplied or misinterpreted, the conclusion may be false.

In summary, option analysis shows that True would require a precise, consistent calculation demonstrating that the five-year price equals 2.70 given the specified dividends, growth, and discount rate. False would be selected if that calculation does not yield 2.70 or if the stated conditions are not applied correctly. The request to determine truth hinges on performing the proper time-value calculation with consistent cash-flow timing, which the simple statement does not transparently provide.

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]

View Explanation

Log in for full answers

Similar Questions

Company ABC’s ordinary shares are currently selling at $24.00 per share. The company is expected to pay a dividend of $1.92 per share, which is predicted to grow at 4% per annum forever. What is the share's expected rate of return?

Company ABC’s ordinary shares are currently selling at $24.00 per share. The company is expected to pay a dividend of $1.92 per share, which is predicted to grow at 4% per annum forever. What is the share's expected rate of return?