Part 1Compute the price of a share of stock that pays a $5.005.00 per year dividend and that you expect to be able to sell in one year for $3030, assuming you require a 1010% return. The price of the share is $[input]enter your response here . (Round your response to the nearest penny.)

Question

Part 1Compute the price of a share of stock that pays a ​$5.005.00 per year dividend and that you expect to be able to sell in one year for ​$3030​, assuming you require a 1010​% return. The price of the share is ​$[input]enter your response here . ​(Round your response to the nearest​ penny.)

BlackTom AI · Accepted Answer

We begin by restating the problem to ensure we’re solving the intended scenario. The stock pays a dividend of 5.00 per year, you expect to sell the stock next year for 30.00, and you require a 10% return. The task is to find the current price P0 that satisfies your required return.

Key idea: the total return from holding the stock for one year consists of the dividend received plus the price change from P0 to P1. The formula for the required return r is:
(r) = (D1 + P1 − P0) / P0
Rearranging gives the present price P0 = (D1 + P1) / (1 + r).

Plug in the given values:
D1 = 5.00, P1 = 30.00, r = 0.10.
P0 = (5.00 + 30.00) / 1.10 = 35.00 / 1.10 = 31.818... .

Rounding to the nearest penny yields P0 = 31.82.

Note on the absence of answer options: there were no multiple-choice options provided in this item. If options existed, you would check each against the same derivation, ensuring the chosen one matches 31.82 when rounded to two decimals.

Common alternative calculations to watch for (to avoid mistakes):
- If someone wrote P0 = D1 + P1 / (1 + r) without parentheses, they’d effectively compute 5.00 + 30.00/1.10 ≈ 5.00 + 27.27 = 32.27, which is incorrect because it ignores the proper allocation of the discount factor to the total cash flows.
- If someone used P0 = (D1 + P1) × (1 + r) by mistake, that would inflate the price to over 38.50, which is inconsistent with the required return framework.
- If the dividend were misinterpreted as received at the end of the period or at time zero, the cash-flow timing would change and the result would differ; here the dividend is assumed to be received during the year (D1) and the sale occurs at year end (P1).

In summary, using the standard present-value relation for a one-period holding period return with cash flow D1 and terminal price P1 leads to P0 = (D1 + P1)/(1 + r) = 31.82, which matches the expected rounded value.

Quiz:Quiz 2

Part 1Compute the price of a share of stock that pays a $5.005.00 per year dividend and that you expect to be able to sell in one year for $3030, assuming you require a 1010% return. The price of the share is $[input]enter your response here . (Round your response to the nearest penny.)

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