Calculate the Fair Price of Stock Today

What is the fair price for the stock today?

An investor plans to purchase a share of stock today, hold it for one year until it pays an annual dividend of $1.32, and then sell it immediately in the open market at an expected price of $37. What is a fair price for the stock today if the investor uses 10% as the discount rate? Round your answer to the nearest penny.

Answer:

The fair price of the stock today can be calculated by using the Present Discounted Value (PDV) formula by taking into account the expected dividend, selling price, and discount rate.

To calculate the fair price of the stock today, we need to apply the Present Discounted Value (PDV) formula. The PDV formula helps determine the current worth of future returns based on a specified discount rate. In this case, the investor plans to receive an annual dividend of $1.32 and sell the stock for $37 after one year.

The PDV formula is as follows:

PV = D/(1+r) + P/(1+r)n

Where:

D = Annual dividend ($1.32)

P = Expected selling price in one year ($37)

r = Discount rate (10% or 0.10)

n = Number of periods (1 year)

By substituting these values into the formula, we can calculate the fair price of the stock today by:

PV = 1.32 / (1 + 0.10) + 37 / (1 + 0.10)1

The resulting value will give us the fair price for the stock that the investor should pay today to receive the expected dividend and future selling price.

Understanding how to calculate the Present Discounted Value is essential for investors to make informed decisions on stock purchases based on expected returns and discount rates.

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