Pinecrest Inc. has a 13% required rate of return. It does not expect to initiate dividends for 10 years, at which time it will pay $5 per share in dividends. At that time Pinecrest expects its dividends to grow at 5% forever
What is an estimate of Pinecrest's price in 10 years (P10) if its dividend at the end of year 10 is $5.00? What is its price in today's dollars if you desire a rate of return of 13%? Repeat the problem, but replace the 10 years with 30 years and compare the two sets of prices. Describe the relationship between the number of years before you receive dividends and today's price.
What will be an ideal response?
Answer: We use the formula: Price = Div10 × . Inserting in our values using 10 years, we get:
Price = P10 = $5 × = = $65.625 or about $65.63. To get today's price, we use the PVIF of with r = 0.13 and n = 10 to get: P0 = = $19.33236 or about $19.33.For 30 years, we get the same value since the number of years have no effect if prior dividends were not paid. For example, we still have: Price = P30 = $5 × = = $65.625 or about $65.63. To get today's price we use the PVIF of with r = 0.13 and n = 30 to get: P0 = = $1.67771 or about $1.68. We see that the longer it takes to begin dividends, the less today's price will be. By waiting an additional 20 years beyond the first 10 years, today's value fell from $19.33 to $1.68. Thus, the relationship between the number of years before you receive dividends and today's price is a negative relationship that tells us that firms that do not pay dividends or have to delay dividends are less valuable.
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