Patience, Inc., just paid a dividend of $2.80 per share on its stock. The dividends are expected to

Patience, Inc., just paid a dividend of $2.80 per share on its stock. The dividends are expected to grow at a constant rate of 6.75 percent per year, indefinitely. Assume investors require an 12 percent return on this stock.

 

Requirement 1:

What is the current price? (Do not include the dollar sign ($). Round your answer to 2 decimal places (e.g., 32.16).)

 

Current price

$

 

Requirement 2:

What will the price be in four years and in sixteen years? (Do not include the dollar signs ($). Round your answers to 2 decimal places (e.g., 32.16).)

 

Four years	$
Sixteen years	$

Explanation: 1:

The constant dividend growth model is:

Pt = Dt × (1 + g) / (R – g)

So, the price of the stock today is:

P0 = D0 (1 + g) / (R – g)

P0 = $2.80 (1.0675) / (0.12 – 0.0675)

P0 = $56.93

2:

The dividend at year 5 is the dividend today times the FVIF for the growth rate in dividends and five years, so:

P4 = D4 (1 + g) / (R – g)

P4 = D0 (1 + g)5 / (R – g)

P4 = $2.80 (1.0675)5 / (0.12 – 0.0675)

P4 = $73.93

We can do the same thing to find the dividend in Year 17, which gives us the price in Year 16, so:

P16 = D16 (1 + g) / (R – g)

P16 = D0 (1 + g)17 / (R – g)

P16 = $2.80 (1.0675)17 / (0.12 – 0.0675)

P16 = $161.90

There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in four years, and we have already calculated the stock price today. The stock price in four years will be:

P4 = P0(1 + g)4

P4 = $56.93(1 + 0.0675)4

P4 = $73.93

And the stock price in 16 years will be:

P16 = P0(1 + g)16

P16 = $56.93(1 + 0.0675)16

P16 = $161.90