Anton, Inc., just paid a dividend of $2.40 per share on its stock. The dividends are expected to grow at

Anton, Inc., just paid a dividend of $2.40 per share on its stock. The dividends are expected to grow at a constant rate of 6.25 percent per year, indefinitely. Assume investors require a return of 12 percent on this stock.

Requirement 1:

What is the current price? (Do not round intermediate calculations. 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 round intermediate calculations. 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 = $2.40 (1.0625) / (0.12 – 0.0625)

P0 = $44.35

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 = $2.40 (1.0625)5 / (0.12 – 0.0625)

P4 = $56.52

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 = $2.40 (1.0625)17 / (0.12 – 0.0625)

P16 = $116.99

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 Year four, and we have already calculated the stock price today. The stock price in Year four will be:

P4 = P0(1 + g)4

P4 = $44.35(1 + 0.0625)4

P4 = $56.52

And the stock price in Year 16 will be:

P16 = P0(1 + g)16

P16 = $44.35(1 + 0.0625)16

P16 = $116.99

Good Values, Inc., is all-equity-financed. The total market value of the firm currently is

Good Values, Inc., is all-equity-financed. The total market value of the firm currently is $240,000, and there are 3,000 shares outstanding. Good Values plans to repurchase $24,000 worth of stock. Ignore taxes.

a.	What will be the stock price before and after the repurchase?

	Stock Price
Before	$ per share
After	per share

Explanation:

a.

The repurchase will have no tax implications. Because the repurchase does not create a tax obligation for the shareholders, the value of the firm today is the value of the firm’s assets ($240,000) divided by 3,000 shares, or $80 per share. The firm will repurchase 300 shares for $24,000. After the repurchase, the stock will sell at a price of $216,000/2,700 = $80 per share.

The price is the same as before the repurchase.

Investors require an after-tax rate of return of 10% on their stock investments. Assume that the tax rate on dividends is 30% while capital gains escape taxation. A firm will pay a $1 per share dividend 1 year from now, after which it is expected to sell at a price of $10.

a.	Find the current price of the stock. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Current price

$

b.	Find the expected before-tax rate of return for a 1-year holding period. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Before-tax rate of return

%

c.	Now suppose that the dividend will be $2 per share. If the expected after-tax rate of return is still 10%, and investors still expect the stock to sell at $10 in 1 year, at what price must the stock now sell? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price

$

d-1.	What is the before-tax rate of return? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Before-tax rate of return

%

d-2.	Why is it now higher than in part (b)?

The before-tax return is higher because the larger dividend creates a   greater tax burden.

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for the actual calculations.

a. 

Price = PV (after-tax dividend plus final share price) =	[$1 × (1 − 0.30)] + $10	= $9.73
	1.10

b.

Before-tax rate of return =	dividend + capital gain	=	$1.00 + ($10.00 − $9.73)	= 0.1308 = 13.08%
	price		$9.73

c. 

Price = PV (after-tax dividend plus final share price) =	[$2 × (1 − 0.30)] + $10	= $10.36
	1.10

d-1.

Before-tax rate of return =	dividend + capital gain	=	$2 + ($10 − $10.36)	= 0.1579 = 15.79%
	price		$10.36

d-2.

The before-tax return must increase in order to provide the same after-tax return of 10%.