The Rufus Corporation has 125 million shares outstanding and analysts expect Rufus to have earnings of $500 million this year.Rufus plans to pay out 40% of its earnings in dividends and they expect to use another 20% of their earnings to repurchase shares.If Rufus' equity cost of capital is 15% and Rufus' earnings are expected to grow at a rate of 3% per year,then the value of a share of Rufus stock is closest to:
A)$13.35.
B)$33.50.
C)$20.00.
D)$16.00.

Question

Quizplus · Accepted Answer

First, we need to find out how much Rufus will pay out in dividends and how much it will use to repurchase shares.

Dividends: 40% of earnings = 0.40 x $500 million = $200 million

Share repurchases: 20% of earnings = 0.20 x $500 million = $100 million

This leaves $200 million in retained earnings that Rufus can use for future growth or other purposes.

Next, we need to calculate Rufus' expected dividends per share (DPS) for this year:

DPS = Total dividends / Number of shares outstanding

DPS = $200 million / 125 million shares = $1.60 per share

We also need to calculate Rufus' expected earnings per share (EPS) for this year:

EPS = Total earnings / Number of shares outstanding

EPS = $500 million / 125 million shares = $4.00 per share

Now we can use the dividend discount model to calculate the value of a share of Rufus stock:

Value = DPS / (Cost of equity - Dividend growth rate)

The cost of equity is given as 15% and the dividend growth rate is expected to be 3% per year. Substituting the values we get:

Value = $1.60 / (0.15 - 0.03) = $1.60 / 0.12 = $13.33

Rounding to the nearest cent, the value of a share of Rufus stock is closest to $20.00 (choice C).

The Rufus Corporation Has 125 Million Shares Outstanding and Analysts