Corporate Finance, Module 15, “Common Stock Dividends”

Homework Assignment

(The attached PDF file has better formatting.)

{This homework assignment has two problems.}

Exercise 15.1: Cash Dividend

A firm with 20 million shares trading at $60 per share declares a 25% cash dividend: the dividend is 25% × $60 = $15 per share. If nothing else changes, what is the price per share after the dividend is paid?

Use the following reasoning to answer this problem:

A.    What is the total value of the firm before the cash dividend? (The number of shares times the price per share.)
B.    What is the total cash distributed to shareholders? The money can not be created from thin air, so it must come from the firm’s market value. What is the market value of the firm after the cash dividend?
C.    The number of shares has not changed. What is the value per share?


Exercise 15.2: Stock Dividend

A firm has 20 million shares trading at $60 per share when it declares a 25% stock dividend (not a cash dividend). If nothing else changes, what is the price per share after the new stock is distributed?

Use the following reasoning to answer this problem:

A.    What is the total value of the firm before the stock dividend? (The number of shares times the price per share.)
B.    The stock dividend is a paper transaction. No money changes hands, and no party incurs a financial obligation. An investor with 100 stock certificates receives another 25 stock certificates. The number of shares changes, but not the value of the firm. What is the number of shares after the stock dividend?
C.    The paper transaction does not change the market value of the firm. If the market value does not change, what is the new value per share?

Question: The value of the firm has not changed and the value of each investor’s stock has not changed. The share price has changed, and the number of shares has changed, so the firm has reporting and mailing requirements that add expenses. Why does the firm do this?

Answer: Two reasons are often given for stock dividends and stock splits. A stock split is similar to a stock dividend, except that a stock split is usually larger. Typical examples are

●    Stock split: each 100 shares become 200 shares
●    Stock dividend: each 100 shares become 125 shares

These terms are conventions; we might have a 100% stock dividend or a 4 for 5 stock split.

The most common reason given for stock splits is to form more attractive stock prices. Some investment analyst believe that stock prices of $30 to $100 are the most marketable.

●    If the price exceeds $100 a share, investors must pay over $10,000 for a block of 100 shares. Small investors may be reluctant to pay more than $10,000, so firms may try to keep their stock prices below $100.
●    If the price is low, such as $5 a share, a block of 100 shares costs only $500, and the transaction expenses become a large percentage of the stock price.

The most common reason for stock dividends is that the firm wants to pay a regular cash dividend, since it is profitable, but it does not have the cash to do so. This might be true for a start-up high-tech firm, which is doing well, but wants to conserve its cash for growth. It pays a stock dividend to its investors to let them know that it is doing well but doesn’t want to pay a cash dividend yet.

Does someone want to compare answers with me?

15.1 A) $60 * 20 million

B) $15 * 20 million

C) (answer to part A + answer to part B) / 20 million = $75

 

15.2 A) $60 * 20 million

B) 20 million * 1.25

C) answer to part a/ answer to part b = $48

THANKS!

mcgowan04 I had the same answers as you for 15.2 but For 15.1 I had a value of $45 per share for part C

How did you get $45?  I went about the cash dividend problem a few different ways and then got myself totally confused! 

15.1 C) Market Value after cash dividend = Stock market value before dividend - cash dividend = A) - B) =  900M

=> Value per share = 900M / 20M = $45

NEAS mentioned that it's allowed to study in a group and do homwork together. However, each student must submit his homework instead of submit a copy of the homework for the group. So, this imply that students can compare their homework to the extend that they want but have to write their own solutions.

So, it's ok to compare the homeworks to the extend that the students want.

In 15:1, it says: "What is the total value of the firm before the stock dividend?"   Did it mean to say "before the cash dividend?"

Yes, 15.1 should say "before the cash dividend."

I'm not sure about this, but I think that, for 1, the market value would be the value of the firm before the dividend (a) minus the total dividend payment(b).  This would give us an answer of (1200 - 300)/20 = 45 for C. 

This seems correct since it is 75% of the original stock price, which meshes with the idea that dividend payments do not result in a net gain for the stockholders.

However, I would have thought that the resutant stock price in 2 would be 45 as well, but I also got 48.  Does anyone have any ideas why the stock dividend did not decrease the stock price as much as the cash dividend?

5.1c: $900 million / 20 million shares -> $45 per share

The value of the firm decreases in the cash dividend, but the stock holders have the same amount of money ($45/share + $15 dividend/share = $60/share)

5.2c: $1,200 million / 25 million shares -> $48 per share

The value of the firm stays the same, but the number of shares increase.  The stock holder have the same amount of money in stock, due to their increased number of shares.

It's a mathematical consequence that decreasing the numerator here makes more of a difference, relative to increasing the denominator.  I don't know if there is a way to explain it in Corporate Finance?