An example provides insight into the dividend irrelevance proposition. Suppose that now is time 0, and one year from now is time 1. Carter Company just paid its time 0 dividend (assume dividends are paid once per year), and plans to publicly announce its dividend policy for the next year. It is considering the following two policies (all dollar amounts in $millions).
Policy I: At time 1, dividends = $110, new share sales = 0, treasury stock purchases = 0
Policy II: At time 1, dividends = $121, new share sales = $11, treasury stock purchases = 0
The time 1 total equity value (the $2,200 in column (3) of the exhibit below) is the time 1 market value of all shares (shares that were outstanding at time 0 and new shares issued at time 1. It is the ex-dividend (post time 1 dividend) value of the firm’s equity at time 1. This amount ($2,200) is the same under policies I and II because the firm’s assets and financial structure are exactly the same under I and II (implying the same time 1 total value of all the equity outstanding at time 1). We assume that the buyers of the new time 1 stock pay a fair price for the stock.
Time 1 dividend
Time 1 total equity value (time 0 shares + new time 1 shares) (3)
Time 1 value of new time 1 shares
(4)Time 1 value of old time 0 shares
[= (3) (4)]
Now let’s compute the time 0 value of the Carter stock if Carter announces policy I, and if it announces policy II. Assume an equity discount rate (k) of 10%.
= = = $2,100 (1)
= = = $2,100 (2)
In the numerator of (2), ($2,200 $11) is the time 1 value of the time 0 shares (the shares that were outstanding at time 0, which equals the value of all the shares at time 1 minus the value of the new shares issued at time 1). The time 0 value of those shares is...