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. Dividend policy (1) Time 1 dividend (2) 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)] (5) I$110$2,2000$2,200 II$121$2,200$11$2,189 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)
Policy Irrelevance Proposition
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 independent of dividend policy. At time 1, under policy II, the time 0 shareholders give up an $11 ownership interest in the firm’s shares in exchange for an $11 dividend payments; the transaction is a wash. This wash effect holds for any dividend policy change if there are no personal taxes.