Reading: The Irrelevance of Payouts

What if the firm decided to repurchase shares instead of paying out dividends? Remember from before, that, in the current situation, the firm has an equity value of 200 and, given 10 shares outstanding, a stock price of 20.

What happens if the firm decides to repurchase shares instead of paying out a dividend today? Let us consider the three payout scenarios from before, assuming that the firm repurchases shares in the open market at the prevailing stock price of 20:

1. Repurchase volume equal to the initial cash flow of 100;
2. A smaller initial repurchase volume of 40;
3. A larger initial repurchase volume of 160.

From before, we know that the announcement of the changes in the payout amounts leaves the value of the firm as well as its stock price unaffected. We have denoted these valuations with the prime symbol ('), so E' was 200 and P' was 20. 

Repurchase volume equal to cash flows (100)

At a repurchase price (P_R) of 20, the firm will repurchase a total number of 5 shares (N_R), so that after the repurchase, there will be 5 shares remaining (N*):

\( N_R = \frac{Payout}{P_R} = \frac{100}{20} = 5. \) 

\( N^* = N - N_R = 10 - 5 = 5 \)

The shareholders who do not sell their shares receive no payout today, but they receive the full payout of 110 in one year. Consequently, from today's perspective, the equity value for the remaining shareholders (E*) is 100 and the stock price (P*), therefore, remains at 20:

\( E^* = 0 + \frac{Div_1}{(1+k_A)} = 0 + \frac{110}{1.1} = 100 \)

\( P^* = \frac{E^*}{N^*} = \frac{100}{5} = 20 \)

Shareholders should therefore be indifferent between dividend payments and share repurchases, as both alternatives lead to the same outcome.

Smaller (40) initial repurchase volume

It may not come as a surprise that the same result applies when the firm has a smaller or larger initial repurchase volume. 

If the initial repurchase volume is only 40, the firm will buy back only 2 shares so that there will be 8 shares outstanding after the repurchase. As before, we assume that the retained capital of 60 is invested at the cost of capital, so that the remaining shareholders expect to collect a payout of 176 in 1 year: 

\( N_R = \frac{Payout}{P_R} = \frac{40}{20} = 2. \) 

\( N^* = N - N_R = 10 - 2 = 8 \)

\( Div_1 = 110 + 60 \times 1.1 = 176 \)

For the remaining shareholders, the equity value is therefore 160 and the theoretical stock price remains at 20:

\( E^* = 0 + \frac{Div_1}{(1+k_A)} = 0 + \frac{176}{1.1} = 160 \)

\( P^* = \frac{E^*}{N^*} = \frac{160}{8} = 20 \)

Larger (160) initial repurchase volume

If the initial repurchase volume is 160, the firm will buy back 8 shares so that there will be 2 shares outstanding after the repurchase. As before, we assume that the additional capital of 50 is raised at a cost of capital of 10%, so that the remaining shareholders will only receive a cash flow of 44 in one year: 

\( N_R = \frac{Payout}{P_R} = \frac{160}{20} = 8. \) 

\( N^* = N - N_R = 10 - 8 = 2 \)

\( Div_1 = 110 - 60 \times 1.1 = 44 \)

For the remaining shareholders, the equity value is therefore 40 and the theoretical stock price remains at 20:

\( E^* = 0 + \frac{Div_1}{(1+k_A)} = 0 + \frac{44}{1.1} = 40 \)

\( P^* = \frac{E^*}{N^*} = \frac{40}{2} = 20 \)