Reading: The Irrelevance of Payouts

In the preceding example, we have implicitly assumed that the firm conducts an open market buyback program and, therefore, repurchases shares at the prevailing market price. What if that is not the case? What if the firm repurchases shares at a price that differs from the prevailing market price, for example by conducting a fixed-price tender offer or a Dutch auction?

Two scenarios are conceivable: The buyback price is lower or higher than the current market price. Let us quickly look at the value implications of these two scenarios. Note that the module Capital Structure contains a similar discussion in the context of a (levered) recapitalization of a firm.

Buyback price (P_R) lower than the current stock price (P)

Suppose the firm offers to repurchase shares at a price of 15 (P_R) instead of the prevailing market price of 20 (P).

At such a low price, no shareholder is willing to tender shares and the buyback program fails. As a consequence, the firm does not repurchase any shares (N_R = 0) and retains all of today's cash flow of 100. These funds are invested at the market rate so that the payout of this additional project will be 110 in one year (= 100 × 1.1). Together with the originally expected cash flow of 110 in one year, the total payout will be 220 (Div₁). Therefore, the value of the firm remains at 200 and the stock price remains at 20:

\( E^* = Div_0 + \frac{Div_1}{(1+k_A)} = 0 + \frac{220}{1.1} = 200 \)

\( P^* = \frac{E^*}{N^*} = \frac{200}{10} = 20 \)

Shareholder value, therefore, remains unaffected.

Buyback price (P_R) larger than the current stock price (P)

But what if the buyback price exceeds the current stock price? Let's assume that the firm extends a fixed-price offer to use today's cash flow of 100 to repurchase shares at a price of 25 (P_R) instead of the prevailing market price of 20 (P).

In such a situation, all shareholders will tender their shares. However, as the buyback volume is limited to the current cash flow of 100, the firm will only repurchase 4 shares:

\( N_R = \frac{Payout}{P_R} = \frac{100}{25} = 4 \) 

Put differently, shares will be repurchased on a prorated basis. Of the 10 tendered shares only 4 will be repurchased so that the prorated portion of the tendered share is 40% (4 out of 10).

After the buyback, there will consequently be 6 shares outstanding who have a claim on the payout of year one.

\( N^* = N - N_R = 10 - 4 = 6 \)

Given a cash flow of 110 in one year, the market value of the equity after the repurchase will be 100. And given that there will be 6 shares outstanding, the stock price will drop to 16.67:

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

\( P^* = \frac{E^*}{N^*} = \frac{100}{6} = 16.67 \)

Does this drop in the stock price imply that the buyback program destroys value? Not quite. The reason is that the decrease in the stock price from 20 to 16.67 is fully compensated by the fact that the shareholders have sold 4 shares back to the company at a price that exceeds the fair market value (25 instead of 20). 

Put differently, for every tendered share, shareholders have sold back 40% at a price of 25 and retained the remaining 60% at a price of 16.67. The total value of one tendered share, therefore equals the fair stock price of 20:

Value of tendered share = Prorated portion × P_R + (1 - Prorated portion) × P* = 0.4 × 25 + 0.6 × 16.67 = 20.

Therefore, the actual repurchase price does, in principle, have no value implications. The reason is that a higher buyback price will lower the prorated portion of the tendered shares and the program will repurchase fewer shares.