7. Tax Considerations

7.2. A2: Reinvest and Repurchase Shares

Alternatively, the firm could return its after-tax proceeds from the reinvestment project via a buyback program to its shareholders. In that case, not the full buyback amount will be subject to taxation, but only the capital gains the shareholders realize when selling their shares.

Let us assume the firm will repurchase shares at a repurchase price (PR,1) of 20 and that the selling shareholders have purchased these shares at an average buying price (PB) of 15. Consequently, only a fraction of 25% of the firm's payout will be subject to capital gains taxes:

 

Taxable portion of PR,1 = \( \frac{P_{R,1}-P_B}{P_{R,1}} = 1- \frac{P_B}{P_{R,1}} = 1 - \frac{15}{20} = 0.25 \)

 

If only 25% of the proceeds are taxed at the capital gains tax rate (τG) of 15%, shareholders factually pay a tax rate of 3.75% when participating in the buyback program:

 

Factual buyback tax rate = Taxable portion of PR,1 × τG = \( \tau_G \times (1- \frac{P_B}{P_{R,1}}) = 0.15 \times 0.25 = 0.0375 \) 

 

Put differently, for each dollar the firm returns via buybacks, shareholders will pay 3.75 cents in capital gains taxes. Remember from the preceding section, that the corresponding tax bill associated with dividend payments is 15 cents. Put differently, for each dollar returned via buybacks instead of dividends, shareholders save 11.25 cents in taxes!

 

Given an overall cash balance of 106'820 at the end of year one (see preceding section for the computation of that value), the after-tax payout to shareholders will be 102'814 if the firm engages in a buyback program:

 

\( \text{After-tax Buyback}_1 = \text{Cash}_1 \times (1 - \text{Factual buyback tax rate}) = 106'820 \times (1 - 0.0375) = 102'814 \)

 

In sum, a specific excess cash balance today (Cash0) that is reinvested and then used in one year to repurchase shares yields the following after-tax payment to shareholders: 

 

\( \text{After-tax Payout}_\text{Reinvest, Buyback} = \text{Cash}_0 \times (1+ ROIC_C \times (1-\tau_C)) \times (1-\tau_G \times (1-\frac{P_B}{P_{R,1}})) \)