Question

As discussed in the text, in the absence of market imperfections and tax effects, we would expect the share price to decline by the amount of the dividend payment when the stock goes ex dividend. Once we consider the role of taxes, however, this is not necessarily true. One model has been proposed that incorporates tax effects into determining the ex-dividend price:¹

  

(P₀ – P_X)/D = (1 – T_P)/(1 – T_G)

  

where P₀ is the price just before the stock goes ex, P_X is the ex-dividend share price, D is the amount of the dividend per share, T_P is the relevant marginal personal tax rate on dividends, and T_G is the effective marginal tax rate on capital gains.

  

a.	If TP = TG = 0, how much will the share price fall when the stock goes ex?

  

• P_X

• P₀

• D

b.	If TP = 29 percent and TG = 0, how much will the share price fall? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

    

c.	If TP = 29 percent and TG = 38 percent, how much will the share price fall? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)

   

d.

Suppose the only owners of stock are corporations. Recall that corporations get at least a 50 percent exemption from taxation on the dividend income they receive, but they do not get such an exemption on capital gains. If the corporation’s income and capital gains tax rates are both 40 percent, what does this model predict the ex-dividend share price will be? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)

   

Answer 1

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Answer:

a. If Tp=Tg=0, then share price will fall by D only.

b. Tp=29%, Tg=0

    P0 - Px = D(1-Tp)/(1-Tg)

    => fall in share price = D* (1 - 0.29)/(1 - 0) = D x 0.71 or 0.71D

c. Tp=29%, Tg=38%

    P0 - Px = D(1-Tp)/(1-Tg)

    => fall in share price = D* (1 - 0.29)/(1 - 0.38) = D* (0.71)/(0.62) => 1.1452D

d. Tp=40%, Tg=40%
    P0 - Px = D(1-Tp)/(1-Tg)

    ex. dividend price = Previous price - decrease in price

     at least 50% of dividend income will be exempt, only 30% would be taxed. effectively the tax rate on dividend would be 0.4*0.5 = 20%

     D * (1 - 0.2)/(1-0.4) = 1.3333D is the decrease

ex-dividend price = P0 - 1.3333D