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:
  
(P₀ – P_X) / D = (1 – T_P) / (1 – T_G)

Here 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 T_P = T_G = 0, how much will the share price fall when the stock goes ex? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Share price decline             D

b. If T_P = 20 percent and T_G = 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.)

Share price decline              D

c. If T_P = 20 percent and if T_G = 15 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.)

Share price decline             D

d. Suppose the only owners of stock are corporations. Recall that corporations get at least a 70 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 change in the ex-dividend share price will be? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.)

Share price decline              D

Answer 1

(Po-Px)/D = (1- T_P)/(1- T_G)

Here Po is the price just before the stock goes ex.

Px 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

1. T_P = T_G = 0

(Po-Px)/D = (1- 0)/(1- 0)

(Po-Px)/D = 1

(Po- D) = Px

(Po- Px) = D

Share price decline is equal to dividend amount

2. T_P = 20%, T_G = 0

(Po-Px)/D = (1- 0.20)/(1- 0)

(Po-Px)/D = 0.80

(Po- 0.80 D) = Px

(Po- Px) = 0.80D

Share price decline is equal to 0.80 times of dividend amount

3.T_P = 20%, T_G =15%

(Po-Px)/D = (1- 0.20)/(1- 0.15)

(Po-Px)/D = 0.9412

(Po- 0.9412 D) = Px

(Po- Px) = 0.9412D

Share price decline is equal to 0.9412 times of dividend amount

4. T_P = T_G = 40%

(Po-Px)/D = (1- 0.40x0.3)/(1- 0.40)

(Po-Px)/D = 1.4667

(Po- 1.4667D) = Px

(Po- 1.4667D) = Px

Share price decline is equal to 1.4667 times of dividend amount

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