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 – PX) / D = (1 – TP) / (1 – TG)

  

where P0 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, TP is the relevant marginal personal tax rate on dividends, and TG 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?

P0 PX D

  

b.	If TP = 21 percent and TG = 0, how much will the share price fall? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.)

  

Share price

D

  

c.	If TP = 21 percent and TG = 42 percent, how much will the share price fall? (Do not round intermediate calculations. Round your answer to 4 decimal places, e.g., 32.1616.)

  

Share price

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 38 percent, what does this model predict the ex-dividend share price will be?

Answer 1

Understanding the meaning of various terms used in the question (In order to simply the question from understanding point of view) :-

a)Market imperfections - It is an economics theory which states that demand and supply can never be equal and therefore there is no economy in the world has a perfect market.

b)Tax Effect - In relevant to this question it means that tax effect is a measure to control the demand and supply, because tax cuts boost demand by increasing disposable income and by encouraging businesses to hire and invest more. Tax increases do the reverse.

c)Ex-dividend date for a stock - Is one business day before the record date, means that an investor who buys the stock on its ex-dividend date or later will not be eligible to receive the declared dividend fro the company.

Now understanding the question in a layman way,

Hence the question says that in the absence of market imperfections or an economy where demand and supply is not equal and tax effects are not used to control the economy. Hence in such an economy we would expect the share price of a company to decline by the amount of dividend paid because the dividend amount paid will be deducted out of the share price (Share price - Dividend= Share price on ex dividend date ). But once the role of tax is taken in accounts then the above statement does not stands true, because as per on economics model increase or decrease in tax will affect the price of share on ex-dividend date.

Now , as per the question:

  (P0 – PX) / D = (1 – TP) / (1 – TG)  

where    P0 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,

            TP is the relevant marginal personal tax rate on dividends, and

          TG is the effective marginal tax rate on capital gains.

Answer to Question a)       if, TP=TG=0 so once the value of TP and TG is substituted in the equation (P0 – PX) / D = (1 – TP) / (1 – TG)  

we get                                       Po-Px= D (bringing D on the opposite side of equals symbol )

               We get                        Px= Po-D         

                Which means the price of share is reduced by amount of dividend D

Answer to Question b)        If TP=0.21, TG=0    (substituting this values in the below equation)

                            (P0 – PX) / D = (1 – TP) / (1 – TG)  

We get :                   (Po-Px)/D= (1-0.21)/1

Then                              Po-Px=0.79D

Then                            Px= Po-0.79D

Which means the share price will fall by 0.79D

Answer to Question c)      If Tp=0.21 &Tg=0.42            (substituting this values in the below equation)

                            (P0 – PX) / D = (1 – TP) / (1 – TG)  

   We get                  Po-Px/D=(1-0.21)/(1-0.42)

    Then,                (Po-Px)/D = 0.79/0.58

     Then,                    (Po-Px)/D = 1.3620

                                      Po-Px    = 1.3620D

                                          Px= Po- 1.3620D

Which means share price fall by 1.3620 to the amount of Dividend

Answer to Question D)       Since corporation are only owners then TP= 0.70*0.38 which is equal to 0.27 and TG =0.38,   substituting this values in the below equation ,

                 (P0 – PX) / D = (1 – TP) / (1 – TG)  

We get             Po-Px/D= (1-0.27)/(1-0.38)

    Then,                Po-Px=1.1774D

                                Px= Po-1.1774D      which means share price will fall by 1.1774 times of dividend.