Question

What should be the current price of a stock, which is expected to be sold for $45 one year from now, pays a dividend of $5, and has an expected after-tax return of 20%? The tax rate on dividends is 40% and the tax rate on capital gains is 20%.

Answer 1

In the above question after tax return is given hence we need to find out after tax cashflows ie after tax value recieved from sale of stock & after tax dividend.

Capital Gain = Stock price after 1 year - Stock price today

After Tax dividend = Dividend in next year * ( 1 - tax rate on dividends)

= 5 * ( 1 - 0. 40) = 3

Let the price of the stock today = P0

After Tax amount recieved from sale of shares after 1 year = Stock price after 1 year - tax on capital gain

= 45 - ( 45 - P0)* 0.20

= 45 - 9 + 0.20P0

= 36 + 0.20P0

The value of the stock today = After Tax amount recieved from sale of shares / ( 1+ r) + after tax dividend / ( 1 + r)

P0 = (36 + 0.20P0) / 1.20 + 3/1.20

P0 *1.20 = 36 + 0.20P0 + 3

P0 = 39

The value of the stock today = $39