Question

You hold 1000 shares of Rusty Company and each is worth $5. You paid $1 for each share several years ago. You anticipate its stock price will increase by 10% per year. You would like to sell your Rusty Company stock and buy Geeky, Inc. stock with the proceeds because you see even more upside for Geeky, Inc.

How fast must Geeky, Inc. stock grow for you to be indifferent (after-tax) between: (a) holding Rusty Company stock and doing nothing and (b) selling Rusty Company stock and reinvesting in Geeky, Inc. Whatever you do, assume that in three years you will liquidate your holdings to pay for your daughter’s college education. Assume the capital gains tax rate is 15%, and that neither stock pays dividends.

Answer 1

a) Holding Rusty Company stock for 3 years and liquidating it

Cost Price of Rusty Company = $1*1000 = $1,000

Assuming its stock price will increase 10% per year, Stock price at the end of 3 years = Current share price* (1+growth rate)ⁿ

= 5* (1+.1)³  = $6.655

Selling price after 3 years for Rusty Company = $6.655*1000 =$6,655

Capital gain before tax = Selling Price - Cost Price = $6,655 - $1,000 = $5,655

Capital gain after tax = $5,655 * 85% = $4,806.75

Hence, Geeky, Inc. stock must grow as such the after tax income comes to $4,806.75

b) Selling Rusty Company Stock and reinvesting in Geeky

Cost Price for Geeky = Current Sale Price for Rusty = $5 *1000 = $5,000

Hence capital gain before tax for Rusty Company should be $5,655 for indifferent after tax income in both cases.

Current Price of Geeky shares must be then $5000 + $5,655 = $10,655

Growth rate for Geeky shares = (Current Price /Cost Price)^1/3 -1 = ($10,655/$5,000)^1/3  -1 = 28.68%

Therefore, Geeky, Inc stock should grow at 28.68% for indifferent after tax income.