Question

From “After-Tax problems” Section: About twenty thousand acres of swampland in the southern U.S. was purchased for $6,000,000. The purchaser intends to keep it for twenty years and then sell it for a profit. The purchaser speculates that he can get a 6% after-tax rate-of-return even though he estimates an average 2% annual inflation rate during that period. Suppose income taxes are 15% of capital gains. What price must he sell the entire acreage for at the end of twenty years to achieve his speculated rate of return? Show work.

Answer 1

Let sale price be X.

Capital gain = Sale Price - Purchase price

= X - 6,000,000

Tax on capital gains = Capital gain x Tax rate

= (X - 6,000,000) x 15%

Proceeds net of capital gain taxes = Sale price - Capital gain taxes

= X - (X - 6,000,000) x 15%

After tax rate of return, r = 6%

Period = N = 20 years.

To generate the desired return, Sale Price (X) should be such that

Proceeds net of capital gain taxes = Purchase Price x (1 + r)N

X - (X - 6,000,000) x 15% = 6,000,000 x (1 + 6%)20

Solving the above equation, we get

X= $21,579,780

Hence, the price he must sell the entire acreage for at the end of twenty years to achieve his speculated rate of return is $21,579,780.