Question

Let the interest rate before taxes be 4% and assume the inflation rate is 3.5%. Three individual farmers are in 20%, 30%, and 40% tax brackets, respectively.

a. Determine how much (after taxes) each farmer could afford to bid for a piece of land expected to return $60.00 per year (in today’s purchasing power) into the foreseeable

future. Assume that the inflationary component of the opportunity cost is not taxed but the real component is taxed.

b. Now assume that real component and one-half of the inflationary component of the opportunity cost are taxed. How does this change the maximal bid prices each producer

would be willing to pay?

Answer 1

a) Farmer A: Tax bracket (t) = 20%

Real rate after tax = 4% * (1-t) = 4%*(1-0.2) = 3.2% or 0.032

Annual returns = $60 in perpetuity

Present value of a perpetuity = Annual cash flows / After tax cost of capital = 60 / 0.032 = $1875

Farmer A can afford to bid $1875 for the piece of land

Farmer B: Tax bracket (t) = 30%

Real rate after tax = 4% * (1-t) = 4%*(1-0.3) = 2.8% or 0.028

Annual returns = $60 in perpetuity

Present value of a perpetuity = Annual cash flows / After tax cost of capital = 60 / 0.028 = $2143

Farmer B can afford to bid $2143 for the piece of land

Farmer C: Tax bracket (t) = 40%

Real rate after tax = 4% * (1-t) = 4%*(1-0.4) = 2.4% or 0.024

Annual returns = $60 in perpetuity

Present value of a perpetuity = Annual cash flows / After tax cost of capital = 60 / 0.024 = $2500

Farmer C can afford to bid $2500 for the piece of land

b) Real rate = 4%

Inflation Rate = 3.5%

Half of the inflation rate is taxed

Cost of capital = real rate + (Inflation rate/2) = 4 + (3.5/2) = 5.75%

Farmer A: Tax bracket (t) = 20%

Cost of Capital after tax = 5.75% * (1-t) = 5.75%*(1-0.2) = 4.60% or 0.04

Annual returns = $60 in perpetuity

Present value of a perpetuity = Annual cash flows / After tax cost of capital = 60 / 0.04 = $1500

Farmer A can afford to bid $1500 for the piece of land

Farmer B: Tax bracket (t) = 30%

Cost of capital after tax = 5.75% * (1-t) = 5.75%*(1-0.3) = 4.025% or 0.04025

Annual returns = $60 in perpetuity

Present value of a perpetuity = Annual cash flows / After tax cost of capital = 60 / 0.04025 = $1491

Farmer B can afford to bid $1491 for the piece of land

Farmer C: Tax bracket (t) = 40%

Cost of capital after tax = 5.75% * (1-t) = 5.75%*(1-0.4) = 3.45% or 0.0345

Annual returns = $60 in perpetuity

Present value of a perpetuity = Annual cash flows / After tax cost of capital = 60 / 0.0345 = $1739

Farmer C can afford to bid $1739 for the piece of land