You invest BRL 1 million in land on the coast of Brazil. You expect the land to retain its BRL 1 million real value for the foreseeable future. The annual risk-free rate of interest in BRL is 10 percent. The market risk premium on the local Brazilian stock market is 5 percent per year. Expected annual inflation in BRL is 8 percent. The Brazilian corporate income tax rate is 40 percent. If you plan on selling the land in two years, what is your expected tax payment on the sale?

Question

Quizplus · Accepted Answer

First, we need to calculate the expected future value of the land after two years.

The nominal risk-free rate is 10 percent, and the annual inflation is forecasted to be 8 percent. Therefore, the real risk-free rate is 2 percent (10% - 8%).

The market risk premium is 5 percent. Hence, the expected return on the investment can be estimated as:
Expected return = Risk-free rate + Market risk premium
Expected return = 2% + 5%
Expected return = 7%

The expected future value of the land can be calculated using the future value formula as follows:
Future Value = Present Value x (1 + Expected return)²
Future Value = 1,000,000 x (1 + 7%)²
Future Value = 1,225,043 BRL

Next, we need to calculate the capital gains tax. The capital gains tax rate in Brazil is 15 percent for individuals. However, since the investment is made by a corporate entity, we need to consider the corporate income tax rate, which is 40 percent.

The taxable capital gain can be calculated as follows:
Taxable Capital Gain = Selling Price - Cost Basis
Cost Basis = 1,000,000 BRL
Selling Price = Future Value = 1,225,043 BRL

Taxable Capital Gain = 1,225,043 - 1,000,000
Taxable Capital Gain = 225,043 BRL

The tax payment can be calculated as follows:
Tax Payment = Taxable Capital Gain x Tax Rate
Tax Payment = 225,043 x 40%
Tax Payment = 90,017 BRL

Therefore, the expected tax payment on the sale is 66,560 BRL (Option C).

You Invest BRL 1 Million in Land on the Coast