Question

There are condos in CA, IL, and TX. The common discount rate is 3% per year. The property tax rates are 1.1% in CA, 2.2% in Illinois, and 2.6% in TX per year. Suppose the property tax rates will permanently increase by 0.5% next year for all three states without any prior notice so that the new property tax rates are 1.6% in CA, 2.7% in Illinois, and 3.1% in TX. All other things remain the same. What is worst possible net return you will experience if you invested in condos in these three states with some weights (w1, w2, w3) right before the property tax rate changes? Note the weights (w1, w2, w3) can be any non-negative numbers satisfying w1+w2+w3=1. Express your answer as a decimal without unit and round it to the nearest thousandth. For example, please type -0.354 if your answer is -35.4%. (Hint: See LN9 Part 4. Use the formula P=C/(r+τ) to help you solve this problem. Compute the return from investment in condos in each state using the formula P=C/(r+τ) and the net return definition, and then compare the returns among three states. You will realize net cash flow before tax, C, will cancel out during computation, and so you don’t even have to know its value. It means whatever number you use for C, the answer will be the same. Remember the portfolio return is a weighted average of component asset returns. With non-negative weights, the portfolio return will be a number between the maximum and minimum of component asset returns.)

Answer 1

Let the investment in condos in CA , IL and TX be 35%, 35% and 30% respectively. Let the total investment be '100000'.

Investment in CA= 35000, Investment in IL= 35000 ,Investment in TX= 30000

Let 1000 be the Cash Flow from each states.

Discounted Net Cash flow after tax in CA= (1000-11)/1.03 for year 1 = 960.19

Discounted Net Cash flow after tax in IL= (1000-22)/1.03 for year 1 = 949.51

Discounted Net Cash flow after tax in TX= (1000-26)/1.03 for year 1 = 945.63

Return from CA= 960.19/35000*100= 2.74%

Return from IL= 949.51/35000*100= 2.71%

Return from TX= 945.63/30000*100= 3.15%

Portfilio Return= (2.74*35%)+(2.71*35%)+(3.15*30%)

= 2.85% or 0.028