Online HW 6: Expected Value and Std Dev of Random Variables Page 1: Previous Page Page 2 of 3 1 2 a a You intend to buy a parcel of land for $1,500,000 with the intention of selling it in two years. The price you will get for it in 2 years depends on whether the land is Page 2: rezoned or not. A real estate consultant estimates the probabilities and probable 5 . 5 selling price to be: G 6 A Rezoned As Probability Price in 2 yrs 6 7 8 No change 70% $1,400,000 & 8 A Industrial 10% $2,500,000 Residential 20% $1,200,000 Page 3: 9 10 | | 11 A Question 5 (1 point) Retake question A b Compute the standard deviation of the selling price? Round your answer to 2 decimal 12113 14 places, if needed. a & 8 Your Answer: 15 16 a| o | | Answer units & Question 8 (1 point) retake question Suppose you need to borrow the $1,500,000 to buy the land, at 6% compounded monthly, with the entire loan repaid in 2 years. What is the expected loss or profit? Round your answer to 2 decimal places. Include a minus '-' sign if there is a loss. Your Answer: Answer units w Hide hint for Question 8 find the future value of the $1,500,000 borrowed at 6%, compounded monthly for 2 years. E(X)= p=5umx-p(x) = Z x - plx) - JE _ e _ i _ P a \\IZ(;:, w)* Px,) or & NIZ'Y' Plx,)p Plans are being made to build another airport in the Lower Mainland. Two possible locations for the new airport, Site A and Site B, have been identified. A final decision regarding the new airport location will not be known for another year. Magnolia Inns hotel chain hopes to build a hotel near the new airport. Land values around the two potential airport sites are increasing as investors speculate that property values will increase greatly in the vicinity of the new airport. Magnolia Inns wants to purchase the land now, before land prices increase any further. The land near Site A will cost Magnolia Inns $18,000,000 If they purchase the land near Site A and the new airport is built at Site A, they expect a total revenue of $31,000,000 (present value) If they purchase the land at Site A and the new airport is built at Site B instead, they will not build the hotel and sell the land. The land will lose its value and they estimate a selling price of $4,000,000 (present value) The land near Site B will cost Magnolia Inns $12,000,000 (it's a smaller piece of land and the hotel will have to be smaller) If they purchase the land near Site B and the new airport is built at Site B, they expect a total revenue of $23.000,000 (present value) If they purchase the land at Site B and the new airport is built at Site A instead, they will not build the hotel and sell the land. The land will lose its value and they estimate a selling price of 4,000,000 (present value) A Question 9 (1 point) Betake quastion If they purchase the land near Site A and the airport is built at Site A, what is their estimated profit? Estimated Profit = $ [:] w Hide hint for Question 9 Profit = Revenue - Costs The land near Site A will cost $18,000,000 If the airport is built at Site A, they estimate revenue of $31,000,000 & Question 12 (1 point) Retake question If they purchase the land near Site B and the airport is NOT built at Site B, what is their estimated profit? Estimated Profit= % :] w Hide hint for Question 12 Profit = Revenue - Costs The land near Site B will cost $12,000,000 If the airport is NOT built at Site B, they will be able to resell the land for $4,000,000 If experience a loss, write profit as a negative value. It is discovered that there is a 60% probability the airport will be built at Site A; there is a 40% probability the airport will be built at Site B