The Dow Jones Travel Index reported what business travelers pay for hotel rooms

Question

The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows: Atlanta $163 Minneapolis $125 Boston 177 New Orleans 167 Chicago 166 New York 245 Cleveland 126 Orlando 146 Dallas 123 Phoenix 139 Denver 120 Pittsburgh 134 Detroit 144 San Francisco 167 Houston 173 Seattle 162 Los Angeles 160 St. Louis 145 Miami 192 Washington, D.C. 207 a) What is the mean hotel room rate? b) What is the median hotel room rate? c) What is the mode? d) What is the first quartile? What is the meaning of first quartile? e) What is the third quartile? What is the meaning of first quartile? Problem 2 Choi, Laibson and Madrian conducted an experiment to study the choices made in fund selection. Suppose 100 undergraduate students and 100 MBA students were selected. When presented with 4 S&P 500 Index funds that were identical expect for their fees, undergraduate and MBA students chose the funds as follows: Student Group FUND Undergraduates MBA Lowest cost fund 19 19 Second lowest cost fund 37 40 Third lowest cost fund 17 23 Highest cost fund 27 18 If a student is selected at random, what is the probability that he or she a) selected the lowest or second lowest cost fund? b) Selected the lowest cost fund and is an undergraduate? c) Selected the lowest cost fund or is an undergraduate? d) Given that a student is an undergraduate, what is the probability that he or she selected the highest cost fund? Problem 3. In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005). a) In a sample of 10 workers, what is the probability that exactly threeworkers take public transportation daily? b) In a sample of 10 workers, what is the probability that at least three workers take public transportation daily? Problem 4. Trading volume on the New York Stock Exchange is heaviest during the first half hour (early morning) and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of shares) for 13 days in January and February are shown here (Barron’s, January 23, 2006; February 13, 2006; and February 27, 2006). 214 163 265 194 180 202 198 212 201 174 171 211 211 The probability distribution of trading volume is approximately normal. a) Compute the mean and standard deviation to use as estimates of the population mean and standard deviation. b) What is the probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares? c) What is the probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares? Unit 5: Financial Mathematics Problem 5. A client invests $500,000 in a bond fund project to earn 7% annually. Estimate the value of this investment after 10 years. Problem 6. For liquidity purposes a client keeps $100,000 in a bank account. The bank quotes a stated annual interest rate of 7%. How much will your client have in this account at the end a. One year b. Two years Assuming no withdrawals (so all the interest are reinvested) with 1. Quarterly compounding 2. Monthly compounding 3. Continuous compounding Problem 7. A couple plans to set aside $20,000 per year in a portfolio that earns 7% a year. If they make their first saving contribution one year from now, how much will they have at the end of 20 years? Problem 8. To cover the first year’s total college tuition payments for his two children, a father will make a $75,000 payment five years from now. How much will he need to invest today to meet this payment if the investment earns 6% annually? Problem 9 Two major investment projects each have the same initial capital outlay of $2,000 million. The expected net revenues on the respective projects over the next 4 years are outlined below ($ millions) Project A Project B Year 0 -2000 -2000 Year 1 1000 200 Year 2 800 600 Year 3 600 800 Year 4 200 1200 a. Calculate the payback period for each of the projects b. Assuming that the required rate of return is 10% calculate the NPV of each project. c. Which of them would you choose if you had only 2000$ millions? d. If you had money enough to invest in both would you choose both or just one of them? Justify your answer.

The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows: Atlanta $163 Minneapolis $125 Boston 177 New Orleans 167 Chicago 166 New York 245 Cleveland 126 Orlando 146 Dallas 123 Phoenix 139 Denver 120 Pittsburgh 134 Detroit 144 San Francisco 167 Houston 173 Seattle 162 Los Angeles 160 St. Louis 145 Miami 192 Washington, D.C. 207 a) What is the mean hotel room rate? b) What is the median hotel room rate? c) What is the mode? d) What is the first quartile? What is the meaning of first quartile? e) What is the third quartile? What is the meaning of first quartile? Problem 2 Choi, Laibson and Madrian conducted an experiment to study the choices made in fund selection. Suppose 100 undergraduate students and 100 MBA students were selected. When presented with 4 S&P 500 Index funds that were identical expect for their fees, undergraduate and MBA students chose the funds as follows: Student Group FUND Undergraduates MBA Lowest cost fund 19 19 Second lowest cost fund 37 40 Third lowest cost fund 17 23 Highest cost fund 27 18 If a student is selected at random, what is the probability that he or she a) selected the lowest or second lowest cost fund? b) Selected the lowest cost fund and is an undergraduate? c) Selected the lowest cost fund or is an undergraduate? d) Given that a student is an undergraduate, what is the probability that he or she selected the highest cost fund? Problem 3. In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005). a) In a sample of 10 workers, what is the probability that exactly threeworkers take public transportation daily? b) In a sample of 10 workers, what is the probability that at least three workers take public transportation daily? Problem 4. Trading volume on the New York Stock Exchange is heaviest during the first half hour (early morning) and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of shares) for 13 days in January and February are shown here (Barron’s, January 23, 2006; February 13, 2006; and February 27, 2006). 214 163 265 194 180 202 198 212 201 174 171 211 211 The probability distribution of trading volume is approximately normal. a) Compute the mean and standard deviation to use as estimates of the population mean and standard deviation. b) What is the probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares? c) What is the probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares? Unit 5: Financial Mathematics Problem 5. A client invests $500,000 in a bond fund project to earn 7% annually. Estimate the value of this investment after 10 years. Problem 6. For liquidity purposes a client keeps $100,000 in a bank account. The bank quotes a stated annual interest rate of 7%. How much will your client have in this account at the end a. One year b. Two years Assuming no withdrawals (so all the interest are reinvested) with 1. Quarterly compounding 2. Monthly compounding 3. Continuous compounding Problem 7. A couple plans to set aside $20,000 per year in a portfolio that earns 7% a year. If they make their first saving contribution one year from now, how much will they have at the end of 20 years? Problem 8. To cover the first year’s total college tuition payments for his two children, a father will make a $75,000 payment five years from now. How much will he need to invest today to meet this payment if the investment earns 6% annually? Problem 9 Two major investment projects each have the same initial capital outlay of $2,000 million. The expected net revenues on the respective projects over the next 4 years are outlined below ($ millions) Project A Project B Year 0 -2000 -2000 Year 1 1000 200 Year 2 800 600 Year 3 600 800 Year 4 200 1200 a. Calculate the payback period for each of the projects b. Assuming that the required rate of return is 10% calculate the NPV of each project. c. Which of them would you choose if you had only 2000$ millions? d. If you had money enough to invest in both would you choose both or just one of them? Justify your answer.
The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows: Atlanta $163 Minneapolis $125 Boston 177 New Orleans 167 Chicago 166 New York 245 Cleveland 126 Orlando 146 Dallas 123 Phoenix 139 Denver 120 Pittsburgh 134 Detroit 144 San Francisco 167 Houston 173 Seattle 162 Los Angeles 160 St. Louis 145 Miami 192 Washington, D.C. 207 a) What is the mean hotel room rate? b) What is the median hotel room rate? c) What is the mode? d) What is the first quartile? What is the meaning of first quartile? e) What is the third quartile? What is the meaning of first quartile? Problem 2 Choi, Laibson and Madrian conducted an experiment to study the choices made in fund selection. Suppose 100 undergraduate students and 100 MBA students were selected. When presented with 4 S&P 500 Index funds that were identical expect for their fees, undergraduate and MBA students chose the funds as follows: Student Group FUND Undergraduates MBA Lowest cost fund 19 19 Second lowest cost fund 37 40 Third lowest cost fund 17 23 Highest cost fund 27 18 If a student is selected at random, what is the probability that he or she a) selected the lowest or second lowest cost fund? b) Selected the lowest cost fund and is an undergraduate? c) Selected the lowest cost fund or is an undergraduate? d) Given that a student is an undergraduate, what is the probability that he or she selected the highest cost fund? Problem 3. In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005). a) In a sample of 10 workers, what is the probability that exactly threeworkers take public transportation daily? b) In a sample of 10 workers, what is the probability that at least three workers take public transportation daily? Problem 4. Trading volume on the New York Stock Exchange is heaviest during the first half hour (early morning) and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of shares) for 13 days in January and February are shown here (Barron’s, January 23, 2006; February 13, 2006; and February 27, 2006). 214 163 265 194 180 202 198 212 201 174 171 211 211 The probability distribution of trading volume is approximately normal. a) Compute the mean and standard deviation to use as estimates of the population mean and standard deviation. b) What is the probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares? c) What is the probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares? Unit 5: Financial Mathematics Problem 5. A client invests $500,000 in a bond fund project to earn 7% annually. Estimate the value of this investment after 10 years. Problem 6. For liquidity purposes a client keeps $100,000 in a bank account. The bank quotes a stated annual interest rate of 7%. How much will your client have in this account at the end a. One year b. Two years Assuming no withdrawals (so all the interest are reinvested) with 1. Quarterly compounding 2. Monthly compounding 3. Continuous compounding Problem 7. A couple plans to set aside $20,000 per year in a portfolio that earns 7% a year. If they make their first saving contribution one year from now, how much will they have at the end of 20 years? Problem 8. To cover the first year’s total college tuition payments for his two children, a father will make a $75,000 payment five years from now. How much will he need to invest today to meet this payment if the investment earns 6% annually? Problem 9 Two major investment projects each have the same initial capital outlay of $2,000 million. The expected net revenues on the respective projects over the next 4 years are outlined below ($ millions) Project A Project B Year 0 -2000 -2000 Year 1 1000 200 Year 2 800 600 Year 3 600 800 Year 4 200 1200 a. Calculate the payback period for each of the projects b. Assuming that the required rate of return is 10% calculate the NPV of each project. c. Which of them would you choose if you had only 2000$ millions? d. If you had money enough to invest in both would you choose both or just one of them? Justify your answer.

Explanation / Answer

Dallas

Minneapolis

Cleveland

Phoenix

Orlando

Atlanta

Chicago

New Orleand

Boston

New York

City Rate per Night Denver 120

Dallas

123

Minneapolis

125

Cleveland

126 Pittsburgh 134

Phoenix

139 Detroit 144 St. Louis 145

Orlando

146 Los Angeles 160 Seattle 162

Atlanta

163

Chicago

166

New Orleand

167 San Francisco 167 Houston 173

Boston

177 Miami 192 Washington, D.C. 207

New York

245 3181 Answer a. Mean = $3,181 / 20 = $159.05 Answer b. Median = ($160 + $162) / 2 Median = $161 Answer c. Mode = $167 (Mode is the value that occurs maximum number of times in the table) Answer d. For Q1, or the 25th percentile, i = (25/100) (20) = 5.   Q1 = ($134 +$139) / 2 = $136.50 (Q1 is the average of the values in the 5th and 6th position) Answer e. For Q3, or the 75th percentile, i = (75/100) (20) = 15 Q3 = ($167 +$173) / 2 = $170 (Q3 is the average of the values in the 15th and 16th position)

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