Use appropriate section headings to make sure you answer each question in a separate section. Please also attach your Excel Worksheet to illustrate how you constructed your simulation model. Problem 1: Develop two simulation models of tossing two six-sided dice (Numbered 1 Through 6 on the six faces). Model 1: Simulate rolling a single dice twice and add the total. Model 2: Simulate a combined roll of two dice, giving a number from 2 through 12 with appropriate probabilities. Problem 2 An advertisement in the newspaper offers a new car for sale or lease. The purchase price of the car is $43,240, or the car can be leased for 24 months for a monthly payment of $458, with a $7,500 downpayment. Under the lease option, there is a charge of 24 cents/mile for mileage above 30,000 miles for the 24 months, and a $550 security deposit, which is refundable at the end of the lease, must be deposited with the dealer. The car may be purchased at the end of the lease for $29,732. All other charges (taxes, maintenance, plates, etc.) are the same under both options. A. Develop a simulation model to compare the net present value of buying or leasing the car for 24 months. To compare the two options a number of assumptions must be made. Assume that: a. The mileage driven over 24 months can be approximated by an exponential distribution with mean 25,000 miles. b. The best estimate of the interest rate over the next 24 months is a normal distribution with mean 8.5% and standard deviation 1%. c. The value of the car at the end of 24 months is the same under both options (that is, if the car is purchased, the realizable value at the end of month 24 is $29,732 less 24 cents/mile for each mile over 30,000). B. Use your simulation model to assess the probability that the lease option results in a lower net present value that does the purchase option. Problem 1 Develop two simulation models of tossing two six-sided dice (Numbered 1 Through 6 on the six faces). Model 1: Simulate rolling a single dice twice and add the total. Model 2: Simulate a combined roll of two dice, giving a number from 2 through 12 with appropriate probabilities. Here, we have to develop two simulation models of tossing two six-sided dice. Let assume the dice is unbiased and probability of getting each number of its sides is equal. The probability of getting any number from 1 to 6 is given as 1/6. Let us see the two simulation models given as below: Model 1: Here, we have to simulate rolling a single dice twice and add the total. The simulation model is given as below: Number at first draw Number of second draw Total 6 2 8 2 2 4 6 1 7 4 5 9 6 6 12 2 1 3 1 1 2 3 6 9 3 2 5 1 5 6 4 3 7 1 5 6 5 6 11 5 2 7 2 5 7 3 5 8 4 1 5 2 4 6 3 5 8 3 2 5 5 5 10 4 6 10 4 6 10 1 3 4 2 1 3 1 2 3 3 5 8 6 6 12 6 4 10 6 1 7 2 1 3 5 3 8 2 6 8 2 6 8 4 6 10 3 1 4 2 4 6 5 6 11 6 1 7 6 3 9 5 1 6 3 6 9 4 2 6 5 1 6 3 1 4 1 4 5 6 5 11 4 1 5 1 4 5 Model 2 Here, we have to simulate the data in the same way as described in the above problem, only we have to use two dice at a time and simulate the data. The simulation model is given as below: First dice Second dice Total 3 1 4 6 2 8 6 5 11 5 6 11 4 3 7 1 3 4 1 5 6 6 5 11 6 3 9 4 2 6 1 6 7 2 1 3 3 3 6 5 5 10 4 5 9 6 4 10 4 5 9 1 3 4 6 2 8 2 3 5 3 1 4 2 5 7 1 2 3 5 5 10 6 6 12 5 6 11 1 3 4 1 3 4 6 1 7 2 2 4 2 3 5 3 2 5 2 6 8 5 4 9 6 3 9 4 1 5 1 5 6 4 4 8 1 6 7 1 4 5 Problem 2 An advertisement in the news paper offers a new car for sale or lease. The purchase price of the car is $43,240, or the car can be leased for 24 months for a monthly payment of $458, with a $7,500 down-payment. Under the lease option, there is a charge of 24 cents/mile for mileage above 30,000 miles for the 24 months, and a $550 security deposit, which is refundable at the end of the lease, must be deposited with the dealer. The car may be purchased at the end of the lease for $29,732. All other charges (taxes, maintenance, plates, etc.) are the same under both options. Develop a simulation model to compare the net present value of buying or leasing the car for 24 months. To compare the two options a number of assumptions must be made. Assume that: The mileage driven over 24 months can be approximated by an exponential distribution with mean 25,000 miles. The best estimate of the interest rate over the next 24 months is a normal distribution with mean 8.5% and standard deviation 1%. The value of the car at the end of 24 months is the same under both options (that is, if the car is purchased, the realizable value at the end of month 24 is $29,732 less 24 cents/mile for each mile over 30,000). Use your simulation model to asses the probability that the lease option results in a lower net present value that does the purchase option. Here, we have to develop the simulation model for the comparison of the net present value of buying or leasing the car for 24 months. Here, we are given that the mileage driven over 24 months is follows an exponential distribution with mean of 25,000 and the interest rate follows a normal distribution with mean 8.5% and standard deviation 1%. The simulation model is given as below: Month Mileage Interest rate 1 22572.00482 7.67448164 2 32147.53646 10.9301624 3 14302.70087 4.862918296 4 21090.46523 7.170758178 5 35524.63528 12.078376 6 36230.30911 12.3183051 7 28463.0791 9.677446896 8 29710.9287 10.10171576 9 22415.78188 7.621365839 10 23535.74534 8.002153416 11 37421.00929 12.72314316 12 18674.53701 6.349342582 13 30224.65781 10.27638366 14 32864.64211 11.17397832 15 15753.75127 5.35627543 16 15819.55135 5.378647458 17 31936.61036 10.85844752 18 31501.07301 10.71036482 19 13747.64512 4.674199342 20 32473.9606 11.04114661 21 15741.32865 5.352051741 22 28291.53281 9.619121154 23 28011.25999 9.523828398 24 30112.62347 10.23829198 Problem 1 Develop two simulation models of tossing two six-sided dice (Numbered 1 Through 6 on the six faces). Model 1: Simulate rolling a single dice twice and add the total. Model 2: Simulate a combined roll of two dice, giving a number from 2 through 12 with appropriate probabilities. Here, we have to develop two simulation models of tossing two six-sided dice. Let assume the dice is unbiased and probability of getting each number of its sides is equal. The probability of getting any number from 1 to 6 is given as 1/6. Let us see the two simulation models given as below: Model 1: Here, we have to simulate rolling a single dice twice and add the total. The simulation model is given as below: Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Roll 1 5 1 1 5 2 4 3 4 2 4 4 6 5 5 4 1 6 3 2 5 Roll 2 5 3 6 2 4 1 2 4 4 3 1 5 1 3 5 1 6 1 1 1 Sum 10 4 7 7 6 5 5 8 6 7 5 11 6 8 9 2 12 4 3 6 Model 2 Here, we have to simulate the data in the same way as described in the above problem, only we have to use two dice at a time and simulate the data. The simulation model is given as below: The space is follow: 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 Now, we compute the probability for each Total 2 3 4 5 6 7 8 9 10 11 12 Sum P 0.02 8 0.05 6 0.08 3 0.11 1 0.13 9 0.16 7 0.13 9 0.11 1 0.08 3 0.05 6 0.02 8 1 6 7 8 9 10 11 12 Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Dice 1 1 4 4 3 4 6 3 5 5 1 1 6 6 4 6 4 6 4 4 3 Dice 2 1 6 4 4 2 6 6 3 6 1 5 4 4 1 2 1 3 3 4 4 Sum 2 10 8 7 6 12 9 8 11 2 6 10 10 5 8 5 9 7 8 7 p 0.03 0.08 0.14 0.17 0.14 0.03 0.11 0.14 0.06 0.03 0.14 0.08 0.08 0.11 0.14 0.11 0.11 0.17 0.14 0.17 Problem 2 An advertisement in the news paper offers a new car for sale or lease. The purchase price of the car is $43,240, or the car can be leased for 24 months for a monthly payment of $458, with a $7,500 down-payment. Under the lease option, there is a charge of 24 cents/mile for mileage above 30,000 miles for the 24 months, and a $550 security deposit, which is refundable at the end of the lease, must be deposited with the dealer. The car may be purchased at the end of the lease for $29,732. All other charges (taxes, maintenance, plates, etc.) are the same under both options. Develop a simulation model to compare the net present value of buying or leasing the car for 24 months. To compare the two options a number of assumptions must be made. Assume that: The mileage driven over 24 months can be approximated by an exponential distribution with mean 25,000 miles. The best estimate of the interest rate over the next 24 months is a normal distribution with mean 8.5% and standard deviation 1%. The value of the car at the end of 24 months is the same under both options (that is, if the car is purchased, the realizable value at the end of month 24 is $29,732 less 24 cents/mile for each mile over 30,000). Use your simulation model to asses the probability that the lease option results in a lower net present value that does the purchase option. Here, we have to develop the simulation model for the comparison of the net present value of buying or leasing the car for 24 months. Here, we are given that the mileage driven over 24 months is follows an exponential distribution with mean of 25,000 and the interest rate follows a normal distribution with mean 8.5% and standard deviation 1%. The data collected is follow: Price Monthly Payment Duration Downpayment Amount borrowed Charge Security Deposit Interest Rate $43,240.00 $458.00 24 months $7,500.00 $35,740.00 0.24 $/mile $550.00 8.90% Now we compute the variables to start the simulation Exponential Distribution Mean 25000 1.4132 Mileage Driven 35331.20 Mileage Extra Extra Charge 5331.20 $1,279.4 9 The simulation model is given as below: Cashflow Month Leasing 0 1 2 3 4 5 6 7 8 9 10 11 12 $1,061.31 $1,572.62 $2,083.94 $2,595.25 $3,106.56 $3,617.87 $4,129.18 $4,640.50 $5,151.81 $5,663.12 $6,174.43 $6,685.74 Buy $43,240.00 $43,531.87 $43,825.70 $44,121.53 $44,419.34 $44,719.17 $45,021.02 $45,324.91 $45,630.85 $45,938.86 $46,248.94 $46,561.12 $46,875.40 Extra Charge per Month $53.31 13 14 15 16 17 18 19 20 21 22 23 24 $7,197.06 $7,708.37 $8,219.68 $8,730.99 $9,242.30 $9,753.62 $10,264.93 $10,776.24 $11,287.55 $11,798.86 $12,310.18 $12,271.49 $47,191.81 $47,510.35 $47,831.04 $48,153.90 $48,478.94 $48,806.16 $49,135.60 $49,467.27 $49,801.17 $50,137.32 $50,475.74 $50,816.45 Accumulated Realizable Value $12,271.49 $29,732.00 $50,816.45 $29,732.00 NPV $49,503.49 $50,816.45 Lease option has a fewer probability to result in a greater NPV. In this case, is advisable leasing and then buy after the 24 months under the conditions agreed above. Problem 1 Develop two simulation models of tossing two six-sided dice (Numbered 1 Through 6 on the six faces). Model 1: Simulate rolling a single dice twice and add the total. Model 2: Simulate a combined roll of two dice, giving a number from 2 through 12 with appropriate probabilities. Here, we have to develop two simulation models of tossing two six-sided dice. Let assume the dice is unbiased and probability of getting each number of its sides is equal. The probability of getting any number from 1 to 6 is given as 1/6. Let us see the two simulation models given as below: Model 1: Here, we have to simulate rolling a single dice twice and add the total. The simulation model is given as below: Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Roll 1 5 1 1 5 2 4 3 4 2 4 4 6 5 5 4 1 6 3 2 5 Roll 2 5 3 6 2 4 1 2 4 4 3 1 5 1 3 5 1 6 1 1 1 Sum 10 4 7 7 6 5 5 8 6 7 5 11 6 8 9 2 12 4 3 6 Model 2 Here, we have to simulate the data in the same way as described in the above problem, only we have to use two dice at a time and simulate the data. The simulation model is given as below: The space is follow: 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 Now, we compute the probability for each Total 2 3 4 5 6 7 8 9 10 11 12 Sum P 0.02 8 0.05 6 0.08 3 0.11 1 0.13 9 0.16 7 0.13 9 0.11 1 0.08 3 0.05 6 0.02 8 1 6 7 8 9 10 11 12 Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Dice 1 1 4 4 3 4 6 3 5 5 1 1 6 6 4 6 4 6 4 4 3 Dice 2 1 6 4 4 2 6 6 3 6 1 5 4 4 1 2 1 3 3 4 4 Sum 2 10 8 7 6 12 9 8 11 2 6 10 10 5 8 5 9 7 8 7 p 0.03 0.08 0.14 0.17 0.14 0.03 0.11 0.14 0.06 0.03 0.14 0.08 0.08 0.11 0.14 0.11 0.11 0.17 0.14 0.17 Problem 2 An advertisement in the news paper offers a new car for sale or lease. The purchase price of the car is $43,240, or the car can be leased for 24 months for a monthly payment of $458, with a $7,500 down-payment. Under the lease option, there is a charge of 24 cents/mile for mileage above 30,000 miles for the 24 months, and a $550 security deposit, which is refundable at the end of the lease, must be deposited with the dealer. The car may be purchased at the end of the lease for $29,732. All other charges (taxes, maintenance, plates, etc.) are the same under both options. Develop a simulation model to compare the net present value of buying or leasing the car for 24 months. To compare the two options a number of assumptions must be made. Assume that: The mileage driven over 24 months can be approximated by an exponential distribution with mean 25,000 miles. The best estimate of the interest rate over the next 24 months is a normal distribution with mean 8.5% and standard deviation 1%. The value of the car at the end of 24 months is the same under both options (that is, if the car is purchased, the realizable value at the end of month 24 is $29,732 less 24 cents/mile for each mile over 30,000). Use your simulation model to asses the probability that the lease option results in a lower net present value that does the purchase option. Here, we have to develop the simulation model for the comparison of the net present value of buying or leasing the car for 24 months. Here, we are given that the mileage driven over 24 months is follows an exponential distribution with mean of 25,000 and the interest rate follows a normal distribution with mean 8.5% and standard deviation 1%. The data collected is follow: Price Monthly Payment Duration Downpayment Amount borrowed Charge Security Deposit Interest Rate $43,240.00 $458.00 24 months $7,500.00 $35,740.00 0.24 $/mile $550.00 8.90% Now we compute the variables to start the simulation Exponential Distribution Mean 25000 1.4132 Mileage Driven 35331.20 Mileage Extra Extra Charge 5331.20 $1,279.4 9 The simulation model is given as below: Cashflow Month Leasing 0 1 2 3 4 5 6 7 8 9 10 11 12 $1,061.31 $1,572.62 $2,083.94 $2,595.25 $3,106.56 $3,617.87 $4,129.18 $4,640.50 $5,151.81 $5,663.12 $6,174.43 $6,685.74 Buy $43,240.00 $43,531.87 $43,825.70 $44,121.53 $44,419.34 $44,719.17 $45,021.02 $45,324.91 $45,630.85 $45,938.86 $46,248.94 $46,561.12 $46,875.40 Extra Charge per Month $53.31 13 14 15 16 17 18 19 20 21 22 23 24 $7,197.06 $7,708.37 $8,219.68 $8,730.99 $9,242.30 $9,753.62 $10,264.93 $10,776.24 $11,287.55 $11,798.86 $12,310.18 $12,271.49 $47,191.81 $47,510.35 $47,831.04 $48,153.90 $48,478.94 $48,806.16 $49,135.60 $49,467.27 $49,801.17 $50,137.32 $50,475.74 $50,816.45 Accumulated Realizable Value $12,271.49 $29,732.00 $50,816.45 $29,732.00 NPV $49,503.49 $50,816.45 Lease option has a fewer probability to result in a greater NPV. In this case, is advisable leasing and then buy after the 24 months under the conditions agreed above. Model 1 Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Roll 1 5 6 1 1 4 5 2 2 2 3 1 2 6 3 2 5 6 3 3 1 Roll 2 2 1 6 1 1 6 3 1 3 5 1 5 1 5 5 2 4 1 3 1 Model 2 Sum 7 7 7 2 5 11 5 3 5 8 2 7 7 8 7 7 10 4 6 2 Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Dice 1 5 6 3 6 6 1 1 6 1 2 4 6 1 3 5 4 6 6 2 1 Dice 2 1 1 5 5 6 6 6 5 5 1 3 6 2 5 3 5 4 2 6 2 Sum 6 7 8 11 12 7 7 11 6 3 7 12 3 8 8 9 10 8 8 3 2 p 0.14 0.17 0.14 0.06 0.03 0.17 0.17 0.06 0.14 0.06 0.17 0.03 0.06 0.14 0.14 0.11 0.08 0.14 0.14 0.06 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 Total 2 3 4 5 6 7 8 9 10 11 12 P 0.0278 0.0556 0.0833 0.1111 0.1389 0.1667 0.1389 0.1111 0.0833 0.0556 0.0278 1 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 Price Monthly Payment Duration Downpayment Amount borrowed Charge Security Deposit Interest Rate $43,240.00 $458.00 24 months $7,500.00 $35,740.00 0.24 $/mile $550.00 8.10% Exponential Distribution Mean 25000 Mileage Driven 1.8683 F9 to simulate! Cashflow Leasing Month 46708.14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 $1,175.08 $1,800.16 $2,425.24 $3,050.33 $3,675.41 $4,300.49 $4,925.57 $5,550.65 $6,175.73 $6,800.81 $7,425.90 $8,050.98 $8,676.06 $9,301.14 $9,926.22 $10,551.30 $11,176.38 $11,801.46 $12,426.55 $13,051.63 $13,676.71 $14,301.79 $14,926.87 $15,001.95 Sell $43,240.00 $43,531.87 $43,825.70 $44,121.53 $44,419.34 $44,719.17 $45,021.02 $45,324.91 $45,630.85 $45,938.86 $46,248.94 $46,561.12 $46,875.40 $47,191.81 $47,510.35 $47,831.04 $48,153.90 $48,478.94 $48,806.16 $49,135.60 $49,467.27 $49,801.17 $50,137.32 $50,475.74 $50,816.45 Accumulated Realizable Value $15,001.95 $29,732.00 $50,816.45 $29,732.00 Mileage Extra Extra Charge 16708.14 $4,009.95 Extra Charge per Month $167.08 NPV $52,233.95 $50,816.45 Purchase option has a fewer probability to result in a greater NPV Question 1 of 3 Be sure to explain your answer thoroughly and attach your Excel worksheet to support your findings. We acquired new office furniture for the office. The invoice for $6,000 offers two ways to pay: we can pay the entire amount by September 1, or we can pay $3060 by September 1 and $3,000 by January 1. How does our decision depend on the interest rate at which we can invest our funds? Question 2 of 3 The chief cashier of a bank must manage the cash holding so as to gain interest by investing excess cash where possible, but as the same time keep sufficient cash on hand to meet the bank's needs. A major issue for the chief is the uncertainty that results from the Federal Reserve Board's (the Fed's) clearing balance. The clearing balance is the difference between the dollar value of checks written by the bank's customers and cleared through the Fed, and the dollar value of checks received but written on the other banks and clear through the Fed. The chief cashier has recorded that last eight weeks of clearing balances (a longer period is available, but we will use just eight weeks here). The 40 observations of daily check clearing are shown below: $21,697,208 -$32,977,193 $60,311,999 $29,981,227 $28,030,404 -$8,448,464 $53,479,593 $38,561,233 -$10,243,791 $30,056,844 $117,896,711 -$1,672,896 $24,650,044 $61,116,423 -$4,794,679 $24,066,627 $37,844,391 $81,001,561 $57,425,429 $28,157,292 $10,019,384 $21,886,686 $27,584,465 $8,059,567 -$3,648,650 $73,625,609 $34,537,810 $5,757,982 $40,873,515 $59,296, 515 $29,387,165 -$31,816,724 $3,894,647 $5,027,402 $21,449,620 $31,467,912 $31,238,163 $23,307,164 $93,434,414 $65,555,653 1. Provide point and interval estimates of the mean daily clearing balance. 2. Provide point and interval predictions (or forecasts) of tomorrow's clearing balance. Be sure to explain your answer thoroughly and attach your Excel worksheet to support your findings. Question 3 of 3 A hotel has 500 rooms. During a typical week in the holiday season, the hotel is busy on Monday, Tuesday, Wednesday, and Thursday nights, primarily with business people, but there is generally space available on Friday, Saturday, and Sunday nights. -Hotel management provided the following demand estimates, as shown in Table 8.1: -Assume linear demand functions over the range of all non-negative room rates and demands. 1) What is the revenue-maximizing room rate if the hotel posts only a single rate good for any day of the week? What weekly occupancy results? 2) What are the revenue-maximizing room rates if the hotel posts a \"mid-week\" rate good for the peak demand period (MTWT), and a different \"weekend\" rate good for Friday, Saturday, or Sunday. What is the new weekly occupancy? What is the revenue increase? 3) Another option is for the hotel to offer a discounted weekly rate in order to attract vacationers who will stay for the full week. Management estimates that demand will be 40 per week at $900/week and 160 per week at $800/week. Again, assume a linear demand curve. 4) If the hotel posts a weekly rate and a single daily rate (good for any night), what are the revenuemaximizing prices? What is the occupancy rate? What is the revenue gain? 5) If the hotel posts three rates: a mid-week rate, a weekend rate, and a weekly rate, what are the revenue-maximizing prices? What is the occupancy rate? What is the revenue gain? Be sure to explain your answer thoroughly and attach your Excel worksheet Problem 1 Develop two simulation models of tossing two six-sided dice (Numbered 1 Through 6 on the six faces). Model 1: Simulate rolling a single dice twice and add the total. Model 2: Simulate a combined roll of two dice, giving a number from 2 through 12 with appropriate probabilities. Here, we have to develop two simulation models of tossing two six-sided dice. Let assume the dice is unbiased and probability of getting each number of its sides is equal. The probability of getting any number from 1 to 6 is given as 1/6. Let us see the two simulation models given as below: Model 1: Here, we have to simulate rolling a single dice twice and add the total. The simulation model is given as below: Number at first draw Number of second draw Total 6 2 8 2 2 4 6 1 7 4 5 9 6 6 12 2 1 3 1 1 2 3 6 9 3 2 5 1 5 6 4 3 7 1 5 6 5 6 11 5 2 7 2 5 7 3 5 8 4 1 5 2 4 6 3 5 8 3 2 5 5 5 10 4 6 10 4 6 10 1 3 4 2 1 3 1 2 3 3 5 8 6 6 12 6 4 10 6 1 7 2 1 3 5 3 8 2 6 8 2 6 8 4 6 10 3 1 4 2 4 6 5 6 11 6 1 7 6 3 9 5 1 6 3 6 9 4 2 6 5 1 6 3 1 4 1 4 5 6 5 11 4 1 5 1 4 5 Model 2 Here, we have to simulate the data in the same way as described in the above problem, only we have to use two dice at a time and simulate the data. The simulation model is given as below: First dice Second dice Total 3 1 4 6 2 8 6 5 11 5 6 11 4 3 7 1 3 4 1 5 6 6 5 11 6 3 9 4 2 6 1 6 7 2 1 3 3 3 6 5 5 10 4 5 9 6 4 10 4 5 9 1 3 4 6 2 8 2 3 5 3 1 4 2 5 7 1 2 3 5 5 10 6 6 12 5 6 11 1 3 4 1 3 4 6 1 7 2 2 4 2 3 5 3 2 5 2 6 8 5 4 9 6 3 9 4 1 5 1 5 6 4 4 8 1 6 7 1 4 5 Problem 2 An advertisement in the news paper offers a new car for sale or lease. The purchase price of the car is $43,240, or the car can be leased for 24 months for a monthly payment of $458, with a $7,500 down-payment. Under the lease option, there is a charge of 24 cents/mile for mileage above 30,000 miles for the 24 months, and a $550 security deposit, which is refundable at the end of the lease, must be deposited with the dealer. The car may be purchased at the end of the lease for $29,732. All other charges (taxes, maintenance, plates, etc.) are the same under both options. Develop a simulation model to compare the net present value of buying or leasing the car for 24 months. To compare the two options a number of assumptions must be made. Assume that: The mileage driven over 24 months can be approximated by an exponential distribution with mean 25,000 miles. The best estimate of the interest rate over the next 24 months is a normal distribution with mean 8.5% and standard deviation 1%. The value of the car at the end of 24 months is the same under both options (that is, if the car is purchased, the realizable value at the end of month 24 is $29,732 less 24 cents/mile for each mile over 30,000). Use your simulation model to asses the probability that the lease option results in a lower net present value that does the purchase option. Here, we have to develop the simulation model for the comparison of the net present value of buying or leasing the car for 24 months. Here, we are given that the mileage driven over 24 months is follows an exponential distribution with mean of 25,000 and the interest rate follows a normal distribution with mean 8.5% and standard deviation 1%. The simulation model is given as below: Month Mileage Interest rate 1 22572.00482 7.67448164 2 32147.53646 10.9301624 3 14302.70087 4.862918296 4 21090.46523 7.170758178 5 35524.63528 12.078376 6 36230.30911 12.3183051 7 28463.0791 9.677446896 8 29710.9287 10.10171576 9 22415.78188 7.621365839 10 23535.74534 8.002153416 11 37421.00929 12.72314316 12 18674.53701 6.349342582 13 30224.65781 10.27638366 14 32864.64211 11.17397832 15 15753.75127 5.35627543 16 15819.55135 5.378647458 17 31936.61036 10.85844752 18 31501.07301 10.71036482 19 13747.64512 4.674199342 20 32473.9606 11.04114661 21 15741.32865 5.352051741 22 28291.53281 9.619121154 23 28011.25999 9.523828398 24 30112.62347 10.23829198 Problem 1 Develop two simulation models of tossing two six-sided dice (Numbered 1 Through 6 on the six faces). Model 1: Simulate rolling a single dice twice and add the total. Model 2: Simulate a combined roll of two dice, giving a number from 2 through 12 with appropriate probabilities. Here, we have to develop two simulation models of tossing two six-sided dice. Let assume the dice is unbiased and probability of getting each number of its sides is equal. The probability of getting any number from 1 to 6 is given as 1/6. Let us see the two simulation models given as below: Model 1: Here, we have to simulate rolling a single dice twice and add the total. The simulation model is given as below: Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Roll 1 5 1 1 5 2 4 3 4 2 4 4 6 5 5 4 1 6 3 2 5 Roll 2 5 3 6 2 4 1 2 4 4 3 1 5 1 3 5 1 6 1 1 1 Sum 10 4 7 7 6 5 5 8 6 7 5 11 6 8 9 2 12 4 3 6 Model 2 Here, we have to simulate the data in the same way as described in the above problem, only we have to use two dice at a time and simulate the data. The simulation model is given as below: The space is follow: 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 Now, we compute the probability for each Total 2 3 4 5 6 7 8 9 10 11 12 Sum P 0.02 8 0.05 6 0.08 3 0.11 1 0.13 9 0.16 7 0.13 9 0.11 1 0.08 3 0.05 6 0.02 8 1 6 7 8 9 10 11 12 Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Dice 1 1 4 4 3 4 6 3 5 5 1 1 6 6 4 6 4 6 4 4 3 Dice 2 1 6 4 4 2 6 6 3 6 1 5 4 4 1 2 1 3 3 4 4 Sum 2 10 8 7 6 12 9 8 11 2 6 10 10 5 8 5 9 7 8 7 p 0.03 0.08 0.14 0.17 0.14 0.03 0.11 0.14 0.06 0.03 0.14 0.08 0.08 0.11 0.14 0.11 0.11 0.17 0.14 0.17 Problem 2 An advertisement in the news paper offers a new car for sale or lease. The purchase price of the car is $43,240, or the car can be leased for 24 months for a monthly payment of $458, with a $7,500 down-payment. Under the lease option, there is a charge of 24 cents/mile for mileage above 30,000 miles for the 24 months, and a $550 security deposit, which is refundable at the end of the lease, must be deposited with the dealer. The car may be purchased at the end of the lease for $29,732. All other charges (taxes, maintenance, plates, etc.) are the same under both options. Develop a simulation model to compare the net present value of buying or leasing the car for 24 months. To compare the two options a number of assumptions must be made. Assume that: The mileage driven over 24 months can be approximated by an exponential distribution with mean 25,000 miles. The best estimate of the interest rate over the next 24 months is a normal distribution with mean 8.5% and standard deviation 1%. The value of the car at the end of 24 months is the same under both options (that is, if the car is purchased, the realizable value at the end of month 24 is $29,732 less 24 cents/mile for each mile over 30,000). Use your simulation model to asses the probability that the lease option results in a lower net present value that does the purchase option. Here, we have to develop the simulation model for the comparison of the net present value of buying or leasing the car for 24 months. Here, we are given that the mileage driven over 24 months is follows an exponential distribution with mean of 25,000 and the interest rate follows a normal distribution with mean 8.5% and standard deviation 1%. The data collected is follow: Price Monthly Payment Duration Downpayment Amount borrowed Charge Security Deposit Interest Rate $43,240.00 $458.00 24 months $7,500.00 $35,740.00 0.24 $/mile $550.00 8.90% Now we compute the variables to start the simulation Exponential Distribution Mean 25000 1.4132 Mileage Driven 35331.20 Mileage Extra Extra Charge 5331.20 $1,279.4 9 The simulation model is given as below: Cashflow Month Leasing 0 1 2 3 4 5 6 7 8 9 10 11 12 $1,061.31 $1,572.62 $2,083.94 $2,595.25 $3,106.56 $3,617.87 $4,129.18 $4,640.50 $5,151.81 $5,663.12 $6,174.43 $6,685.74 Buy $43,240.00 $43,531.87 $43,825.70 $44,121.53 $44,419.34 $44,719.17 $45,021.02 $45,324.91 $45,630.85 $45,938.86 $46,248.94 $46,561.12 $46,875.40 Extra Charge per Month $53.31 13 14 15 16 17 18 19 20 21 22 23 24 $7,197.06 $7,708.37 $8,219.68 $8,730.99 $9,242.30 $9,753.62 $10,264.93 $10,776.24 $11,287.55 $11,798.86 $12,310.18 $12,271.49 $47,191.81 $47,510.35 $47,831.04 $48,153.90 $48,478.94 $48,806.16 $49,135.60 $49,467.27 $49,801.17 $50,137.32 $50,475.74 $50,816.45 Accumulated Realizable Value $12,271.49 $29,732.00 $50,816.45 $29,732.00 NPV $49,503.49 $50,816.45 Lease option has a fewer probability to result in a greater NPV. In this case, is advisable leasing and then buy after the 24 months under the conditions agreed above. Problem 1 Develop two simulation models of tossing two six-sided dice (Numbered 1 Through 6 on the six faces). Model 1: Simulate rolling a single dice twice and add the total. Model 2: Simulate a combined roll of two dice, giving a number from 2 through 12 with appropriate probabilities. Here, we have to develop two simulation models of tossing two six-sided dice. Let assume the dice is unbiased and probability of getting each number of its sides is equal. The probability of getting any number from 1 to 6 is given as 1/6. Let us see the two simulation models given as below: Model 1: Here, we have to simulate rolling a single dice twice and add the total. The simulation model is given as below: Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Roll 1 5 1 1 5 2 4 3 4 2 4 4 6 5 5 4 1 6 3 2 5 Roll 2 5 3 6 2 4 1 2 4 4 3 1 5 1 3 5 1 6 1 1 1 Sum 10 4 7 7 6 5 5 8 6 7 5 11 6 8 9 2 12 4 3 6 Model 2 Here, we have to simulate the data in the same way as described in the above problem, only we have to use two dice at a time and simulate the data. The simulation model is given as below: The space is follow: 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 Now, we compute the probability for each Total 2 3 4 5 6 7 8 9 10 11 12 Sum P 0.02 8 0.05 6 0.08 3 0.11 1 0.13 9 0.16 7 0.13 9 0.11 1 0.08 3 0.05 6 0.02 8 1 6 7 8 9 10 11 12 Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Dice 1 1 4 4 3 4 6 3 5 5 1 1 6 6 4 6 4 6 4 4 3 Dice 2 1 6 4 4 2 6 6 3 6 1 5 4 4 1 2 1 3 3 4 4 Sum 2 10 8 7 6 12 9 8 11 2 6 10 10 5 8 5 9 7 8 7 p 0.03 0.08 0.14 0.17 0.14 0.03 0.11 0.14 0.06 0.03 0.14 0.08 0.08 0.11 0.14 0.11 0.11 0.17 0.14 0.17 Problem 2 An advertisement in the news paper offers a new car for sale or lease. The purchase price of the car is $43,240, or the car can be leased for 24 months for a monthly payment of $458, with a $7,500 down-payment. Under the lease option, there is a charge of 24 cents/mile for mileage above 30,000 miles for the 24 months, and a $550 security deposit, which is refundable at the end of the lease, must be deposited with the dealer. The car may be purchased at the end of the lease for $29,732. All other charges (taxes, maintenance, plates, etc.) are the same under both options. Develop a simulation model to compare the net present value of buying or leasing the car for 24 months. To compare the two options a number of assumptions must be made. Assume that: The mileage driven over 24 months can be approximated by an exponential distribution with mean 25,000 miles. The best estimate of the interest rate over the next 24 months is a normal distribution with mean 8.5% and standard deviation 1%. The value of the car at the end of 24 months is the same under both options (that is, if the car is purchased, the realizable value at the end of month 24 is $29,732 less 24 cents/mile for each mile over 30,000). Use your simulation model to asses the probability that the lease option results in a lower net present value that does the purchase option. Here, we have to develop the simulation model for the comparison of the net present value of buying or leasing the car for 24 months. Here, we are given that the mileage driven over 24 months is follows an exponential distribution with mean of 25,000 and the interest rate follows a normal distribution with mean 8.5% and standard deviation 1%. The data collected is follow: Price Monthly Payment Duration Downpayment Amount borrowed Charge Security Deposit Interest Rate $43,240.00 $458.00 24 months $7,500.00 $35,740.00 0.24 $/mile $550.00 8.90% Now we compute the variables to start the simulation Exponential Distribution Mean 25000 1.4132 Mileage Driven 35331.20 Mileage Extra Extra Charge 5331.20 $1,279.4 9 The simulation model is given as below: Cashflow Month Leasing 0 1 2 3 4 5 6 7 8 9 10 11 12 $1,061.31 $1,572.62 $2,083.94 $2,595.25 $3,106.56 $3,617.87 $4,129.18 $4,640.50 $5,151.81 $5,663.12 $6,174.43 $6,685.74 Buy $43,240.00 $43,531.87 $43,825.70 $44,121.53 $44,419.34 $44,719.17 $45,021.02 $45,324.91 $45,630.85 $45,938.86 $46,248.94 $46,561.12 $46,875.40 Extra Charge per Month $53.31 13 14 15 16 17 18 19 20 21 22 23 24 $7,197.06 $7,708.37 $8,219.68 $8,730.99 $9,242.30 $9,753.62 $10,264.93 $10,776.24 $11,287.55 $11,798.86 $12,310.18 $12,271.49 $47,191.81 $47,510.35 $47,831.04 $48,153.90 $48,478.94 $48,806.16 $49,135.60 $49,467.27 $49,801.17 $50,137.32 $50,475.74 $50,816.45 Accumulated Realizable Value $12,271.49 $29,732.00 $50,816.45 $29,732.00 NPV $49,503.49 $50,816.45 Lease option has a fewer probability to result in a greater NPV. In this case, is advisable leasing and then buy after the 24 months under the conditions agreed above. Model 1 Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Roll 1 5 6 1 1 4 5 2 2 2 3 1 2 6 3 2 5 6 3 3 1 Roll 2 2 1 6 1 1 6 3 1 3 5 1 5 1 5 5 2 4 1 3 1 Model 2 Sum 7 7 7 2 5 11 5 3 5 8 2 7 7 8 7 7 10 4 6 2 Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Dice 1 5 6 3 6 6 1 1 6 1 2 4 6 1 3 5 4 6 6 2 1 Dice 2 1 1 5 5 6 6 6 5 5 1 3 6 2 5 3 5 4 2 6 2 Sum 6 7 8 11 12 7 7 11 6 3 7 12 3 8 8 9 10 8 8 3 2 p 0.14 0.17 0.14 0.06 0.03 0.17 0.17 0.06 0.14 0.06 0.17 0.03 0.06 0.14 0.14 0.11 0.08 0.14 0.14 0.06 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 Total 2 3 4 5 6 7 8 9 10 11 12 P 0.0278 0.0556 0.0833 0.1111 0.1389 0.1667 0.1389 0.1111 0.0833 0.0556 0.0278 1 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 Price Monthly Payment Duration Downpayment Amount borrowed Charge Security Deposit Interest Rate $43,240.00 $458.00 24 months $7,500.00 $35,740.00 0.24 $/mile $550.00 8.10% Exponential Distribution Mean 25000 Mileage Driven 1.8683 F9 to simulate! Cashflow Leasing Month 46708.14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 $1,175.08 $1,800.16 $2,425.24 $3,050.33 $3,675.41 $4,300.49 $4,925.57 $5,550.65 $6,175.73 $6,800.81 $7,425.90 $8,050.98 $8,676.06 $9,301.14 $9,926.22 $10,551.30 $11,176.38 $11,801.46 $12,426.55 $13,051.63 $13,676.71 $14,301.79 $14,926.87 $15,001.95 Sell $43,240.00 $43,531.87 $43,825.70 $44,121.53 $44,419.34 $44,719.17 $45,021.02 $45,324.91 $45,630.85 $45,938.86 $46,248.94 $46,561.12 $46,875.40 $47,191.81 $47,510.35 $47,831.04 $48,153.90 $48,478.94 $48,806.16 $49,135.60 $49,467.27 $49,801.17 $50,137.32 $50,475.74 $50,816.45 Accumulated Realizable Value $15,001.95 $29,732.00 $50,816.45 $29,732.00 Mileage Extra Extra Charge 16708.14 $4,009.95 Extra Charge per Month $167.08 NPV $52,233.95 $50,816.45 Purchase option has a fewer probability to result in a greater NPV Question 1 of 3 Be sure to explain your answer thoroughly and attach your Excel worksheet to support your findings. We acquired new office furniture for the office. The invoice for $6,000 offers two ways to pay: we can pay the entire amount by September 1, or we can pay $3060 by September 1 and $3,000 by January 1. How does our decision depend on the interest rate at which we can invest our funds? Question 2 of 3 The chief cashier of a bank must manage the cash holding so as to gain interest by investing excess cash where possible, but as the same time keep sufficient cash on hand to meet the bank's needs. A major issue for the chief is the uncertainty that results from the Federal Reserve Board's (the Fed's) clearing balance. The clearing balance is the difference between the dollar value of checks written by the bank's customers and cleared through the Fed, and the dollar value of checks received but written on the other banks and clear through the Fed. The chief cashier has recorded that last eight weeks of clearing balances (a longer period is available, but we will use just eight weeks here). The 40 observations of daily check clearing are shown below: $21,697,208 -$32,977,193 $60,311,999 $29,981,227 $28,030,404 -$8,448,464 $53,479,593 $38,561,233 -$10,243,791 $30,056,844 $117,896,711 -$1,672,896 $24,650,044 $61,116,423 -$4,794,679 $24,066,627 $37,844,391 $81,001,561 $57,425,429 $28,157,292 $10,019,384 $21,886,686 $27,584,465 $8,059,567 -$3,648,650 $73,625,609 $34,537,810 $5,757,982 $40,873,515 $59,296, 515 $29,387,165 -$31,816,724 $3,894,647 $5,027,402 $21,449,620 $31,467,912 $31,238,163 $23,307,164 $93,434,414 $65,555,653 1. Provide point and interval estimates of the mean daily clearing balance. 2. Provide point and interval predictions (or forecasts) of tomorrow's clearing balance. Be sure to explain your answer thoroughly and attach your Excel worksheet to support your findings. Question 3 of 3 A hotel has 500 rooms. During a typical week in the holiday season, the hotel is busy on Monday, Tuesday, Wednesday, and Thursday nights, primarily with business people, but there is generally space available on Friday, Saturday, and Sunday nights. -Hotel management provided the following demand estimates, as shown in Table 8.1: -Assume linear demand functions over the range of all non-negative room rates and demands. 1) What is the revenue-maximizing room rate if the hotel posts only a single rate good for any day of the week? What weekly occupancy results? 2) What are the revenue-maximizing room rates if the hotel posts a \"mid-week\" rate good for the peak demand period (MTWT), and a different \"weekend\" rate good for Friday, Saturday, or Sunday. What is the new weekly occupancy? What is the revenue increase? 3) Another option is for the hotel to offer a discounted weekly rate in order to attract vacationers who will stay for the full week. Management estimates that demand will be 40 per week at $900/week and 160 per week at $800/week. Again, assume a linear demand curve. 4) If the hotel posts a weekly rate and a single daily rate (good for any night), what are the revenuemaximizing prices? What is the occupancy rate? What is the revenue gain? 5) If the hotel posts three rates: a mid-week rate, a weekend rate, and a weekly rate, what are the revenue-maximizing prices? What is the occupancy rate? What is the revenue gain? Be sure to explain your answer thoroughly and attach your Excel worksheet