Qrb_Uofp_Week_#6_Solutions

Sevilla & Somers text; Topic 18, exploration 3 The following table contains information on the 2002 resident population of the U.S., by age. (Source: The New York Times Almanac 2004, page 277.) a.) If a resident of the U.S. is chosen at random, find the probability that he or she is 25 to 44 years old. P(25 - 44) = 1270419/4486508 = 0.2832 b.) If a resident is chosen at random, find the probability that he or she is older than 24 years old. P(> 24) = (1270419 + 1068243 + 588542)/4486508 = 0.6524 c.) In what age category does the median age fall' The median age falls in the 25 - 44 category. Emery, Finnerty & Stowe - Ch. 6, problems A6, B6, & B10 (a only)- A6. (Expected portfolio return) Musumeci Capital Management has invested its portfolio as shown here. What is Musumeci’s expected portfolio return' Solution: Given that portfolio weight in Money Market securities = 10% = 0.1 and expected return = 4% Portfolio weight in corporate bond = 20% = 0.2 and expected return = 8% Portfolio weight in Equities = 70% = 0.7 and expected return = 12 % Expected return = Where p is probability and x investment Then expected return = 0.1*4 + 0.2*8 + 0.7*12 = 0.4 + 1.6 + 8.4 = 10.4 % B6. (Expected return and risk) Procter & Gamble is considering three possible capital investment projects. The projected returns depend on the future state of the economy as given here. a. Calculate each project’s expected return, variance, and standard deviation. b.Rank the projects on the basis of (1) expected return and (2) risk. Which project would you choose' Since Expected return = Where p is probability and x investment Variance = And Standard deviation = (a) Using MS-Excel state of economy probability of occurrence project return 1 2 3 % recession 0.1 9 3 15 stable 0.7 13 10 11 Boom 0.2 17 22 5 expected return 13.4 11.7 10.2 variance 4.64 30.61 8.46 standard deviation 2.15406592 5.532630477 2.908608 (b)Rank: According to expected return “project return 1” is better than others According to risk “project return 1” is again better option B10. (Excel: Calculating means, standard deviations, covariance, and correlation) Given the probability distributions of returns for stock X and stock Y, compute: Since Expected return = Where p is probability and x investment a.the expected return for each stock, x and y here probabilty stock X stock y 1 2 0.2 5 12 0.2 10 10 0.4 12 8 0.15 14 0 0.05 18 2 expected return 11.7 7.7 Cooper text: Ch. 7, question 5 Lind, Marchal, & Wathen text: Ch. 8, exercise 31 The Sony Corporation produces a Walkman that requires two AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely follows the normal probability distribution with a standard deviation of 5.5 hours. As a part of their testing program Sony tests samples of 25 batteries. a. What can you say about the shape of the distribution of sample mean' The shape of the distribution is bell-shaped, because it states that "The distribution of the battery lives closely follows the normal probability distribution" which is bell-shaped curve. b. What is the standard error of the distribution of the sample mean' Following are the formulas to calculate some of the confidence limits of the sample means: 90%: mean +- 1.64 * Standard Error 95%: mean +- 1.96 * Standard Error 99%: mean +- 2.58 * Standard Error In this case the population mean is 35.0 hours and the upper and lower limits of the sample means for different confidence limits are: 90% 36.80, 33.20 95% 37.16, 32.84 99% 37.84, 32.16 c. What proportion of the samples will have a mean useful life of more than 36 hours' Here z = (36-35)/5.5 = 0.1818 P(x > 36) = P(z > 0.1818) = 0.0714 (see z-table for value 0.1818) Therefore, 7.1% of the samples will have a mean useful life of more than 36 hours d. What proportion of the sample will have a mean useful life greater than 34.5 hours' Here z = (34.5-35)/5.5 = -0.09091 P(x > 34.5) = P(z > -0.09091) = 0.0359+0.5 = 0.5359 (see z-table for value) Therefore, 53.59% of the samples will have a mean useful life of more than 34.5 hours e. What proportion of the sample will have a mean useful life between 34.5 and 36.0 hours' P(34.5 < x < 36) = P(-0.09091 < z < 0.1818) = 0.5359+(0.0714+0.5) = 96.45 Sevilla & Somers text: Topic 8, exploration 12 The Purchasing Management Index (PMI) is the primary component of the Economic Conditions website. Indices are reported for the overall economy, new orders, production, inventories, employment, delivery lead time, prices and confidence. The overall PMI is a composite index based on new orders, production, delivery lead time, inventories, and employment. An index above 50.0% indicates expansion while an index below 50.0% indicates contraction. The indices are calculated from surveys of purchasing managers in Missouri. The PMI measures five factors in business: new orders, inventory levels, production, supplier delivers, and employment conditions. Each of these five factors are adjusted and weighed according to time of year and other events. A PMI over 50% means that manufacturing is growing and expanding. A PMI under 50% means that manufacturing is declining. a PMI of 42.7% or more over a long period of time means the economy as a whole is expanding. A PMI of 42.7% of below over a long period of time means the economy as a whole is contracting. Calculation PMI is calculated by surveying purchasing managers for data about new orders, production, employment, deliveries, and inventory, in descending order of importance. It is based on a survey of over 250 companies within twenty-one industries covering all 50 states, and it is released on the first business day of the month at 10 am EST and reflects the previous month's data. A reading over 50% indicates that manufacturing is growing, while a reading below 50% means it is shrinking. The PMI has been used by economists and government officials to forecast the future state of the economy. It provides an early indication of where the economy is headed in the next three to six months. Missouri's Purchasing Managers' Index (PMI) declined in April. The state's PMI score fell to 58.5 from 60.6 in March according to the monthly Mid-American Business Conditions Survey, conducted by Creighton University, Omaha, NE. This is the lowest level for the Missouri index since September 2003 and the first time the state's index has been below 60 since January 2004. Despite April's decline, Missouri's score has remained above the critical 50 mark for 39 consecutive months, indicating continued expansion in the state, but at a slower rate. Economists consider the index, which measures such factors as new orders, production, supplier delivery times, backlogs, inventories, prices, employment, import orders and exports, a key economic indicator. Typically, a score greater than 50 indicates an expansionary economy, while a score below 50 forecasts a sluggish economy for the next three to six months. The national PMI for manufacturing industries was down in April, decreasing to 53.3 from 55.2 in March. A drop in the new orders portion of the index contributed to the decline. The nation's PMI for non-manufacturing industries also decreased in April, down 1.4 points to 61.7. However, the score indicates sustained expansion in the services sector and is expected to remain above 60 in the coming months. Lind, Marchal, & Wathen text: Ch. 18, exercises 27, 28, 33, 34 & 56 27. Compute a simple price index for each of the four items. Use 2000 as the base period. Simple price index = Price of new year/Price of base year x 100 Margarine (pound) = $0.89/$0.81 x 100 109.88 Shortening (pound) = $0.94/$0.84 x 100 111.90 Milk (1/2 gallon) = $1.43/$1.44 x 100 99.31 Potato chips = $3.07/$2.91 x 100 105.5 28. Compute a simple aggregate price index. Use 2000 as the base period. Simple aggregate price index = Sum of price of new year/Sum of price of base year x 100 = $6.33/$6.00 x 100 =105.50 33. Compute a simple price index for each of the three items. Use 2000 as the base period. RC-33 = $0.60/$0.50 x 100 120.00 SM-14 = $0.90/$1.2 x 100 75.00 WC50 = $1.00/$0.85 x 100 117.65 34. Compute a simple aggregate price index for 2004. Use 2000 as the base period. Simple aggregate price index = $2.50/$2.55 x 100 = 98.04 56. From 1988 to 2002, the cost of 30-second TV spot has been increasing at a rate lower than the increases in the Customer Price Index - All Urban Consumers. For example, the cost of 30-second TV spot in 1988 increased by 20 per cent relative to the 1967 level compared to the 72 per cent increase in the CPI. Interestingly, the cost of a 30-second TV spot in 2002 decreased relative to the 2001 level and it still increased from its 1967 level, 352%, at a rate lower than the increase in CPI. On the other hand, the cost of a ticket to the Super Bowl exhibited exponential increase relative to the its level in 1967 and relative to the increases in the CPI and the cost of a 30-second TV spot, also relative to 1967. For example, the cost of a ticket in 2002 is 4,000 per cent its level in 1967 while the CPI increased by only 439% while the cost of a 30-second TV spot increased by only 352%. The differences in the rate of increases in the cost of a 30-second TV spot, ticket to the Super Bowl and the CPI can be attributed to the demand on each of these three items. From 1967 to 2002, the popularity of the Super Bowl soared which resulted to phenomenal increase in the demand for tickets, and hence resulted to exponential price increase. References: http://www.investorwords.com/5674/National_Association_of_Purchasing_Managers_index.html