The thermodynamic sound speed \( c \) is defined in Sec. 7.1. Prove that: \[ c=\sqrt{\frac{V C_{P}}{A C_{V K}}} \] where \( V \) is molar volume and \( \mathscr{\text { is molar mass. To what does this general result }} \) reduce for: \( (a) \) an ideal gas? \( (b) \) an incompressible liquid? What do these results suggest qualitatively about the speed of sound in liquids relative to gases? The thermodynamic sound speed $c$ is defined in Sec. 7.1. Prove that: \[ c=\sqrt{\frac{V C_{P}}{M C_{V K}}} \] where $V$ is molar volume and $\mathscr{A}$ is molar mass. To what does this general result reduce for: $(a)$ an ideal gas? (b) an incompressible liquid? What do these results suggest qualitatively about the speed of sound in liquids relative to gases?

Rodney (a fictional person) was self-employed, running a successful business, seemingly healthy, and never thought he would have financial problems. Being self-employed, he lacked health insurance. One day on the job, Rodney suffered a heart attack and was hospitalized for a week. As a result, he owed more than $100,000 in hospital and medical bills to the hospital. After the heart attack, Rodney could not work in his physically demanding line of work, and his business suffered dramatically. The bills and mortgage payments kept piling up, and Rodney was sinking fast. On top of the medical bills and mortgage, he owed thousands of dollars to multiple companies and creditors. Rodney considered selling his house to get out of the financial crisis he was in, but the value of the house had dropped significantly. After much consideration, Rodney decided to file for Chapter 7, bankruptcy. In the end, he decided he would rather have a bankruptcy on his record instead of dealing with a mountain of debt. For each question, provide the correct answer and a complete explanation of why it is the correct answer. 1. In Chapter 7 bankruptcy, ___________occurs when a debtor turns over all assets to a trustee, an individual who takes over administration of the debtor's estate. a. An order of relief b. An automatic stay c. Relief d. Liquidation e. Bankruptcy 2. Who is defined as a debtor for liquidation purposes under Chapter 7? Can Rodney file for Chapter 7 bankruptcy? a. Banks; Rodney cannot file. b. Individuals; Rodney can file. c. Health Maintenance Organizations; Rodney cannot file. d. Partnerships: Rodney cannot file e. Corporations; Rodney cannot file 3. Suppose that Rodney did not intend to file for voluntary liquidation. Could he be forced into bankruptcy under Chapter 7? a. No, he must file the Chapter 7 bankruptcy himself. b. Yes, because he has more than 12 creditors. c. Yes, because he has a single creditor with a claim of more than $14,425 in debt. d. No, because people who are self-employed cannot be forced into filing for Chapter 7. 4. Rodney has a lot of creditors that are trying to sue him for the debt he owes. One benefit of filing for Chapter 7 is that once a petition is filed, the code provides for a(n) _______________for almost all creditor litigation against the debtor. a. Liquidation b. Order of relief c. Creditor’s meeting d. Preferential payment    e. Automatic stay 5. If the filing of Rodney's voluntary petition is proper, the petition automatically becomes a(n) a. Fraudulent transfer b. Creditor’s meeting c. Preferential payment d. Discharged debt    e. Order of relief. 6. Suppose Rodney fails to show up at his creditors' meeting with his creditors because he is scared to meet with the hospital representatives. What is a possible consequence of his failure to show? a. His creditors will be allowed to sue him for failure to show.   b. The court may refuse to grant the bankruptcy c. Rodney will be charged with a criminal offense. d. There is no penalty for missing a creditor’s meeting. e. His appointed trustee will be penalized, but Rodney will not.

Timpco, a retailer, makes both cash and credit sales (i.e., sales on open account). Information regarding budgeted sales for the last quarter of the year is as follows: \begin{tabular}{lcrr} & October & November & December \\ Cash sales & $\$ 95,000$ & $\$ 83,000$ & $\$ 89,000$ \\ Credit sales & 95,000 & 99,600 & 97,900 \\ \cline { 2 - 4 } Total & $\$ 190,000$ & $\$ 182,600$ & $\$ 186,900$ \\ & & & \\ \hline \end{tabular} Past experience shows that $5 \%$ of credit sales are uncollectible. Of the credit sales that are collectible, $60 \%$ are collected in the month of sale; the remaining $40 \%$ are collected in the month following the month of sale. Customers are granted a $1.5 \%$ discount for payment within 10 days of billing. Approximately $75 \%$ of collectible credit sales take advantage of the cash discount. Inventory purchases each month are $100 \%$ of the cost of the following month's projected sales. (The gross profit rate for Timpco is approximately 30\%.) All merchandise purchases are made on credit, with $20 \%$ paid in the month of purchase and the remainder paid in the following month. No cash discounts for early payment are in effect. Required: 1. Calculate the budgeted total cash receipts for November and December. (Round your intermediate calculations and final answers to the nearest whole dollar amount) \begin{tabular}{|l|l|l|} \hline & November & December \\ \hline Total cash receipts & & \\ \hline \end{tabular} 2. Calculate budgeted cash payments for November and December (budgeted total sales for January of the coming year $=\$ 181,000)$. (Do not round intermediate calculations. Round your final answers to nearest whole dollar amount.) \begin{tabular}{|l|l|l|} \hline & November & December \\ \hline Budgeted cash payments & & \\ \hline \end{tabular}

EXERCISE $295.1$ Find the core and the Shapley value of the game $\langle\{1,2,3,4\}, v\rangle$ in which $v(\{1,2,3,4\})=3, v(S)=0$ if S includes at most one of the players in $\{1,2,3\}$ , and $v(S)=2$ otherwise. Explain the source of the difference between the two solutions. EXERCISE 295.1 Find the core and the Shapley value of the game $\langle\{1,2,3,4\}, v\rangle$ in which $v(\{1,2,3,4\})=3, v(S)=0$ if $S$ includes at most one of the players in $\{1,2,3\}$, and $v(S)=2$ otherwise. Explain the source of the difference between the two solutions.

Before the mid-1970s, systems programmers and businesspeople (including accountants) did not communicate well with one another. The programmers were criticized for using too much jargon, and the businesspeople were criticized for not adequately expressing their needs. Efforts have been made to overcome this communication gap, but room for improvement still exists. What problems do you think may result from this communication gap? What can you do to help further close the gap when you enter the workforce?

Fredo loves watching Downton Abbey on his local public TV station, but he never sends any money to support the station during its fund-raising drives. a. What name do economists have for people like Fredo? b. How can the government solve the problem caused by people like Fredo? c. Can you think of ways the private market can solve this problem? How does the option of cable TV alter the situation? Fredo loves watching Downton Abbey on his local public TV station, but he never sends any money to support the station during its fund-raising drives. a. What name do economists have for people like Fredo? b. How can the government solve the problem caused by people like Fredo? c. Can you think of ways the private market can solve this problem? How does the option of cable TV alter the situation?

Forecasting is critical in modern times. Business organizations manifested more concern with anticipating the future, and as a consequence, a number of highly successful consulting firms emerged to provide forecasting help for governments and businesses. You are required: iii. Identify the different levels that forecasting of business trends takes place. iv. Give 3 examples where long-range forecasting can be used v. Do you think forecasting is always correct and accurate? Discuss this assertion in detail

Suppose that the production of crayons (q) is conducted at two locations and uses only labor as an input. The production function in location 1 is given by q_{1}=10 $l_{1}$^{0.5} and in location 2 by $q_{2}=50 $l_{2}$^{0.5}$ a. If a single firm produces crayons in both locations, then it will obviously want to get as large an output as possible given the labor input it uses. How should it allocate labor between the locations to do so? Explain precisely the relationship between $l_{1}$ and $l_{2}$ . b. Assuming that the firm operates in the efficient manner described in part (a), how does total output (q) depend on the total amount of labor hired (l) ? Suppose that the production of crayons $(q)$ is conducted at two locations and uses only labor as an input. The production function in location 1 is given by $q_{1}=10 l_{1}^{0.5}$ and in location 2 by $q_{2}=50 d_{2}^{0 .}$. a. If a single firm produces crayons in both locations, then it will obviously want to get as large an output as possible given the labor input it uses. How should it allocate labor between the locations to do so? Explain precisely the relationship between $l_{1}$ and $l_{2}$. b. Assuming that the firm operates in the efficient manner described in part (a), how does total output $(q)$ depend on the total amount of labor hired $(l)$ ?

Air France-KLM (AF), a Franco-Dutch company, prepares its financial statements according to International Financial Reporting Standards. AF&qpos;s financial statements and disclosure notes for the year ended December 31 , 2017 , are available in Connect. This material is also available under the Finance link at the company&qpos;s website (www.airfranceklm-finance.com). Required: 1. AF provides share-based compensation in the form of PPSs, Phantom Performance Shares. Recipients receive compensation in what form? Are such plans reported in the balance sheet as (a) assets, (b) liabilities, or (c) equity? [Hint: See Note 29: "Share-Based Compensation."] 2. Are AF&qpos;s PPSs cliff vesting or graded vesting?>3. The PPS options are performance-based, which means that under either U.S. GAAP or IFRS the amount expensed depends on whether it&qpos;s "probable" that the performance target will be met. Does this mean it&qpos;s equally likely that performance-based PPSs will be expensed at the same amount under U.S. GAAP as under IFRS? 4. What amount(s) of earnings per share did AF report in its income statement for the year ended December 31, 2017? If AF used U.S. GAAP, would it have reported EPS using the same classification? Air France-KLM (AF), a Franco-Dutch company, prepares its financial statements according to International Financial Reporting Standards. AF's financial statements and disclosure notes for the year ended December 31, 2017, are available in Connect. This material is also available under the Finance link at the company's website (www.airfranceklm-finance.com). Required: 1. AF provides share-based compensation in the form of PPSs, Phantom Performance Shares. Recipients receive compensation in what form? Are such plans reported in the balance sheet as (a) assets, (b) liabilities, or (c) equity? [Hint: See Note 29: "Share-Based Compensation."] 2. Are AF's PPSs cliff vesting or graded vesting? 3. The PPS options are performance-based, which means that under either U.S. GAAP or IFRS the amount expensed depends on whether it's "probable" that the performance target will be met. Does this mean it's equally likely that performance-based PPSs will be expensed at the same amount under U.S. GAAP as under IFRS? 4. What amount(s) of earnings per share did AF report in its income statement for the year ended December 31, 2017? If AF used U.S. GAAP, would it have reported EPS using the same classification?

A Toronto Porsche automobile dealership sells twenty Porsche Cayennes, twelve (12) Boxsters, forty (40) 911s and five (5) Cayman cars per year. Porsche is considering opening another dealership in downtown Toronto The existing Porsche dealer is expecting to sell 15% fewer Cayenne cars, eight (8) fewer 911 cars, three (3) fewer Boxster cars and 20% fewer Cayman cars per year. The overall lose in sales volume that the Porsche dealership will experience is: 16.52% decrease 17.74% decrease 18.52% decrease 19.48% decrease

Imagine you are a manager of an e-commerce company. Your company’s customer service department has just received some similar negative feedback from several customers who complain about your company's supply chain management process. Those customers request your company to respond to their feedback within a day. How do you analyze this problem and What steps do you need to implement to solve the mentioned problem? (3 points)

Table 9.9 gives data on quadrennial presidential elections in the United States from 1916 to $2004 .^{*}$ a. Using the data given in Table 9.9, develop a suitable model to predict the Democratic share of the two-party presidential vote. b. How would you use this model to predict the outcome of a presidential election?> I Indicator variable ( 1 if there is a Democratic incumbert at the time of the election and -1 if there is a Republican incumbent). N Number of quar lers in the first 15 quarters of the administration in which the growth rate of real per capita GDP is greater than $3.2 \%$ . A Absolute yalue of the growth rate of the GDP deflator in the first 15 ouarlers of the administation.>c. Chatterjee et al. suggested considering the following model as a trial model to predict presidential elections: \[ $V=\beta_{0}+\beta_{1} I+\beta_{2} D+\beta_{3} W+\beta_{4}(G I)+\beta_{5} P+\beta_{6} N+u$ \] Estimate this model and comment on the results in relation to the results of the model you have chosen. Table 9.9 gives data on quadrennial presidential elections in the United States from 1916 to 2004 . a. Using the data given in Table 9.9, develop a suitable model to predict the Democratic share of the two-party presidential vote. b. How would you use this model to predict the outcome of a presidential election? TABLE 9.9 U.S. Presidential Elections, 1916-2004 \begin{tabular}{clllrcrrr} \hline Obs. & Year & \multicolumn{1}{c}{$\boldsymbol{V}$} & $\boldsymbol{W}$ & $\boldsymbol{D}$ & $\boldsymbol{G}$ & $\boldsymbol{I}$ & $\boldsymbol{N}$ & $\boldsymbol{P}$ \\ 1 & 1916 & 0.5168 & 0 & 1 & 2.229 & 1 & 3 & 4.252 \\ 2 & 1920 & 0.3612 & 1 & 0 & -11.46 & 1 & 5 & 16.535 \\ 3 & 1924 & 0.4176 & 0 & -1 & -3.872 & -1 & 10 & 5.161 \\ 4 & 1928 & 0.4118 & 0 & 0 & 4.623 & -1 & 7 & 0.183 \\ 5 & 1932 & 0.5916 & 0 & -1 & -14.9 & -1 & 4 & 7.069 \\ 6 & 1936 & 0.6246 & 0 & 1 & 11.921 & 1 & 9 & 2.362 \\ 7 & 1940 & 0.55 & 0 & 1 & 3.708 & 1 & 8 & 0.028 \\ 8 & 1944 & 0.5377 & 1 & 1 & 4.119 & 1 & 14 & 5.678 \\ 9 & 1948 & 0.5237 & 1 & 1 & 1.849 & 1 & 5 & 8.722 \\ 10 & 1952 & 0.446 & 0 & 0 & 0.627 & 1 & 6 & 2.288 \\ 11 & 1956 & 0.4224 & 0 & -1 & -1.527 & -1 & 5 & 1.936 \\ 12 & 1960 & 0.5009 & 0 & 0 & 0.114 & -1 & 5 & 1.932 \\ 13 & 1964 & 0.6134 & 0 & 1 & 5.054 & 1 & 10 & 1.247 \\ 14 & 1968 & 0.496 & 0 & 0 & 4.836 & 1 & 7 & 3.215 \\ 15 & 1972 & 0.3821 & 0 & -1 & 6.278 & -1 & 4 & 4.766 \\ 16 & 1976 & 0.5105 & 0 & 0 & 3.663 & -1 & 4 & 7.657 \\ 17 & 1980 & 0.447 & 0 & 1 & -3.789 & 1 & 5 & 8.093 \\ 18 & 1984 & 0.4083 & 0 & -1 & 5.387 & -1 & 7 & 5.403 \\ 19 & 1988 & 0.461 & 0 & 0 & 2.068 & -1 & 6 & 3.272 \\ 20 & 1992 & 0.5345 & 0 & -1 & 2.293 & -1 & 1 & 3.692 \\ 21 & 1996 & 0.5474 & 0 & 1 & 2.918 & 1 & 3 & 2.268 \\ 22 & 2000 & 0.50265 & 0 & 0 & 1.219 & 1 & 8 & 1.605 \\ 23 & 2004 & 0.51233 & 0 & 1 & 2.69 & -1 & 1 & 2.325 \\ \hline \end{tabular} Notes: Year Election year $V$ Incumbert share of the two-party presidential vote. W Indicator variable (1 for the elections of 1920, 1944, and 1948, and 0 otherwise). $D$ Indicator variable ( 1 if a Democratic incumbent is running for election, -1 if a Republican incumbent is running for election, and 0 otherwise). $G$ Growth rate of real per capita GDP in the first three quarters of the election year. $I$ Indicator variable ( 1 if there is a Democratic incumbent at the time of the election and -1 if there is a Republican incumbent). $N$ Number of quar ters in the first 15 quar ters of the administration in which the growth rate of real per capita GDP is greater than $3.2 \%$. $P \quad$ Absolute value of the growth rate of the GDP deflator in the first 15 quar ters of the administration. c. Chatterjee et al. suggested considering the following model as a trial model to predict presidential elections: \[ V=\beta_{0}+\beta_{1} I+\beta_{2} D+\beta_{3} W+\beta_{4}(G I)+\beta_{5} P+\beta_{6} N+u \] Estimate this model and comment on the results in relation to the results of the model you have chosen.

To study the rate of growth of population in Belize over the period 1970-1992, Mukherjee et al. estimated the following models: ${ }^{*}$ Model I: $\widehat{\ln (\mathrm{Pop})_{t}}=\quad 4.73+0.024 t$ $t=(781.25) \quad(54.71)$ Model II: $\quad \widehat{\ln (\text { Pop })_{t}}=\quad 4.77+0.015 t-0.075 D_{t}+0.011\left(D_{t} t\right)$ $t=(2477.92) \quad(34.01) \quad(-17.03)$ where Pop = population in millions, t= trend variable, $D_{t}=1$ for observations beginning in 1978 and 0 before 1978 , and \ln stands for natural logarithm. a. In Model I, what is the rate of growth of Belize&qpos;s population over the sample period? b. Are the population growth rates statistically different pre- and post-1978? How do you know? If they are different, what are the growth rates for 1972-1977 and 1978-1992? To study the rate of growth of population in Belize over the period 1970-1992, Mukherjee et al. estimated the following models: \[ \begin{array}{l} \text { Model I: } \widehat{\ln (\text { Pop })_{t}}=4.73+0.024 t \\ t=(781.25)(54.71) \\ \text { Model II: } \widehat{\ln (\text { Pop })_{t}}=4.77+0.015 t-0.075 D_{t}+0.011\left(D_{t} t\right) \\ t=(2477.92)(34.01) \quad(-17.03) \quad(25.54) \\ \end{array} \] where Pop $=$ population in millions, $t=$ trend variable, $D_{t}=1$ for observations beginning in 1978 and 0 before 1978, and ln stands for natural logarithm. a. In Model I, what is the rate of growth of Belize's population over the sample period? b. Are the population growth rates statistically different pre- and post-1978? How do you know? If they are different, what are the growth rates for 1972-1977 and 1978-1992?

Reestimate the model in Exercise 9.22 by adding the regressor, expenditure on durable goods. a. Is there a difference in the regression results you obtained in Exercise 9.22 and in this exercise? If so, what explains the difference? b . If there is seasonality in the durable goods expenditure data, how would you account for it?>Refer to the quarterly appliance sales data given in Table 9.3. Consider the following model: \[ \text { Sales }_{i}=$\alpha$_{1}+$\alpha$_{2} D_{2 i}+$\alpha$_{3} D_{3 i}+$\alpha$_{4} D_{4 i}+u_{i} \] where the D &qpos;s are dummies taking 1 and 0 values for quarters II through IV. a. Estimate the preceding model for dishwashers, disposers, and washing machines individually. b. How would you interpret the estimated slope coefficients? c. How would you use the estimated $\alpha$ &qpos;s to deseasonalize the sales data for individual appliances?>Note: DISH = dishwashers; DISP = garbage disposers; FRIG = refrigerators; WASH = washing machines; DUR = durable goods expenditure, billions of 1982 dollars. Reestimate the model in Exercise 9.22 by adding the regressor, expenditure on durable goods. a. Is there a difference in the regression results you obtained in Exercise 9.22 and in this exercise? If so, what explains the difference? $b$. If there is seasonality in the durable goods expenditure data, how would you account for it? Refer to the quarterly appliance sales data given in Table 9.3. Consider the following model: \[ \text { Sales }_{i}=\alpha_{1}+\alpha_{2} D_{2 i}+\alpha_{3} D_{3 i}+\alpha_{4} D_{4 i}+u_{i} \] where the $D$ 's are dummies taking 1 and 0 values for quarters II through IV. a. Estimate the preceding model for dishwashers, disposers, and washing machines individually. b. How would you interpret the estimated slope coefficients? c. How would you use the estimated $\alpha$ 's to deseasonalize the sales data for individual appliances? \begin{tabular}{lcccccccccc} TABLE 9.3 & DISH & DISP & FRIG & WASH & DUR & DISH & DISP & FRIG & WASH & DUR \\ Quartery Data on & 841 & 798 & 1317 & 1271 & 252.6 & 480 & 706 & 943 & 1036 & 247.7 \\ Appliance Sales (in & 957 & 837 & 1615 & 1295 & 272.4 & 530 & 582 & 1175 & 1019 & 249.1 \\ thousands) and & 999 & 821 & 1662 & 1313 & 270.9 & 557 & 659 & 1269 & 1047 & 251.8 \\ Expenditure on & 960 & 858 & 1295 & 1150 & 273.9 & 602 & 837 & 973 & 918 & 262 \\ Durable Goods & 894 & 837 & 1271 & 1289 & 268.9 & 658 & 867 & 1102 & 1137 & 263.3 \\ (1978-I to 1985-IV) & 851 & 838 & 1555 & 1245 & 262.9 & 749 & 860 & 1344 & 1167 & 280 \\ Source: Bussiness Stafsics and & 863 & 832 & 1639 & 1270 & 270.9 & 827 & 918 & 1641 & 1230 & 288.5 \\ SurveyofCurrent Business, & 878 & 818 & 1238 & 1103 & 263.4 & 858 & 1017 & 1225 & 1081 & 300.5 \\ Department of Commerce & 792 & 868 & 1277 & 1273 & 260.6 & 808 & 1063 & 1429 & 1326 & 312.6 \\ (various issues). & 589 & 623 & 1258 & 1031 & 231.9 & 840 & 955 & 1699 & 1228 & 322.5 \\ & 657 & 662 & 1417 & 1143 & 242.7 & 893 & 973 & 1749 & 1297 & 324.3 \\ & 699 & 822 & 1185 & 1101 & 248.6 & 950 & 1096 & 1117 & 1198 & 333.1 \\ & 675 & 871 & 1196 & 1181 & 258.7 & 838 & 1086 & 1242 & 1292 & 344.8 \\ & 652 & 791 & 1410 & 1116 & 248.4 & 884 & 990 & 1684 & 1342 & 350.3 \\ & 628 & 759 & 1417 & 1190 & 255.5 & 905 & 1028 & 1764 & 1323 & 369.1 \\ & 529 & 734 & 919 & 1125 & 240.4 & 909 & 1003 & 1328 & 1274 & 356.4 \\ \hline \end{tabular} Note: DISH = dishwashers; DISP $=$ garbage disposers; FRIG $=$ refrigerators; WASH $=$ washing machines; DUR $=$ durable goods expenditure, billions of 1982 dollars.

Refer to Section 8.8 and the data in Table 8.9 concerning disposable personal income and personal savings for the period 1970-1995. In that section, the Chow test was introduced to see if a structural change occurred within the data between two time periods. Table 8.11 includes updated data containing the values from 1970-2005. According to the National Bureau of Economic Research, the most recent U.S. business contraction cycle ended in late 2001. Split the data into three sections: (1) 1970-1981, (2) 1982–2001, and (3) 2002-2005. a. Estimate both the model for the full dataset (years 1970-2005) and the third section (post-2002). Using the Chow test, determine if there is a significant break between the third period and the full dataset. b. With this new data in Table 8.11, determine if there is still a significant difference between the first set of years (1970-1981) and the full dataset, now that there are more observations available. c. Perform the Chow test on the middle period (1982-2001) versus the full dataset to see if the data in this period behave significantly differently than the rest of the data.>\begin{tabular}{lcccccc} TABLE 8.9 & Observation & Savings & Income & Observation & Savings & Income \\ Savings and Personal & 1970 & 61.0 & 727.1 & 1983 & 167.0 & 2522.4 \\ Disposable Income & 1971 & 68.6 & 790.2 & 1984 & 235.7 & 2810.0 \\ (billions of dollars), & 1972 & 63.6 & 855.3 & 1985 & 206.2 & 3002.0 \\ United States, & 1973 & 89.6 & 965.0 & 1986 & 196.5 & 3187.6 \\ 1970-1995 & 1974 & 97.6 & 1054.2 & 1987 & 168.4 & 3363.1 \\ & 1975 & 104.4 & 1159.2 & 1988 & 189.1 & 3640.8 \\ Source: Economic Report & 1976 & 96.4 & 1273.0 & 1989 & 187.8 & 3894.5 \\ of the President 1997, & 1977 & 92.5 & 1401.4 & 1990 & 208.7 & 4166.8 \\ Eble B-28,p. 332. & 1978 & 112.6 & 1580.1 & 1991 & 246.4 & 4343.7 \\ & 1979 & 130.1 & 1769.5 & 1992 & 272.6 & 4613.7 \\ & 1980 & 161.8 & 1973.3 & 1993 & 214.4 & 4790.2 \\ & 1981 & 199.1 & 2200.2 & 1994 & 189.4 & 5021.7 \\ & 1982 & 205.5 & 2347.3 & 1995 & 249.3 & 5320.8 \\ \hline \end{tabular}>8.8 Prediction with Multiple Regression In Section 5.10 we showed how the estimated two-variable regression model can be used for (1) mean prediction, that is, predicting the point on the population regression function (PRF), as well as for (2) individual prediction, that is, predicting an individual value of Y given the value of the regressor X=$X_{0}$ , where $X_{0}$ is the specified numerical value of X . The estimated multiple regression too can be used for similar purposes, and the procedure for doing that is a straightforward extension of the two-variable case, except the formulas for estimating the variances and standard errors of the forecast value (comparable to Eqs. $[5.10 .2]$ and $[5.10 .6]$ of the two-variable model) are rather involved and are better handled by the matrix methods discussed in Appendix C. Of course, most standard regression packages can do this routinely, so there is no need to look up the matrix formulation. It is given in Appendix $\mathbf{C}$ for the benefit of the mathematically inclined students. This appendix also gives a fully worked out example. Refer to Section 8.8 and the data in Table 8.9 concerning disposable personal income and personal savings for the period 1970-1995. In that section, the Chow test was introduced to see if a structural change occurred within the data between two time periods. Table 8.11 includes updated data containing the values from 1970-2005. According to the National Bureau of Economic Research, the most recent U.S. business contraction cycle ended in late 2001. Split the data into three sections: (1) 1970-1981, (2) 1982-2001, and (3) 2002-2005. a. Estimate both the model for the full dataset (years 1970-2005) and the third section (post-2002). Using the Chow test, determine if there is a significant break between the third period and the full dataset. b. With this new data in Table 8.11 , determine if there is still a significant difference between the first set of years (1970-1981) and the full dataset, now that there are more observations available. c. Perform the Chow test on the middle period (1982-2001) versus the full dataset to see if the data in this period behave significantly differently than the rest of the data. \begin{tabular}{|c|c|c|c|c|c|c|} \hline $\begin{array}{l}\text { TABLE } 8.9 \\ \text { Savings and Personal }\end{array}$ & Observation & Savings & Income & Observation & Savings & Income \\ \hline Disposable Income & 1970 & 61.0 & 727.1 & 1983 & 167.0 & 2522.4 \\ \hline (billions of dollars), & 1971 & 68.6 & 790.2 & 1984 & 235.7 & 2810.0 \\ \hline United States, & 1972 & 63.6 & 855.3 & 1985 & 206.2 & 3002.0 \\ \hline \multirow{2}{*}{$1970-1995$} & 1973 & 89.6 & 965.0 & 1986 & 196.5 & 3187.6 \\ \hline & 1974 & 97.6 & 1054.2 & 1987 & 168.4 & 3363.1 \\ \hline \multirow{8}{*}{$\begin{array}{l}\text { Source: Econamic Report } \\ \text { of the President, 1997, } \\ \text { Eble B.28,p. } 332 .\end{array}$} & 1975 & 104.4 & 1159.2 & 1988 & 189.1 & 3640.8 \\ \hline & 1976 & 96.4 & 1273.0 & 1989 & 187.8 & 3894.5 \\ \hline & 1977 & 92.5 & 1401.4 & 1990 & 208.7 & 4166.8 \\ \hline & 1978 & 112.6 & 1580.1 & 1991 & 246.4 & 4343.7 \\ \hline & 1979 & 130.1 & 1769.5 & 1992 & 272.6 & 4613.7 \\ \hline & 1980 & 161.8 & 1973.3 & 1993 & 214.4 & 4790.2 \\ \hline & 1981 & 199.1 & 2200.2 & 1994 & 189.4 & 5021.7 \\ \hline & 1982 & 205.5 & 2347.3 & 1995 & 249.3 & 5320.8 \\ \hline \end{tabular} 8.8 Prediction with Multiple Regression In Section 5.10 we showed how the estimated two-variable regression model can be used for (1) mean prediction, that is, predicting the point on the population regression function (PRF), as well as for (2) individual prediction, that is, predicting an individual value of $Y$ given the value of the regressor $X=X_{0}$, where $X_{0}$ is the specified numerical value of $X$. The estimated multiple regression too can be used for similar purposes, and the procedure for doing that is a straightforward extension of the two-variable case, except the formulas for estimating the variances and standard errors of the forecast value (comparable to Eqs. [5.10.2] and [5.10.6] of the two-variable model) are rather involved and are better handled by the matrix methods discussed in Appendix C. Of course, most standard regression packages can do this routinely, so there is no need to look up the matrix formulation. It is given in Appendix C for the benefit of the mathematically inclined students. This appendix also gives a fully worked out example. \begin{tabular}{|c|c|c|c|} \hline $\begin{array}{l}\text { TABLE } 8.11 \\ \text { Savings and Personal }\end{array}$ & Year & Savings & Income \\ \hline Disposable Income & 1970 & 69.5 & 735.7 \\ \hline (billions of dollars), & 1971 & 80.6 & 801.8 \\ \hline United States, & 1972 & 77.2 & 869.1 \\ \hline $1970-2005$ (billions of & 1973 & 102.7 & 978.3 \\ \hline dollars, except as & 1974 & 113.6 & $1,071.6$ \\ \hline noted; quarterly data & 1975 & 125.6 & $1,187.4$ \\ \hline at seasonally adjusted & 1976 & 122.3 & $1,302.5$ \\ \hline annual rates) & 1977 & 125.3 & $1,435.7$ \\ \hline (2) & 1978 & 142.5 & $1,608.3$ \\ \hline Source Deprinent of & 1979 & 159.1 & $1,793.5$ \\ \hline & 1980 & 201.4 & $2,009.0$ \\ \hline & 1981 & 244.3 & $2,246.1$ \\ \hline & 1982 & 270.8 & $2,421.2$ \\ \hline & 1983 & 233.6 & $2,608.4$ \\ \hline & 1984 & 314.8 & $2,912.0$ \\ \hline & 1985 & 280.0 & $3,109.3$ \\ \hline & 1986 & 268.4 & $3,285.1$ \\ \hline & 1987 & 241.4 & $3,458.3$ \\ \hline & 1988 & 272.9 & $3,748.7$ \\ \hline & 1989 & 287.1 & $4,021.7$ \\ \hline & 1990 & 299.4 & $4,285.8$ \\ \hline & 1991 & 324.2 & $4,464.3$ \\ \hline & 1992 & 366.0 & $4,751.4$ \\ \hline & 1993 & 284.0 & $4,911.9$ \\ \hline & 1994 & 249.5 & $5,151.8$ \\ \hline & 1995 & 250.9 & $5,408.2$ \\ \hline & 1996 & 228.4 & $5,688.5$ \\ \hline & 1997 & 218.3 & $5,988.8$ \\ \hline & 1998 & 276.8 & $6,395.9$ \\ \hline & 1999 & 158.6 & $6,695.0$ \\ \hline & 2000 & 168.5 & $7,194.0$ \\ \hline & 2001 & 132.3 & $7,486.8$ \\ \hline & 2002 & 184.7 & $7,830.1$ \\ \hline & 2003 & 174.9 & $8,162.5$ \\ \hline & 2004 & 174.3 & $8,681.6$ \\ \hline & 2005 & 34.8 & $9,036.1$ \\ \hline \end{tabular}

7.19. The demand for chicken in the United States, 1960-1982. To study the per capita consumption of chicken in the United States, you are given the data in Table 7.9, where Y= per capita consumption of chickens, lb \[ $\begin{aligned} X_{2} &=\text { real disposable income per capita, } \$ \\ X_{3} &=\text { real retail price of chicken per } $\mathrm{lb}, \phi$ \\ X_{4} &=\text { real retail price of pork per } $\mathrm{lb}, \phi$ \\ X_{5} &=\text { real retail price of beef per } $\mathrm{lb}, \phi$ \end{aligned}$ \] $X_{6}=$ composite real price of chicken substitutes per $\mathrm{lb}, \phi$ , which is a weighted average of the real retail prices per lb of pork and beef, the weights being the relative consumptions of beef and pork in total beef and pork consumption>Note: The real prices were obtained by dividing the nominal prices by the Consumer Price Index for food>Now consider the following demand functions: \[ $\begin{array}{l} \ln Y_{t}=\alpha_{1}+\alpha_{2} $\ln X_{2 t}$+\alpha_{3} $\ln X_{3 t}$+u_{t} \\ \ln Y_{t}=\gamma_{1}+$\gamma_{2}$ $\ln X_{2 t}$+$\gamma_{3}$ $\ln X_{3 t}$+\gamma_{4} \ln X_{4 t}+u_{t} \\ \ln Y_{t}=\lambda_{1}+\lambda_{2} $\ln X_{2 t}$+\lambda_{3} $\ln X_{3 t}$+\lambda_{4} \ln X_{5 t}+u_{t} \\ \ln Y_{t}=\theta_{1}+\theta_{2} $\ln X_{2 t}$+\theta_{3} $\ln X_{3 t}$+\theta_{4} \ln X_{4 t}+\theta_{5} \ln X_{5 t}+u_{t} \\ \ln Y_{t}=\beta_{1}+$\beta_{2}$ $\ln X_{2 t}$+$\beta_{3}$ $\ln X_{3 t}$+\beta_{4} \ln X_{6 t}+u_{t} \end{array}$ \] From microeconomic theory it is known that the demand for a commodity generally depends on the real income of the consumer, the real price of the commodity, and the real prices of competing or complementary commodities. In view of these considerations, answer the following questions. a. Which demand function among the ones given here would you choose, and why? b. How would you interpret the coefficients of $\ln X_{2 t}$ and $\ln X_{3 t}$ in these models? c. What is the difference between specifications (2) and (4)? d. What problems do you foresee if you adopt specification (4)? (Hint: Prices of both pork and beef are included along with the price of chicken.) e. Since specification (5) includes the composite price of beef and pork, would you prefer the demand function (5) to the function (4)? Why? f. Are pork and/or beef competing or substitute products to chicken? How do you know? g. Assume function (5) is the "correct" demand function. Estimate the parameters of this model, obtain their standard errors, and $$R^{2}$, \bar{R}^{2}$ , and modified $R^{2}$ . Interpret your results. h . Now suppose you run the "incorrect" model (2). Assess the consequences of this mis-specification by considering the values of $\gamma_{2}$ and $\gamma_{3}$ in relation to $\beta_{2}$ and $\beta_{3}$ , respectively. (Hint: Pay attention to the discussion in Section 7.7.) 7.19. The demand for chicken in the United States, 1960-1982. To study the per capita consumption of chicken in the United States, you are given the data in Table 7.9, where $Y=$ per capita consumption of chickens, lb $X_{2}=$ real disposable income per capita, $\$$ $X_{3}=$ real retail price of chicken per lb, $\notin$ $X_{4}=$ real retail price of pork per lb, $\notin$ $X_{5}=$ real retail price of beef per lb, $\notin$ $X_{6}=$ composite real price of chicken substitutes per $\mathrm{lb}, \boldsymbol{\ell}$, which is a weighted average of the real retail prices per $\mathrm{lb}$ of pork and beef, the weights being the relative consumptions of beef and pork in total beef and pork consumption Note: The real prices were obtained by dividing the nominal prices by the Consumer Price Index for food Now consider the following demand functions: \[ \begin{array}{l} \ln Y_{t}=\alpha_{1}+\alpha_{2} \ln X_{2 t}+\alpha_{3} \ln X_{3 t}+u_{t} \\ \ln Y_{t}=\gamma_{1}+\gamma_{2} \ln X_{2 t}+\gamma_{3} \ln X_{3 t}+\gamma_{4} \ln X_{4 t}+u_{t} \\ \ln Y_{t}=\lambda_{1}+\lambda_{2} \ln X_{2 t}+\lambda_{3} \ln X_{3 t}+\lambda_{4} \ln X_{5 t}+u_{t} \\ \ln Y_{t}=\theta_{1}+\theta_{2} \ln X_{2 t}+\theta_{3} \ln X_{3 t}+\theta_{4} \ln X_{4 t}+\theta_{5} \ln X_{5 t}+u_{t} \\ \ln Y_{t}=\beta_{1}+\beta_{2} \ln X_{2 t}+\beta_{3} \ln X_{3 t}+\beta_{4} \ln X_{6 t}+u_{t} \end{array} \] From microeconomic theory it is known that the demand for a commodity generally depends on the real income of the consumer, the real price of the commodity, and the real prices of competing or complementary commodities. In view of these considerations, answer the following questions. a. Which demand function among the ones given here would you choose, and why? b. How would you interpret the coefficients of $\ln X_{2 t}$ and $\ln X_{3 t}$ in these models? c. What is the difference between specifications (2) and (4)? d. What problems do you foresee if you adopt specification (4)? (Hint: Prices of both pork and beef are included along with the price of chicken.) e. Since specification (5) includes the composite price of beef and pork, would you prefer the demand function (5) to the function (4)? Why? f. Are pork and/or beef competing or substitute products to chicken? How do you know? g. Assume function (5) is the "correct" demand function. Estimate the parameters of this model, obtain their standard errors, and $R^{2}, \bar{R}^{2}$, and modified $R^{2}$. Interpret your results. h. Now suppose you run the "incorrect" model (2). Assess the consequences of this mis-specification by considering the values of $\gamma_{2}$ and $\gamma_{3}$ in relation to $\beta_{2}$ and $\beta_{3}$, respectively. (Hint: Pay attention to the discussion in Section 7.7.)

Refer to the demand for cell phones regression given in Eq. (3.7.3). a. Is the estimated intercept coefficient significant at the 5 percent level of significance? What is the null hypothesis you are testing? b. Is the estimated slope coefficient significant at the 5 percent level? What is the underlying null hypothesis? c. Establish a 95 percent confidence for the true slope coefficient. d. What is the mean forecast value of cell phones demanded if the per capita income is $\$ 9,000$ ? What is the 95 percent confidence interval for the forecast value?> $\begin{aligned} \hat{Y}_{i} &=14.4773+0.0022 X_{i} \\ \text { se }\left(\hat{\beta}_{1}\right) &=6.1523 ; \quad \text { se }\left(\hat{\beta}_{2}\right)=0.00032 \\ r^{2} &=0.6023 \end{aligned}$ Refer to the demand for cell phones regression given in Eq. (3.7.3). a. Is the estimated intercept coefficient significant at the 5 percent level of significance? What is the null hypothesis you are testing? b. Is the estimated slope coefficient significant at the 5 percent level? What is the underlying null hypothesis? c. Establish a 95 percent confidence for the true slope coefficient. d. What is the mean forecast value of cell phones demanded if the per capita income is $\$ 9,000$ ? What is the 95 percent confidence interval for the forecast value? $\begin{aligned} \hat{Y}_{i} & =14.4773+0.0022 X_{i} \\ \text { se }\left(\hat{\beta}_{1}\right) & =6.1523 ; \quad \text { se }\left(\hat{\beta}_{2}\right)=0.00032 \\ r^{2} & =0.6023\end{aligned}$

Set up the ANOVA table in the manner of Table 5.4 for the regression model given in Eq. (3.7.2) and test the hypothesis that there is no relationship between food expenditure and total expenditure in India.> $\begin{aligned} \widehat{\text { FoodExp }_{i}} &=94.2087+0.4368 \text { Totalexp }_{i} & \\ \operatorname{var}\left(\hat{\beta}_{1}\right) &=2560.9401 & & \operatorname{se}\left(\hat{\beta}_{1}\right)=50.8563 \\ \operatorname{var}\left(\hat{\beta}_{2}\right) &=0.0061 & & \operatorname{se}\left(\hat{\beta}_{2}\right) \\ r^{2} &=0.3698 & \hat{\sigma}^{2} &=4469.6913 \end{aligned}$ Set up the ANOVA table in the manner of Table 5.4 for the regression model given in Eq. (3.7.2) and test the hypothesis that there is no relationship between food expenditure and total expenditure in India. $\begin{array}{rlrl}\widehat{\text { FoodExp }}_{i} & =94.2087+0.4368 \text { TotalExp }_{i} \\ \operatorname{var}\left(\hat{\beta}_{1}\right) & =2560.9401 & \operatorname{se}\left(\hat{\beta}_{1}\right) & =50.8563 \\ \operatorname{var}\left(\hat{\beta}_{2}\right) & =0.0061 & \operatorname{se}\left(\hat{\beta}_{2}\right) & =0.0783 \\ r^{2} & =0.3698 & \hat{\sigma}^{2} & =4469.6913\end{array}$ TABLE 5.4 ANOVA Table for the Wages-Education Example

From the scattergram given in Figure 2.9, what general conclusions do you draw? What is the economic theory that underlies this scattergram? (Hint: Look up any international economics textbook and read up on the Heckscher-Ohlin model of trade.) From the scattergram given in Figure 2.9 , what general conclusions do you draw? What is the economic theory that underlies this scattergram? (Hint: Look up any international economics textbook and read up on the Heckscher-Ohlin model of trade.) FIGURE 2.9 Skill intensity of exports and human capital endowment. Data are for 126 industrial and developing countries in 1985. Values along the horizontal axis are logarithms of the ratio of the country's average educational attainment to its land area; vertical axis values are logarithms of the ratio of manufactured to primary-products exports. Source: World Bank, Workd Developnent Report 1995, p. 59. Original sources Export data from United Nations Statistical Office COMTRADE database; education data from UNDP 1990; land data from the World Bank.

Using Financial Information to Identify Companies The following selected financial data pertain to four unidentified companies: \begin{tabular}{lcccc} & \multicolumn{4}{c}{ COMPANIES } \\ \cline { 2 - 5 } & 1 & 2 & 3 & 4 \\ \hline Balance Sheet Data (component \%) & & & & \\ Cash & 3.5 \% & 4.7 \% & 8.2 \% & 11.7 \% \\ Accounts receivable & 16.9 & 28.9 & 16.8 & 51.9 \\ Inventory & 46.8 & 35.6 & 57.3 & 0.0 \\ Property and equipment & 18.3 & 21.7 & 7.6 & 18.7 \\ Income Statement Data (component \%) & & & & \\ Cost of goods sold & 78.0 \% & 77.5 \% & 55.8 \% & 0.0 \% \\ Profit before taxes & 2.1 & 0.7 & 1.2 & 3.2 \\ Selected Ratios & & & & \\ Current ratio & 1.3 & 1.5 & 1.6 & 1.2 \\ Inventory turnover ratio & 3.6 & 9.8 & 1.5 & \mathrm{~N} / \mathrm{A}^{*} \\ "N/A = Not applicable & & & & \end{tabular} The above financial information pertains to the following companies: High-end clothing store Advertising agency Wholesale candy company Car manufacturer Required: Match each company with its financial information. Using Financial Information to Identify Companies The following selected financial data pertain to four unidentified companies: \begin{tabular}{lcccc} & \multicolumn{4}{c}{ COMPANIES } \\ \cline { 2 - 5 } & 1 & 2 & 3 & 4 \\ \hline Balance Sheet Data (component \%) & & & & \\ Cash & $3.5 \%$ & $4.7 \%$ & $8.2 \%$ & $11.7 \%$ \\ Accounts receivable & 16.9 & 28.9 & 16.8 & 51.9 \\ Inventory & 46.8 & 35.6 & 57.3 & 0.0 \\ Property and equipment & 18.3 & 21.7 & 7.6 & 18.7 \\ Income Statement Data (component \%) & & & & \\ Cost of goods sold & $78.0 \%$ & $77.5 \%$ & $55.8 \%$ & $0.0 \%$ \\ Profit before taxes & 2.1 & 0.7 & 1.2 & 3.2 \\ Selected Ratios & & & & \\ Current ratio & 1.3 & 1.5 & 1.6 & 1.2 \\ Inventory turnover ratio & 3.6 & 9.8 & 1.5 & N/A* \\ *N/A = Not applicable & & & & \end{tabular} The above financial information pertains to the following companies: High-end clothing store Advertising agency Wholesale candy company Car manufacturer Required: Match each company with its financial information.

Using Financial Information to Identify Companies The following selected financial data pertain to four unidentified companies: \begin{tabular}{lccccc} & \multicolumn{4}{c}{ COMPANIES } \\ \cline { 2 - 6 } & \multicolumn{1}{c}{2} & 3 & 4 \\ \hline Balance Sheet Data (component \%) & & & & & \\ Cash & 7.3 \% & 21.6 \% & 6.1 \% & 11.3 \% \\ Accounts receivable & 28.2 & 39.7 & 3.2 & 22.9 \\ Inventory & 21.6 & 0.6 & 1.8 & 27.5 \\ Property and equipment & 32.1 & 18.0 & 74.6 & 25.1 \\ Income Statement Data (component \%) & & & & \\ Cost of goods sold & 84.7 \% & 0.0 \% & 0.0 \% & 56.6 \% \\ Profit before taxes & 1.7 & 3.2 & 2.4 & 6.9 \\ Selected Ratios & & & & \\ Current ratio & 1.5 & 1.2 & 0.6 & 1.9 \\ Inventory turnover ratio & 27.4 & \mathrm{~N} / \mathrm{A}^{*} & \mathrm{~N} / \mathrm{A}^{*} & 3.3 \\ * \mathrm{~N} / \mathrm{A}= Not applicable & & & & \end{tabular} The above financial information pertains to the following companies: Travel agency Hotel Meat processing company Drug company Required: Match each company with its financial information. Using Financial Information to Identify Companies The following selected financial data pertain to four unidentified companies: \begin{tabular}{lcccc} & \multicolumn{4}{c}{ COMPANIES } \\ \cline { 2 - 5 } & \multicolumn{4}{c}{4} \\ \hline Balance Sheet Data (component \%) & 2 & 3 & \\ Cash & $7.3 \%$ & $21.6 \%$ & $6.1 \%$ & $11.3 \%$ \\ Accounts receivable & 28.2 & 39.7 & 3.2 & 22.9 \\ Inventory & 21.6 & 0.6 & 1.8 & 27.5 \\ Property and equipment & 32.1 & 18.0 & 74.6 & 25.1 \\ Income Statement Data (component \%) & & & & \\ Cost of goods sold & $84.7 \%$ & $0.0 \%$ & $0.0 \%$ & $56.6 \%$ \\ Profit before taxes & 1.7 & 3.2 & 2.4 & 6.9 \\ Selected Ratios & & & & \\ Current ratio & 1.5 & 1.2 & 0.6 & 1.9 \\ Inventory turnover ratio & 27.4 & $\mathrm{~N} / \mathrm{A}^{*}$ & $\mathrm{~N} / \mathrm{A}^{*}$ & 3.3 \\ *N/A = Not applicable & & & & \end{tabular} The above financial information pertains to the following companies: Travel agency Hotel Meat processing company Drug company Required: Match each company with its financial information.

Determining Financial Statement Effects of Various Liabilities (P9-6) Ford Motor Company is one of the world&qpos;s largest companies, with annual sales of cars and trucks in excess of $\$ 144$ billion. A recent annual report for Ford contained the following note: $\underline{\text { Warranties }}$ Estimated warranty costs are accrued for at the time the vehicle is sold to a dealer. Estimates for warranty cost are made based primarily on historical warranty claim experience. 1. Assume that this year Ford paid cash to service warranty claims in the amount of $\$ 4.0$ billion. Ford also accrued expenses for warranties in the amount of $\$ 3.9$ billion. If Ford had a balance in its accrued warranties>account of $\$ 1.0$ billion to start the year, what is the balance at the end of the year? Bally Total Fitness Holding Corporation operates fitness centers mainly in North America. The following note was contained in a recent annual report for Bally: Revenue Recognition As a general principle, revenue is recognized when the following criteria are met: (i) persuasive evidence of an arrangement exists, (ii) delivery has occurred and services have been rendered, (iii) the price to the buyer is fixed or determinable and, (iv) collectability is reasonably assured. Membership revenue is earned on a straight-line basis over the longer of the contractual term or the estimated membership term. The weighted average membership life is 39 months. 2. Assume that Bally collected \$23 million in December for "New Year&qpos;s Resolution" memberships starting January 1 of next year. What is the amount of unearned revenue that should be reported on this year&qpos;s balance sheet and next year&qpos;s balance sheet associated with the $\$ 23$ million? Determining Financial Statement Effects of Various Liabilities (P9-6) Ford Motor Company is one of the world's largest companies, with annual sales of cars and trucks in excess of \$144 billion. A recent annual report for Ford contained the following note: Warranties Estimated warranty costs are accrued for at the time the vehicle is sold to a dealer. Estimates for warranty cost are made based primarily on historical warranty claim experience. 1. Assume that this year Ford paid cash to service warranty claims in the amount of $\$ 4.0$ billion. Ford also accrued expenses for warranties in the amount of $\$ 3.9$ billion. If Ford had a balance in its accrued warranties account of $\$ 1.0$ billion to start the year, what is the balance at the end of the year? Bally Total Fitness Holding Corporation operates fitness centers mainly in North America. The following note was contained in a recent annual report for Bally: Revenue Recognition As a general principle, revenue is recognized when the following criteria are met: (i) persuasive evidence of an arrangement exists, (ii) delivery has occurred and services have been rendered, (iii) the price to the buyer is fixed or determinable and, (iv) collectability is reasonably assured. Membership revenue is earned on a straight-line basis over the longer of the contractual term or the estimated membership term. The weighted average membership life is 39 months. 2. Assume that Bally collected $\$ 23$ million in December for "New Year's Resolution" memberships starting January 1 of next year. What is the amount of unearned revenue that should be reported on this year's balance sheet and next year's balance sheet associated with the \$23 million?

Explaining the Nature of a Long-Lived Asset and Determining and Recording the Financial Statement Effects of Its Purchase (AP81) On January 2, Summers Company received a machine that the company had ordered with an invoice price of $\$ 85,000$ . Freight costs of $\$ 1,000$ were paid by the vendor per the sales agreement. The company exchanged the following on January 2 to acquire the machine: Issued 2,000 shares of Summers Company common stock, par value \$ 1 (market value, \$3.50 per share). Signed a note payable for $\$ 60,000$ with an 11.5 percent interest rate, (principal plus interest are due April 1 of the current year). The balance of the invoice price was on account with the vendor, to be paid in cash by January 12 . On January 3, Summers Company paid $\$ 2,400$ cash for installation costs to prepare the machine for use. On January 12, Summers Company paid the balance due on its accounts payable to the vendor.>Required: 1. What are the classifications of long-lived assets? Explain their differences. 2. Record the purchase on January 2, the installation costs on January 3, and the subsequent payment on January 12. Show computations. 3. Indicate the accounts, amounts, and effects (+ for increase and - for decrease) of the purchase and subsequent cash payment on the accounting equation. Use the following structure: Date $\quad$ Assets =$\quad$ Liabilities + Stockholders&qpos; Equity 4. What is the cost of the machine recorded on Summers&qpos;s records? Explain the basis you used for any questionable items. Explaining the Nature of a Long-Lived Asset and Determining and Recording the Financial Statement Effects of Its Purchase (AP81) On January 2, Summers Company received a machine that the company had ordered with an invoice price of $\$ 85,000$. Freight costs of $\$ 1,000$ were paid by the vendor per the sales agreement. The company exchanged the following on January 2 to acquire the machine: Issued 2,000 shares of Summers Company common stock, par value $\$ 1$ (market value, \$3.50 per share). Signed a note payable for $\$ 60,000$ with an 11.5 percent interest rate (principal plus interest are due April 1 of the current year). The balance of the invoice price was on account with the vendor, to be paid in cash by January 12. On January 3, Summers Company paid $\$ 2,400$ cash for installation costs to prepare the machine for use. On January 12, Summers Company paid the balance due on its accounts payable to the vendor. Required: 1. What are the classifications of long-lived assets? Explain their differences. 2. Record the purchase on January 2, the installation costs on January 3, and the subsequent payment on January 12. Show computations. 3. Indicate the accounts, amounts, and effects (+ for increase and - for decrease) of the purchase and subsequent cash payment on the accounting equation. Use the following structure: Date Assets $=\quad$ Liabilities $+\quad$ Stockholders' Equity 4. What is the cost of the machine recorded on Summers's records? Explain the basis you used for any questionable items.

Analyzing the Effects of Four Alternative Inventory Methods (AP7-1) Kirtland Corporation uses a periodic inventory system. At the end of the annual accounting period, December 31, the accounting records for the most popular item in inventory showed the following: \begin{tabular}{|lcc|} \hline \multicolumn{1}{|c}{ Transactions } & Units & Unit Cost \\ \hline Beginning inventory, January 1 & 400 & \$ \\ Transactions during the year: & & 3.00 \\ a. Purchase, January 30 & 300 & 3.40 \\ b. Purchase, May 1 & 460 & 4.00 \\ c. Sale (\$5 each) & (160) & \\ d. Sale (\$5 each) & (700) & \\ \hline \end{tabular}>Required: Compute the amount of (a) goods available for sale, (b) ending inventory, and (c) cost of goods sold at December 31 under each of the following inventory costing methods (show computations and round to the nearest dollar): 1. Average cost (round the average cost per unit to the nearest cent). 2. First-in, first-out. 3. Last-in, first-out. 4. Specific identification, assuming that the first sale was selected twofifths from the beginning inventory and three-fifths from the purchase of January 30. Assume that the second sale was selected from the remainder of the beginning inventory, with the balance from the purchase of May 1 . Analyzing the Effects of Four Alternative Inventory Methods (AP7-1) Kirtland Corporation uses a periodic inventory system. At the end of the annual accounting period, December 31, the accounting records for the most popular item in inventory showed the following: \begin{tabular}{|lcc|} \hline \multicolumn{1}{|c}{ Transactions } & Units & Unit Cost \\ \hline Beginning inventory, January 1 & 400 & $\$$ \\ Transactions during the year: & & 3.00 \\ a. Purchase, January 30 & 300 & 3.40 \\ b. Purchase, May 1 & 460 & 4.00 \\ c. Sale (\$5 each) & $(160)$ & \\ d. Sale (\$5 each) & $(700)$ & \\ \hline \end{tabular} Required: Compute the amount of (a) goods available for sale, $(b)$ ending inventory, and $(c)$ cost of goods sold at December 31 under each of the following inventory costing methods (show computations and round to the nearest dollar): 1. Average cost (round the average cost per unit to the nearest cent). 2. First-in, first-out. 3. Last-in, first-out. 4. Specific identification, assuming that the first sale was selected twofifths from the beginning inventory and three-fifths from the purchase of January 30 . Assume that the second sale was selected from the remainder of the beginning inventory, with the balance from the purchase of May 1 .

Recording Journal Entries, Posting Effects to T-Accounts, Preparing Unadjusted Financial Statements, and Performing Ratio Analysis In April 2019, Sarah Jones created a new business, IthacaDeep, Inc., offering therapeutic deep massage for stress reduction, pain management, injury recovery, and relief from muscle strains and tightness experienced by anyone, especially athletes, fitness enthusiasts, runners, and physical>laborers. You have been hired to record the transactions occurring in the first month of operations. Received investment of cash by three organizers and issued to them a total of 200 shares of $\$ 0.05$ par value stock with a market price of $\$ 40$ per share. Borrowed $\$ 20,000$ from a local bank, signing a note due in three years. Signed a one-year lease for a space near a health club, paying $\$ 600$ for April rent and $\$ 1,800$ for rent for May, June, and July. Purchased equipment costing $\$ 15,200$ , paying 20 percent in cash and owing the rest on account to the supplier, due in 60 days. Ordered a business computer and printer from Dell for $\$ 2,900$ . Loaned $\$ 1,000$ to an employee who signed a note due in three months. Purchased supplies for $\$ 2,600$ on account. Paid Facebook $\$ 2,000$ as a budget for advertising. (Facebook charges the advertiser&qpos;s account per click, drawing down the balance. The average click is $\$ 0.27 .)$ Paid $\$ 2,400$ for 12 months of insurance coverage, with one-twelfth covering April and the rest covering the remainder of the fiscal year (end of March next year). Purchased short-term investments for $\$ 10,000$ cash. Along with her four other licensed massage therapists, Sarah and her team provided $\$ 42,000$ of deep tissue service to clients in April who paid half in cash and agreed to pay the rest in May. Paid employees $\$ 18,000$ in wages for work in April. At the end of April, received a $\$ 310$ utility bill for the use of gas and electric in April. The bill will be paid in May. Paid $\$ 1,500$ on the long-term note owed to the bank (ignore interest). Earned and received $\$ 25$ in interest on the short-term investments. Sent the team to Boston in April to receive additional specialty training, costing IthacaDeep $\$ 2,100$ cash. Received $\$ 1,400$ from clients for a series of services to be performed beginning in May. Required: 1. Prepare journal entries for each transaction, using the letter next to each>as a reference. 2. Create $\mathrm{T}$ -accounts and post the effects of the transactions to the $\mathrm{T}$ accounts. 3. Prepare an unadjusted trial balance for IthacaDeep, Inc., at the end of April. 4. Prepare an unadjusted classified income statement (include a line for income tax expense and earnings per share), statement of stockholders&qpos; equity, and classified balance sheet from the trial balance created in requirement ( 3 ) above. 5. Compute the following ratios: (1) current ratio and (2) net profit margin ratio. Round your answers to two decimal points. What do your results suggest about IthacaDeep, Inc.? Recording Journal Entries, Posting Effects to T-Accounts, Preparing Unadjusted Financial Statements, and Performing Ratio Analysis In April 2019, Sarah Jones created a new business, IthacaDeep, Inc., offering therapeutic deep massage for stress reduction, pain management, injury recovery, and relief from muscle strains and tightness experienced by anyone, especially athletes, fitness enthusiasts, runners, and physical laborers. You have been hired to record the transactions occurring in the first month of operations. Received investment of cash by three organizers and issued to them a total of 200 shares of $\$ 0.05$ par value stock with a market price of $\$ 40$ per share. Borrowed \$20,000 from a local bank, signing a note due in three years. Signed a one-year lease for a space near a health club, paying $\$ 600$ for April rent and \$1,800 for rent for May, June, and July. Purchased equipment costing $\$ 15,200$, paying 20 percent in cash and owing the rest on account to the supplier, due in 60 days. Ordered a business computer and printer from Dell for $\$ 2,900$. Loaned $\$ 1,000$ to an employee who signed a note due in three months. Purchased supplies for $\$ 2,600$ on account. Paid Facebook \$2,000 as a budget for advertising. (Facebook charges the advertiser's account per click, drawing down the balance. The average click is $\$ 0.27$.) Paid \$2,400 for 12 months of insurance coverage, with one-twelfth covering April and the rest covering the remainder of the fiscal year (end of March next year). Purchased short-term investments for $\$ 10,000$ cash. Along with her four other licensed massage therapists, Sarah and her team provided \$42,000 of deep tissue service to clients in April who paid half in cash and agreed to pay the rest in May. Paid employees $\$ 18,000$ in wages for work in April. At the end of April, received a $\$ 310$ utility bill for the use of gas and electric in April. The bill will be paid in May. Paid $\$ 1,500$ on the long-term note owed to the bank (ignore interest). Earned and received \$25 in interest on the short-term investments. Sent the team to Boston in April to receive additional specialty training, costing IthacaDeep $\$ 2,100$ cash. Received $\$ 1,400$ from clients for a series of services to be performed beginning in May. Required: 1. Prepare journal entries for each transaction, using the letter next to each as a reference. 2. Create T-accounts and post the effects of the transactions to the Taccounts. 3. Prepare an unadjusted trial balance for IthacaDeep, Inc., at the end of April. 4. Prepare an unadjusted classified income statement (include a line for income tax expense and earnings per share), statement of stockholders' equity, and classified balance sheet from the trial balance created in requirement (3) above. 5. Compute the following ratios: (1) current ratio and (2) net profit margin ratio. Round your answers to two decimal points. What do your results suggest about IthacaDeep, Inc.?

Using Financial Reports: Evaluating the Reliability of a Balance Sheet Frances Sabatier asked a local bank for a $\$ 50,000$ loan to expand her small company. The bank asked Frances to submit a financial statement of the business to supplement the loan application. Frances prepared the following balance sheet.>Required: The balance sheet has several flaws. However, there is one major deficiency. Identify it and explain its significance. Using Financial Reports: Evaluating the Reliability of a Balance Sheet Frances Sabatier asked a local bank for a $\$ 50,000$ loan to expand her small company. The bank asked Frances to submit a financial statement of the business to supplement the loan application. Frances prepared the following balance sheet. Required: The balance sheet has several flaws. However, there is one major deficiency. Identify it and explain its significance.

Financial Statements for a New Business Plan>Penny Cassidy is considering forming her own pool service and supply company, Penny&qpos;s Pool Service \& Supply, Inc. (PPSS). She has decided to incorporate the business to limit her legal liability. She expects to invest $\$ 20,000$ of her own savings and receive 1,000 shares of common stock. Her plan for the first year of operations forecasts the following amounts at December 31, the end of the current year: Cash in bank, \$2,900; amounts due from customers for services rendered, $\$ 2,300$ ; pool supplies inventory, $\$ 4,600$ ; equipment, $\$ 28,000$ ; amounts owed to Pool Corporation, Inc., a pool supply wholesaler, $\$ 3,500$ ; note payable to the bank, $\$ 5,000$ . Penny forecasts first-year sales of $\$ 60,000$ , wages of $\$ 24,000$ , cost of supplies used of $\$ 8,200$ , other administrative expenses of $\$ 4,500$ , and income tax expense of $\$ 4,000$ . She expects to pay herself a $\$ 10,000$ dividend as the sole stockholder of the company. Required: If Penny&qpos;s estimates are correct, what would the following first-year financial statements look like for Penny&qpos;s Pool Service \& Supply (use Exhibits 1.2, 1.3 , and 1.4 as models)? 1. Income statement 2. Statement of stockholders&qpos; equity 3. Balance sheet Financial Statements for a New Business Plan Penny Cassidy is considering forming her own pool service and supply company, Penny's Pool Service \& Supply, Inc. (PPSS). She has decided to incorporate the business to limit her legal liability. She expects to invest $\$ 20,000$ of her own savings and receive 1,000 shares of common stock. Her plan for the first year of operations forecasts the following amounts at December 31, the end of the current year: Cash in bank, \$2,900; amounts due from customers for services rendered, \$2,300; pool supplies inventory, $\$ 4,600$; equipment, \$28,000; amounts owed to Pool Corporation, Inc., a pool supply wholesaler, $\$ 3,500$; note payable to the bank, $\$ 5,000$. Penny forecasts first-year sales of $\$ 60,000$, wages of $\$ 24,000$, cost of supplies used of $\$ 8,200$, other administrative expenses of $\$ 4,500$, and income tax expense of $\$ 4,000$. She expects to pay herself a $\$ 10,000$ dividend as the sole stockholder of the company. Required: If Penny's estimates are correct, what would the following first-year financial statements look like for Penny's Pool Service \& Supply (use Exhibits 1.2, 1.3 , and 1.4 as models)? 1. Income statement 2. Statement of stockholders' equity 3. Balance sheet

Analyzing a Student&qpos;s Business and Preparing an Income Statement (P1-2) Upon graduation from high school, Sam List immediately accepted a job as an electrician&qpos;s assistant for a large local electrical repair company. After three years of hard work, Sam received an electrician&qpos;s license and decided to start his own business. He had saved $\$ 12,000$ , which he invested in the business. First, he transferred this amount from his savings account to a business bank account for List Electric Repair Company, Incorporated. His lawyer had advised him to start as a corporation. He then purchased a used panel truck for $\$ 9,000$ cash and secondhand tools for $\$ 1,500$ ; rented space in a small building; inserted an ad in the local paper; and opened the doors on October 1. Immediately, Sam was very busy; after one month, he employed an assistant.>Although Sam knew practically nothing about the financial side of the business, he realized that a number of reports were required and that costs and collections had to be controlled carefully. At the end of the year,>prompted in part by concern about his income tax situation (previously he had to report only salary), Sam recognized the need for financial statements. His assistant developed some financial statements for the business. On Dectmber 31, with the help of a friend, she gathered the following data for the three months just ended. Bank account deposits of collections for electric repair services totaled $\$ 32,000$ . The following checks had been written: electrician&qpos;s assistant, $\$ 7,500$ ; payroll taxes, $\$ 175$ ; supplies purchased and used on jobs, $\$ 9,500$ ; oil, gas, and maintenance on truck, $\$ 1,200$ ; insurance, $\$ 700$ ; rent, $\$ 500$ ; utilities and telephone, $\$ 825$ ; and miscellaneous expenses (including advertising), \$600. Also, uncollected bills to customers for electric repair services amounted to $\$ 3,500$ . The $\$ 250$ rent for December had not been paid. Sam estimated the cost of using the truck and tools (depreciation) during the three months to be $\$ 1,200$ . Income taxes for the three-month period were $\$ 3,930$ . Required: 1. Prepare a quarterly income statement for List Electric Repair for the three months October through December. Use the following main captions: Revenues from Services, Expenses, Pretax Income, and Net Income. 2. Do you think that Sam may need one or more additional financial reports for the quarter and thereafter? Explain. Analyzing a Student's Business and Preparing an Income Statement (P1-2) Upon graduation from high school, Sam List immediately accepted a job as an electrician's assistant for a large local electrical repair company. After three years of hard work, Sam received an electrician's license and decided to start his own business. He had saved $\$ 12,000$, which he invested in the business. First, he transferred this amount from his savings account to a business bank account for List Electric Repair Company, Incorporated. His lawyer had advised him to start as a corporation. He then purchased a used panel truck for $\$ 9,000$ cash and secondhand tools for $\$ 1,500$; rented space in a small building; inserted an ad in the local paper; and opened the doors on October 1 . Immediately, Sam was very busy; after one month, he employed an assistant. Although Sam knew practically nothing about the financial side of the business, he realized that a number of reports were required and that costs and collections had to be controlled carefully. At the end of the year, prompted in part by concern about his income tax situation (previously he had to report only salary), Sam recognized the need for financial statements. His anssistant developed some financial statements for the business. On Dectinber 31, with the help of a friend, she gathered the following data for the three months just ended. Bank account deposits of collections for electric repair services totaled $\$ 32,000$. The following checks had been written: electrician's assistant, $\$ 7,500$; payroll taxes, $\$ 175$; supplies purchased and used on jobs, $\$ 9,500$; oil, gas, and maintenance on truck, $\$ 1,200$; insurance, \$700; rent, \$500; utilities and telephone, \$825; and miscellaneous expenses (including advertising), $\$ 600$. Also, uncollected bills to customers for electric repair services amounted to $\$ 3,500$. The $\$ 250$ rent for December had not been paid. Sam estimated the cost of using the truck and tools (depreciation) during the three months to be $\$ 1,200$. Income taxes for the three-month period were $\$ 3,930$. Required: 1. Prepare a quarterly income statement for List Electric Repair for the three months October through December. Use the following main captions: Revenues from Services, Expenses, Pretax Income, and Net Income. 2. Do you think that Sam may need one or more additional financial reports for the quarter and thereafter? Explain.

Dell, Inc. is a global information technology company headquartered in Round Rock, Texas. The following is a reproduction of the terms and amounts in the financial statements contained in the company&qpos;s annual report for the fiscal year ended February 3, 2012 (in millions): \begin{tabular}{lrlr} \hline Net revenue & \$ 62,071 & Retained earnings at & \\ Cash & 13,852 & beginning of year & \$ 24,744 \\ Interest and other expenses & 191 & Cost of products and services & 48,260 \\ Income tax provision & 748 & Retained earnings at end of year & 28,236 \\ Accounts payable & 11,656 & & \\ Research, development and engineering expenses & 856 & Selling and administrative expenses & 8,524 \\ \hline \end{tabular} Choose the relevant data and prepare the income statement for the fiscal year. The final three lines of the income statement should be labeled earnings before income taxes, income tax provision, and net income. Also, using the retained earnings account, compute the amount of cash dividends paid during the fiscal year ending February 3, $2012 .$ Dell, Inc. is a global information technology company headquartered in Round Rock, Texas. The following is a reproduction of the terms and amounts in the financial statements contained in the company's annual report for the fiscal year ended February 3, 2012 (in millions): \begin{tabular}{lrlr} \hline Net revenue & $\$ 62,071$ & Retained earnings at & \\ Cash & 13,852 & beginning of year & $\$ 24,744$ \\ Interest and other expenses & 191 & Cost of products and services & 48,260 \\ Income tax provision & 748 & Retained earnings at end of year & 28,236 \\ Accounts payable & 11,656 & & \\ $\begin{array}{l}\text { Research, development and } \\ \text { engineering expenses }\end{array}$ & 856 & $\begin{array}{l}\text { Selling and administrative } \\ \text { expenses }\end{array}$ & 8,524 \\ \hline \end{tabular} Choose the relevant data and prepare the income statement for the fiscal year. The final three lines of the income statement should be labeled earnings before income taxes, income tax provision, and net income. Also, using the retained earnings account, compute the amount of cash dividends paid during the fiscal year ending February 3, 2012.

1. Steinberg Company sells annual subscriptions to its investment-advice magazine for € 50 . Suppose it sold 5,000 subscriptions in December, 2012, for magazines to be delivered quarterly in $2013 .$ How would Steinberg Company show this on its December 31, 2012, balance sheet? How would it affect the company&qpos;s 2012 income statement? How would it affect the income statement for the first 6 months of 2013 ? 2. Steinberg Company pays its salaried personnel monthly on the fifth day of the following month. That is, it pays January&qpos;s salaries on February 5. The company&qpos;s total salaries for 2012 were $€ 240,000$ , spread evenly over the 12 months. How will this affect the December 31,2012 , balance sheet? When will the December salaries (which are paid on January 5) be charged as expenses on the income statement? 1. Steinberg Company sells annual subscriptions to its investment-advice magazine for $€ 50$. Suppose it sold 5,000 subscriptions in December, 2012, for magazines to be delivered quarterly in 2013. How would Steinberg Company show this on its December 31, 2012, balance sheet? How would it affect the company's 2012 income statement? How would it affect the income statement for the first 6 months of 2013 ? 2. Steinberg Company pays its salaried personnel monthly on the fifth day of the following month. That is, it pays January's salaries on February 5. The company's total salaries for 2012 were $€ 240,000$, spread evenly over the 12 months. How will this affect the December 31, 2012, balance sheet? When will the December salaries (which are paid on January 5) be charged as expenses on the income statement?