The three sales projections below have been made by Country Textiles, which has fixed operating costs of $300,000 and variable operating costs equal to 40% of sales.

$$\begin{array}{rc} {\text { Sales }} & \text { Probability } \\ \hline \$ 600,000 & 0.30 \\ 900,000 & 0.40 \\ 1,200,000 & 0.30 \end{array}$$

The company wants to examine five different capital structures with debt ratios of 0%, 15%, 30%, 45%, and 60%. The $1 million in total assets of the company are taken to be constant. The company's book value for its common stock is$25 per share, and its tax rate is 40%. The five capital structures under consideration have been examined using the supplementary information listed below.

$$\begin{array}{ccc} \begin{array}{c} \text { Capital structure } \\ \text { debt ratio } \end{array} & \begin{array}{c} \text { Before-tax } \\ \text { cost of debt, } r_d \end{array} & \begin{array}{c} \text { Required } \\ \text { return, } r_s \end{array} \\ \hline 0 \% & 0.0 \% & 10.0 \% \\ 15 & 8.0 & 10.5 \\ 30 & 10.0 & 11.6 \\ 45 & 13.0 & 14.0 \\ 60 & 17.0 & 20.0 \end{array}$$

Determine the amount of EBIT that corresponds to each of the three levels of sales.

Graph each of the following equations.

a y = x

b y = -x

c y = | x |

Three students, Anja, Ben, and Celia, are asked to approximate an exponential model for the data shown. Draw a scatter plot and use the data and the graph:

Celia thinks that because the drop between the first two points is so large, the best model might actually have a y-intercept a little below 10 . She uses (0,9.5) to estimate a in her model. To estimate b, she determine the average of the ratios of successive data values. Explain her model.

The balanced equation for the decomposition of ammonium nitrate is

$$2 \mathrm{NH}_4 \mathrm{NO}_3(\mathrm{~s}) \longrightarrow 2 \mathrm{~N}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g})+4 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$$

(a) Write the mole ratios that relate moles of each product to the reactant $\mathrm{NH}_4 \mathrm{NO}_3$.

(b) How many moles of each product would form if $1.00 \mathrm{~mol}$ of $\mathrm{NH}_4 \mathrm{NO}_3$ reacts?

(c) How many moles of each product would form if $12.4 \mathrm{~mol}$ of $\mathrm{NH}_4 \mathrm{NO}_3$ react?

Find the following from the stock table discussed before.

Volume for Ball Corporation (BLL)$\qquad\underline{\qquad\qquad\qquad}$

The condensed financial statements of Elliott Company for the years 2013 and 2014 are presented below.

$$\begin{array}{c} \textbf{ELLIOTT COMPANY}\\ \textbf{Balance Sheets}\\ \textbf{December 31 (in thousands)}\\ \end{array}$$

$$\begin{array}{lcc} &\underline{\textbf{2014}}&\underline{\textbf{2013}}\\[5pt] \text{Current assets}\\ \qquad\text{Cash and cash equivalents}&\text{\$\hspace{10pt}330}&\text{\$\hspace{10pt}360}\\ \qquad\text{Accounts receivable (net)}&\text{\hspace{15pt}470}&\text{\hspace{15pt}400}\\ \qquad\text{Inventory}&\text{\hspace{15pt}460}&\text{\hspace{15pt}390}\\ \qquad\text{Prepaid expenses}&\underline{\text{\hspace{15pt}130}}&\underline{\text{\hspace{15pt}160}}\\ \qquad\qquad\text{Total current assets}&\text{\hspace{8pt}1,390}&\text{\hspace{8pt}1,310}\\ \text{Property, plant, and equipment (net)}&\text{\hspace{15pt}410}&\text{\hspace{15pt}380}\\ \text{Investments}&\text{\hspace{20pt}10}&\text{\hspace{20pt}10}\\ \text{Intangibles and other assets}&\underline{\text{\hspace{15pt}530}}&\underline{\text{\hspace{15pt}510}}\\ \qquad\qquad\text{Total assets}&\underline{\underline{\text{\$\hspace{3pt}2,340}}}&\underline{\underline{\text{\$\hspace{3pt}2,210}}}\\[5pt] \text{Current liabilities}&\text{\$\hspace{10pt}820}&\text{\$\hspace{10pt}790}\\ \text{Long-term liabilities}&\text{\hspace{15pt}480}&\text{\hspace{15pt}380}\\ \text{Stockholders’ equity—common}&\underline{\text{\hspace{8pt}1,040}}&\underline{\text{\hspace{8pt}1,040}}\\ \qquad\qquad\text{Total liabilities and stockholders’ equity}&\underline{\underline{\text{\$\hspace{3pt}2,340}}}&\underline{\underline{\text{\$\hspace{3pt}2,210}}}\\ \end{array}$$

$$\begin{array}{c} \textbf{ELLIOTT COMPANY}\\ \textbf{Income Statements}\\ \textbf{For the Year Ended December 31 (in thousands)}\\ \end{array}$$

$$\begin{array}{lcc} &\underline{\textbf{2014}}&\underline{\textbf{2013}}\\[5pt] \text{Sales revenue}&\underline{\text{\$\hspace{2pt}3,800}}&\underline{\text{\$\hspace{2pt}3,460}}\\ \text{Cost and expenses}\\ \qquad\text{Cost of goods sold}&\text{\hspace{15pt}970}&\text{\hspace{15pt}890}\\ \qquad\text{Selling \& administrative expenses}&\text{\hspace{8pt}2,400}&\text{\hspace{8pt}2,330}\\ \qquad\text{Interest expense}&\underline{\text{\hspace{20pt}10}}&\underline{\text{\hspace{20pt}20}}\\ \qquad\qquad\text{Total costs and expenses}&\underline{\text{\hspace{8pt}3,380}}&\underline{\text{\hspace{8pt}3,240}}\\ \text{Income before income taxes}&\text{\hspace{15pt}420}&\text{\hspace{15pt}220}\\ \text{Income tax expense}&\underline{\text{\hspace{15pt}168}}&\underline{\text{\hspace{20pt}88}}\\ \text{Net income}&\underline{\underline{\text{\$\hspace{10pt}252}}}&\underline{\underline{\text{\$\hspace{10pt}132}}}\\[5pt] \end{array}$$

Compute the following ratios for 2014 and 2013.

(d) Return on assets. (Assets on December 31, 2012, were $1,900.)

The chemical composition of the repeat unit for nylon 6,6 is given by the formula $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{N}_{2} \mathrm{O}_{2}$. Atomic weights for the constituent elements are $A_{\mathrm{C}}=12, A_{\mathrm{H}}=1, A_{\mathrm{N}}=14,$ and $A_{\mathrm{O}}=16$. According to this chemical formula (for nylon 6,6), the percentage (by weight) of carbon in nylon 6,6$is most nearly (A) 31.6% (B) 4.3% (C) 14.2% (D) 63.7%

Bao Wao Designs Inc. purchased a computerized blueprint printer that will assist in the design and display of plans for factory layouts. The cost of the printer was $22,500, and its expected useful life is four years. The company can probably sell the printer for$2,500 at the end of four years. The printer is expected to last 6,000 hours. It was used 1,200 hours in year 1; 1,800 hours in year 2; 2,400 hours in year 3; and 600 hours in year 4.

Required

1. Compute the annual depreciation and carrying value for the new blueprint printer for each of the four years (round to the nearest dollar where necessary) under each of the following methods: (a) straight-line, (b) production, and (c) double-declining-balance.

2. If the printer is sold for $12,000 after year 2, what would be the gain or loss under each method?

3. What conclusions can you draw from the patterns of yearly depreciation and carrying value in requirement 1? Do the three methods differ in their impact on profitability? Do they differ in their effect on the company’s operating cash flows? Explain.

Selected financial data of two competitors, Home Depot and Lowe’s, are presented here. (All dollars are in millions.) Suppose the data were taken from the 2014 financial statements of each company.

$$\begin{array}{c} \underline{\textbf{Income Statement Data for Year}}\\ \end{array}$$

$$\begin{array}{lcc} &\underline{\textbf{Home Depot}}&\underline{\textbf{Lowe's}}\\[3pt] \text{Net sales}&\text{\$\hspace{1pt}77,349}&\text{\$\hspace{1pt}48,283}\\ \text{Cost of goods sold}&\text{\hspace{6pt}51,352}&\text{\hspace{6pt}31,556}\\ \text{Selling and administrative expenses}&\text{\hspace{6pt}18,570}&\text{\hspace{6pt}12,022}\\ \text{Interest expense}&\text{\hspace{18pt}696}&\text{\hspace{18pt}239}\\ \text{Other income}&\text{\hspace{23pt}74}&\text{\hspace{23pt}45}\\ \text{Income taxes}&\underline{\text{\hspace{11pt}2,410}}&\underline{\text{\hspace{11pt}1,702}}\\ \text{Net income}&\underline{\underline{\text{\$\hspace{5pt}4,395}}}&\underline{\underline{\$\text{\hspace{5pt}2,809}}}\\ \end{array}$$

$$\begin{array}{c} \underline{\textbf{Balance Sheet Data (End of Year)}}\\ \end{array}$$

$$\begin{array}{lcc} &\underline{\textbf{Home Depot}}&\underline{\textbf{Lowe's}}\\[3pt] \text{Current assets}&\text{\$\hspace{1pt}14,674}&\text{\$\hspace{5pt}8,686}\\ \text{Noncurrent assets}&\underline{\text{\hspace{6pt}29,650}}&\underline{\text{\hspace{5pt}22,183}}\\ \text{Total assets}&\underline{\underline{\text{\$\hspace{1pt}44,324}}}&\underline{\underline{\$\text{\hspace{1pt}30,869}}}\\[8pt] \text{Current liabilities}&\text{\$\hspace{1pt}12,706}&\text{\$\hspace{5pt}7,751}\\ \text{Long-term liabilities}&\text{\hspace{6pt}13,904}&\text{\hspace{10pt}7,020}\\ \text{Total stockholders’ equity}&\underline{\text{\hspace{6pt}17,714}}&\underline{\text{\hspace{5pt}16,098}}\\ \text{Total liabilities and stockholders’ equity}&\underline{\underline{\text{\$\hspace{1pt}44,324}}}&\underline{\underline{\$\text{\hspace{1pt}30,869}}}\\[8pt] \text{Net cash provided by operating activities}&\text{\$\hspace{1pt}5,727}&\text{\$\hspace{1pt}4,347}\\ \text{Cash paid for capital expenditures}&\text{\$\hspace{1pt}3,558}&\text{\$\hspace{1pt}4,010}\\ \text{Dividends paid}&\text{\$\hspace{1pt}1,709}&\text{\hspace{9pt}\$428}\\[3pt] \text{Average shares outstanding}&\text{\hspace{6pt}1,849}&\text{\hspace{6pt}1,481}\\ \end{array}$$

Instructions

For each company, compute these values and ratios.

(b) Current ratio. (Round to two decimal places.)

Condensed balance sheet and income statement data for Sadecki Corporation are presented here and on the next page.

$$\begin{array}{c} \textbf{SADECKI CORPORATION}\\ \textbf{Balance Sheets}\\ \textbf{December 31}\\ \end{array}$$

$$\begin{array}{lcc} \underline{\textbf{Assets}}&\underline{\textbf{2014}}&\underline{\textbf{2013}}\\[3pt] \text{Cash}&\text{\$\hspace{5pt}28,000}&\text{\$\hspace{5pt}20,000}\\ \text{Receivables (net)}&\text{\hspace{10pt}70,000}&\text{\hspace{10pt}62,000}\\ \text{Other current assets}&\text{\hspace{10pt}90,000}&\text{\hspace{10pt}73,000}\\ \text{Long-term investments}&\text{\hspace{10pt}62,000}&\text{\hspace{10pt}60,000}\\ \text{Property, plant, and equipment (net)}&\underline{\text{\hspace{5pt}510,000}}&\underline{\text{\hspace{5pt}470,000}}\\ \text{Total assets}&\underline{\underline{\text{\$\hspace{1pt}760,000}}}&\underline{\underline{\$\text{\hspace{1pt}685,000}}}\\[8pt] \underline{\textbf{Liabilities and Stockholders’ Equity}}\\[3pt] \text{Current liabilities}&\text{\$\hspace{5pt}75,000}&\text{\$\hspace{5pt}70,000}\\ \text{Long-term liabilities}&\text{\hspace{10pt}80,000}&\text{\hspace{10pt}90,000}\\ \text{Common stock}&\text{\hspace{5pt}330,000}&\text{\hspace{5pt}300,000}\\ \text{Retained earnings}&\underline{\text{\hspace{5pt}275,000}}&\underline{\text{\hspace{5pt}225,000}}\\ \text{Total liabilities and stockholders’ equity}&\underline{\underline{\text{\$\hspace{1pt}760,000}}}&\underline{\underline{\$\text{\hspace{1pt}685,000}}}\\ \end{array}$$

$$\begin{array}{c} \textbf{SADECKI CORPORATION}\\ \textbf{Income Statements}\\ \textbf{For the Years Ended December 31}\\ \end{array}$$

$$\begin{array}{lcc} &\underline{\textbf{2014}}&\underline{\textbf{2013}}\\[3pt] \text{Sales revenue}&\text{\$\hspace{1pt}750,000}&\text{\$\hspace{1pt}680,000}\\ \text{Cost of goods sold}&\text{\hspace{6pt}440,000}&\text{\hspace{6pt}400,000}\\ \text{Operating expenses (including income taxes)}&\underline{\text{\hspace{6pt}240,000}}&\underline{\text{\hspace{6pt}220,000}}\\ \text{Net income}&\underline{\underline{\text{\$\hspace{6pt}70,000}}}&\underline{\underline{\$\text{\hspace{6pt}60,000}}}\\ \end{array}$$

Additional information:

$$\begin{array}{lrr} \text{Net cash provided by operating activities}&\text{\$82,000}&\text{\$56,000}\\ \text{Cash used for capital expenditures}&\text{\$45,000}&\text{\$38,000}\\ \text{Dividends paid}&\text{\$20,000}&\text{\$15,000}\\ \text{Average number of shares outstanding}&\text{33,000}&\text{30,000}\\ \end{array}$$

Instructions

Compute these values and ratios for 2013 and 2014.

(e) Free cash flow.

Factorize the polynomial $z^2-8 z-10$ completely. If the polynomial is not factorable, write prime.

Calculate the radius of a tantalum $\mathrm{(Ta)}$ atom, given that $\mathrm{Ta}$ has a BCC crystal structure, a density of $16.6 ~\mathrm{g} / \mathrm{cm}^{3}$, and an atomic weight of $180.9~\mathrm{ g/mol}$.

The mass ratios of $^ { 40 } \mathrm {Ar}$ to $^ { 40 } \mathrm { K }$ can also be used to date geological materials. Potassium-40 decays by two processes:

$$_ { 19 } ^ { 40 } \mathrm { K } + _ { - 1 } ^ { 0 } \mathrm { e } \longrightarrow _ { 18 } ^ { 40 } \mathrm { Ar } ( 10.7 \% ) \quad \quad t _ { 1 / 2 } = 1.27 \times 10 ^ { 9 }\ \mathrm {yr} \\ _ { 19 } ^ { 40 } \mathrm { K } \longrightarrow _ { 20 } ^ { 40 } \mathrm { Ca } + _ { - 1 } ^ { 0 } \mathrm { e } ( 89.3 \% )$$

How will the measured age of a rock compare with the actual age if some $^ { 40 } \mathrm {Ar}$ has escaped from the sample?

Selected financial data of two competitors, Home Depot and Lowe’s, are presented here. (All dollars are in millions.) Suppose the data were taken from the 2014 financial statements of each company.

$$\begin{array}{c} \underline{\textbf{Income Statement Data for Year}}\\ \end{array}$$

$$\begin{array}{lcc} &\underline{\textbf{Home Depot}}&\underline{\textbf{Lowe's}}\\[3pt] \text{Net sales}&\text{\$\hspace{1pt}77,349}&\text{\$\hspace{1pt}48,283}\\ \text{Cost of goods sold}&\text{\hspace{6pt}51,352}&\text{\hspace{6pt}31,556}\\ \text{Selling and administrative expenses}&\text{\hspace{6pt}18,570}&\text{\hspace{6pt}12,022}\\ \text{Interest expense}&\text{\hspace{18pt}696}&\text{\hspace{18pt}239}\\ \text{Other income}&\text{\hspace{23pt}74}&\text{\hspace{23pt}45}\\ \text{Income taxes}&\underline{\text{\hspace{11pt}2,410}}&\underline{\text{\hspace{11pt}1,702}}\\ \text{Net income}&\underline{\underline{\text{\$\hspace{5pt}4,395}}}&\underline{\underline{\$\text{\hspace{5pt}2,809}}}\\ \end{array}$$

$$\begin{array}{c} \underline{\textbf{Balance Sheet Data (End of Year)}}\\ \end{array}$$

$$\begin{array}{lcc} &\underline{\textbf{Home Depot}}&\underline{\textbf{Lowe's}}\\[3pt] \text{Current assets}&\text{\$\hspace{1pt}14,674}&\text{\$\hspace{5pt}8,686}\\ \text{Noncurrent assets}&\underline{\text{\hspace{6pt}29,650}}&\underline{\text{\hspace{5pt}22,183}}\\ \text{Total assets}&\underline{\underline{\text{\$\hspace{1pt}44,324}}}&\underline{\underline{\$\text{\hspace{1pt}30,869}}}\\[8pt] \text{Current liabilities}&\text{\$\hspace{1pt}12,706}&\text{\$\hspace{5pt}7,751}\\ \text{Long-term liabilities}&\text{\hspace{6pt}13,904}&\text{\hspace{10pt}7,020}\\ \text{Total stockholders’ equity}&\underline{\text{\hspace{6pt}17,714}}&\underline{\text{\hspace{5pt}16,098}}\\ \text{Total liabilities and stockholders’ equity}&\underline{\underline{\text{\$\hspace{1pt}44,324}}}&\underline{\underline{\$\text{\hspace{1pt}30,869}}}\\[8pt] \text{Net cash provided by operating activities}&\text{\$\hspace{1pt}5,727}&\text{\$\hspace{1pt}4,347}\\ \text{Cash paid for capital expenditures}&\text{\$\hspace{1pt}3,558}&\text{\$\hspace{1pt}4,010}\\ \text{Dividends paid}&\text{\$\hspace{1pt}1,709}&\text{\hspace{9pt}\$428}\\[3pt] \text{Average shares outstanding}&\text{\hspace{6pt}1,849}&\text{\hspace{6pt}1,481}\\ \end{array}$$

Instructions

For each company, compute these values and ratios.

(f) Compare the liquidity, profitability, and solvency of the two companies.