The Neal Company wants to estimate next year’s return on equity (ROE) under different financial leverage ratios. Neal’s total capital is $14 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year’s EBIT for three possible states of the world:$4.2 million with a 0.2 probability, $2.8 million with a 0.5 probability, and$700,000 with a 0.3 probability. Calculate Neal’s expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios; then evaluate the results: $$ \begin{matrix} \text{Debt/Capital Ratio} & \text{Interest Rate}\\ \text{0\\%} & \text{--}\\ \text{10} & \text{9\\%}\\ \text{50} & \text{11}\\ \text{60} & \text{14}\\ \end{matrix} $$

Given the following information, calculate the expected value for Firm C’s EPS. Data for Firms A and B are as follows: $\mathrm{E}\left(\mathrm{EPS}_{\mathrm{A}}\right)=\$ 5.10, \sigma_{\mathrm{A}}=\$ 3.61, \mathrm{E}\left(\mathrm{EPS}_{\mathrm{B}}\right)=\$ 4.20$, and $\sigma_{\mathrm{B}}=\$ 2.96$.

$$\begin{matrix} \text{ } & \text{Probability}\\ \text{ } & \text{0.1} & \text{0.2} & \text{0.4} & \text{0.2} & \text{0.1}\\ \text{Firm A: }{\mathrm{EPS}_{\mathrm{A}}} & \text{(\$ 1.50)} & \text{\$ 1.80} & \text{\$ 5.10} & \text{\$ 8.40} & \text{\$ 11.70}\\ \text{Firm B: }{\mathrm{EPS}_{\mathrm{B}}} & \text{(1.20)} & \text{1.50} & \text{4.20} & \text{6.90} & \text{9.60}\\ \text{Firm C: }{\mathrm{EPS}_{\mathrm{C}}} & \text{(2.40)} & \text{1.35} & \text{5.10} & \text{8.85} & \text{12.60}\\ \end{matrix}$$

b. You are given that $\sigma_{\mathrm{C}}=\$ 4.11$. Discuss the relative riskiness of the three firms’ earnings.

Tartan Industries currently has total capital equal to $4 million, has zero debt, is in the 40% federal-plus-state tax bracket, has a net income of$1 million, and distributes 40% of its earnings as dividends. Net income is expected to grow at a constant rate of 3% per year, 200,000 shares of stock are outstanding, and the current WACC is 12.30%. The company is considering a recapitalization where it will issue $2 million in debt and use the proceeds to repurchase stock. Investment bankers have estimated that if the company goes through with the recapitalization, its before-tax cost of debt will be 10% and its cost of equity will rise to 15.5%. a. What is the stock’s current price per share (before the recapitalization)? b. Assuming that the company maintains the same payout ratio, what will be its stock price following the recapitalization? Assume that shares are repurchased at the price calculated in part a.

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is 14 million dollars, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40 percent. The CFO has estimated next year's EBIT for three possible states of the world: 4.2 million dollars with a 0.2 probability, 2.8 million dollars with a 0.5 probability, and 700,000 dollars with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios; then evaluate the results:

$$\begin{array}{cc} \begin{array}{c} \text { Debt/Capital } \\ \text { Ratio } \end{array} & \begin{array}{c} \text { Interest } \\ \text { Rate } \end{array} \\ \hline 0 \text{ percent} & - \\ 10 & 9 \text{ percent} \\ 50 & 11 \\ 60 & 14 \end{array}$$

Is 3.010010001... a repeating decimal? Explain.

Eextract from each given system a maximal subset of irredundant equations: $3 x_{1}+2 x_{2}+2 x_{3}+2 x_{4}=0$, $2 x_{1}+3 x_{2}+3 x_{3}+3 x_{4}=0$,

$$8 x_{1}+7 x_{2}+7 x_{3}+7 x_{4}=0$$

$$\dfrac { M } { 7 } = 15$$

Write sample spaces for the experiments: A person is asked the number of hours (to the nearest hour) he watched television yesterday.

Hartman Motors has $18 million in assets, which were financed with$6 million of debt and $12 million in equity. Hartman’s beta is currently 1.3, and its tax rate is 35$$\mathrm{b}$_$${\mathrm{U}}$.

A company’s fixed operating costs are $430,000, its variable costs are$2.95 per unit, and the product’s sales price is $4.50. What is the company’s break-even point; that is, at what unit sales volume will its income equal its costs?

The Weaver Watch Company sells watches for $\$ 25$, fixed costs are $\$ 140,000$, and variable costs are $\$ 15$ per watch.

a. What is the firm's gain or loss at sales of $8,000$ watches? At $18,000$ watches?

b. What is the break-even point? Illustrate by means of a chart.

c. What would happen to the break-even point if the selling price was raised to $\$ 31$ ? What is the significance of this analysis?

d. What would happen to the break-even point if the selling price was raised to $\$ 31$ but variable costs rose to $\$ 23$ a unit?

Firms HL and LL are identical except for their financial leverage ratios and the interest rates they pay on debt. Each has 20 million dollars in invested capital, has 4 million dollars of EBIT, and is in the 40 percent federal-plus-state tax bracket. Firm HL, however, has a debt-to-capital ratio of 50 percent and pays 12 percent interest on its debt, whereas LL has a 30 percent debt-to-capital ratio and pays only 10 percent interest on its debt. Neither firm uses preferred stock in its capital structure.

a. Calculate the return on invested capital (ROIC) for each firm.

b. Calculate the return on equity (ROE) for each firm.

c. Observing that HL has a higher ROE, LL's treasurer is thinking of raising the debt-to-capital ratio from 30 percent to 60 percent even though that would increase LL's interest rate on all debt to 15 percent. Calculate the new ROE for LL.

A company's fixed operating costs are $\$ 500,000$, its variable costs are $\$ 3.00$ per unit, and the product's sales price is $\$ 4.00$. What is the company's break-even point; that is, at what unit sales volume will its income equal its costs?

Coastal Carolina Heating and Cooling Inc. has a 6-month backlog of orders for its patented solar heating system. To meet this demand, management plans to expand production capacity by 45% with a $20 million investment in plant and machinery. The firm wants to maintain a 35% debt level in its capital structure. It also wants to maintain its past dividend policy of distributing 55% of last year’s net income. In 2016, net income was$5 million. How much external equity must Coastal Carolina seek at the beginning of 2017 to expand capacity as desired? Assume that the firm uses only debt and common equity in its capital structure.