In 2015, Keenan Company paid dividends totaling $3,600,000 on net income of$10.8 million. Note that 2015 was a normal year and that for the past 10 years, earnings have grown at a constant rate of 10%. However, in 2016, earnings are expected to jump to $14.4 million and the firm expects to have profitable investment opportunities of$8.4 million. It is predicted that Keenan will not be able to maintain the 2016 level of earnings growth because the high 2016 earnings level is attributable to an exceptionally profitable new product line introduced that year. After 2016, the company will return to its previous 10% growth rate. Keenan’s target capital structure is 40% debt and 60% equity.

a. Calculate Keenan’s total dividends for 2016 assuming that it follows each of the following policies:

1. Its 2016 dividend payment is set to force dividends to grow at the long-run growth rate in earnings.

2. It continues the 2015 dividend payout ratio.

3. It uses a pure residual dividend policy (40% of the $8.4 million investment is financed with debt and 60% with common equity).

4. It employs a regular dividend-plus-extras policy, with the regular dividend being based on the long-run growth rate and the extra dividend being set according to the residual dividend policy.

b. Which of the preceding policies would you recommend? Restrict your choices to the ones listed but justify your answer.

c. Assume that investors expect Keenan to pay total dividends of$9,000,000 in 2016 and to have the dividend grow at 10% after 2016. The stock’s total market value is $180 million. What is the company’s cost of equity?

d. What is Keenan’s long-run average return on equity?

[Hint: g=Retention rate$\times$ROE=(1.0-Payout rate)(ROE)]

e. Does a 2016 dividend of$9,000,000 seem reasonable in view of your answers to parts c and d? If not, should the dividend be higher or lower? Explain your answer.

Altamonte Telecommunications has a target capital structure that consists of 45% debt and 55% equity. The company anticipates that its capital budget for the upcoming year will be $1,000,000. If Altamonte reports net income of$1,200,000 and it follows a residual dividend payout policy, what will be its dividend payout ratio?

What are the two major subdivisions of the nervous system?

Rubenstein Bros. Clothing is expecting to pay an annual dividend per share of $\$ 0.75$ out of annual earnings per share of $\$ 2.25$. Currently, Rubenstein Bros.' stock is selling for $\$ 12.50$ per share. Adhering to the company's target capital structure, the firm has $\$ 10$ million in total invested capital, of which $40 \%$ is funded by debt. Assume that the firm's book value of equity equals its market value. In past years, the firm has earned a return on equity (ROE) of $18 \%$, which is expected to continue this year and into the foreseeable future.

a. Based on this information, what long-run growth rate can the firm be expected to maintain? (Hint: $\mathrm{g}=$ Retention rate $\times$ ROE.)

b. What is the stock's required return?

c. If the firm changed its dividend policy and paid an annual dividend of $\$ 1.50$ per share, financial analysts would predict that the change in policy will have no effect on the firm's stock price or ROE. Therefore, what must be the firm's new expected long-run growth rate and required return?

d. Suppose instead that the firm has decided to proceed with its original plan of disbursing $\$ 0.75$ per share to shareholders, but the firm intends to do so in the form of a stock dividend rather than a cash dividend. The firm will allot new shares based on the current stock price of $\$ 12.50$. In other words, for every $\$ 12.50$ in dividends due to shareholders, a share of stock will be issued. How large will the stock dividend be relative to the firm's current market capitalization? (Hint: Remember that market capitalization $=\mathrm{P}_0 \times$ number of shares outstanding.)

e. If the plan in part above is implemented, how many new shares of stock will be issued, and by how much will the company's earnings per share be diluted?

Electronics World Inc. paid out $22.4 million in total common dividends and reported$144.7 million of retained earnings at year-end. The prior year’s retained earnings were $95.5 million. What was the net income? Assume that all dividends declared were actually paid.

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 2018, net income was$5 million. How much external equity must Coastal Carolina seek at the beginning of 2019 to expand capacity as desired? Assume that the firm uses only debt and common equity in its capital structure.

True or False$If$A_1$and$A_2$form a partition of a sample space S and if E is an event in S, then$P(A_1|E)= $\dfrac{P(A_2) \cdot P(E|A_2) }{P(E)}$.$

Welch Company is considering three independent projects, each of which requires a $\$ 5$ million investment. The estimated internal rate of return (IRR) and cost of capital for these projects are presented here:

$$\begin{array}{lll}\text { Project } \mathrm{H} \text { (high risk): } & \text { Cost of capital }=16 \% & \text { IRR }=20 \% \\ \text { Project } \mathrm{M} \text { (medium risk): } & \text { Cost of capital }=12 \% & \text { IRR }=10 \% \\ \text { Project L (low risk): } & \text { Cost of capital }=8 \% & \text { IRR }=9 \%\end{array}$$

Note that the projects' costs of capital vary because the projects have different levels of risk. The company's optimal capital structure calls for $50 \%$ debt and $50 \%$ common equity, and it expects to have net income of $\$ 7,287,500$. If Welch establishes its dividends from the residual dividend model, what will be its payout ratio?

r-permutation of $x_1,...,x_n$: ordering of r elements of $x_1,..,x_n$

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.

Water is flowing in a trapezoidal channel at a rate of Q = 20 m^3/s. The critical depth y for such a channel must satisfy the equation

$$0=1-\frac{Q^{2}}{g A_{c}^{3}} B$$

where g = 9.81 m/s^2 , A_c = the cross-sectional area (m^2), and B = the width of the channel at the surface (m). For this case, the width and the cross-sectional area can be related to depth y by B = 3 + y and

$$A_{c}=3 y+\frac{y^{2}}{2}$$

Solve for the critical depth using (a) the graphical method, (b) bisection, and (c) false position. For (b) and (c) use initial guesses of x_l = 0.5 and x_u = 2.5, and iterate until the approximate error falls below 1% or the number of iterations exceeds 10. Discuss your results.

Why do you think wet-rice cultivation is the most common method of growing rice in island Southeast Asia?

After a 5-for-l stock split, Tyler Company paid a dividend of $1.15 per new share, which represents a 7% increase over last year’s pre-split dividend. What was last year’s dividend per share?