A 3-for-2 stock split is being considered by Mammoth Corporation. The equity position of the stockholders is now displayed. Shares of the stock currently cost $120 each. Retained earnings consist of earnings available for Common Stock for the most recent period.

$$\begin{array}{lr} \text { Preferred stock } & \$ 1,000,000 \\ \text { Common stock (100,000 shares at } \$ 3 \text { par) } & 300,000 \\ \text { Paid-in capital in excess of par } & 1,700,000 \\ \text { Retained earnings } & 10,000,000 \\ \quad \text { Total stockholders' equity } & \$ 13,000,000 \end{array}$$

What consequences might the stock split have on Mammoth?

Low-regular-and-extra dividend policy Bennett Farm Equipment Sales, Inc., is in a highly cyclic business. Although the firm has a target payout ratio of 25%, its board realizes that strict adherence to that ratio would result in a fluctuating dividend and create uncertainty for the firm's stockholders. Therefore, the firm has declared a regular dividend of $0.50 per share per year with extra cash dividends to be paid when earnings justify them. Earnings per share for the last several years are shown in the following table.

b. Calculate the difference between the regular 0.50 dividend and a$2.5 payout for each year.

Interest rates on $4$-year Treasury securities are currently $7\%$, while $6$-year Treasury securities yield $7.5 \%$. If the pure expectations theory is correct, what does the market believe that $2$-year securities will be yielding $4$ years from now? Calculate the yield using a geometric average.

One-year Treasury securities yield 4.85%. The market anticipates that 1 year from now, 1-year Treasury securities will yield 5.2%. If the pure expectations theory is correct, what is the yield today for 2-year Treasury securities? Calculate the yield using a geometric average.

The yield on $1$-year Treasury securities is $6 \%, 2$-year securities yield $6.2 \%, 3$-year securities yield $6.3 \%$, and $4$-year securities yield $6.5 \%$. There is no maturity risk premium. Using expectations theory and geometric averages, forecast the yields on the following securities:

A $2$-year security, $1$ year from now

The yield on $1$-year Treasury securities is $6 \%, 2$-year securities yield $6.2 \%, 3$-year securities yield $6.3 \%$, and $4$-year securities yield $6.5 \%$. There is no maturity risk premium. Using expectations theory and geometric averages, forecast the yields on the following securities:

A $1$-year security, $1$ year from now

The yield on $1$-year Treasury securities is $6 \%, 2$-year securities yield $6.2 \%, 3$-year securities yield $6.3 \%$, and $4$-year securities yield $6.5 \%$. There is no maturity risk premium. Using expectations theory and geometric averages, forecast the yields on the following securities:

A $3$-year security, $1$ year from now

One-year Treasury securities yield $5 \%$. The market anticipates that $1$ year from now, $1$-year Treasury securities will yield $6 \%$. If the pure expectations theory is correct, what is the yield today for $2$-year Treasury securities? Calculate the yield using a geometric average.

Using the model in File C11, assuming that a third stock, Stock C, is available for inclusion in the portfolio. Stock C has the following historical returns:

$$\begin{array}{lc} \text{Year} & \text{Stock C's Return, r}_\text{C} \\ \hline 2011 & 32.00 \% \\ 2012 & -11.75 \\ 2013 & 10.75 \\ 2014 & 32.25 \\ 2015 & -6.75 \end{array}$$

Would you prefer to hold the portfolio described in the mentioned problem consisting only of Stocks A and B or a portfolio that also includes Stock C? If others react similarly, how might this fact affect the stocks' prices and rates of return?

You are a manager at Percolated Fiber, which is considering expanding its operations in synthetic fiber manufacturing. Your boss comes into your office, drops a consultant's report on your desk, and complains, "We owe these consultants $\$ 1.7$ million for this report, and I am not sure their analysis makes sense. Before we spend the $\$ 16$ million on new equipment needed for this project, look it over and give me your opinion. "You open the report and find the following estimates (in millions of dollars):

$$\begin{aligned} &\hspace{65mm}\textbf{ Project Year }\\ \hline &\begin{array}{lrrrrr} & \text{1} & \text{2} & \ldots & 9 & \text{10} \\ \hline \text { Sales revenue } & 26 & 26 & & 26 & 26 \\ -\text { Cost of goods sold } & 15.6 & 15.6 & & 15.6 & 15.6 \\ \hline \text {= Gross profit } & 10.4 & 10.4 & & 10.4 & 10.4 \\ -\text { General, sales, and } & 2.24 & 2.24 & & 2.24 & 2.24 \\ \quad \text { administrative expenses } & & & & & \\ -\text { Depreciation } & 2.8 & 2.8 & & 2.8 & 2.8 \\ \hline \text {= Net operating income } & 5.36 & 5.36 & & 5.36 & 5.36 \\ -\text { Income tax } & 1.876 & 1.876 & & 1.876 & 1.876 \\ \hline \text { Net Income } & 3.484 & 3.484 & & 3.484 & 3.484 \end{array} \end{aligned}$$

All of the estimates in the report seem correct. You note that the consultants used straightline depreciation for the new equipment that will be purchased today (year $0$), which is what the accounting department recommended. The report concludes that because the project will increase earnings by $\$ 3.484$ million per year for $10$ years, the project is worth $\$ 34.84$ million. You think back to your halcyon days in finance class and realize there is more work to be done!

First, you note that the consultants have not factored in the fact that the project will require $\$ 14$ million in working capital upfront (year $0$), which will be fully recovered in year $10$ . Next, you see they have attributed $\$ 2.24$ million of general, sales, and administrative expenses to the project, but you know that $\$ 0.64$ million of this amount is overhead that will be incurred even if the project is not accepted. Finally, you know that accounting earnings are not the right thing to focus on!

a. Given the available information, what are the free cash flows in years $0$ through $10$ that should be used to evaluate the proposed project?

b. If the cost of capital for this project is $12 \%$, what is your estimate of the value of the new project?

Hamlin Steel Company wishes to calculate the value of Craft Foundry, a firm that it is considering acquiring for cash. Hamlin wishes to determine the applicable discount rate to use as an input to the constantgrowth valuation model. Craft's stock is not publicly traded. After studying the required returns of firms similar to Craft that are publicly traded, Hamlin believes that an appropriate risk premium on Craft stock is about $5 \%$. The risk-free rate is currently $9 \%$. Craft's dividend per share for each of the past $6$ years is provided in the accompanying table.

$$\begin{array}{cc} \text { Year } & \text { Dividend per share } \\ \hline 2012 & \$ 3.44 \\ 2011 & 3.28 \\ 2010 & 3.15 \\ 2009 & 2.90 \\ 2008 & 2.75 \\ 2007 & 2.45 \end{array}$$

a. Provided that Craft is expected to pay a dividend of $\$ 3.68$ next year, calculate the maximum cash price that Hamlin should pay for each share of Craft.

Bauer Industries is an automobile manufacturer. Management is currently evaluating a proposal to build a plant that will manufacture lightweight trucks. Bauer plans to use a cost of capital of $12.2 \%$ to evaluate this project. Based on extensive research, it has prepared the following incremental free cash flow projections (in millions of dollars):

$$\begin{array}{lccc} & \textbf{ Year 0 } & \textbf{ Years 1-9 } & \textbf{ Year 10} \\ \hline \text { Revenues } & & 103.0 & 103.0 \\ \text { - Manufacturing expenses (other than } & & -36.4 & -36.4 \\ \text { depreciation) } \\ \text { - Marketing expenses } & & -9.6 & -9.6 \\ \text { - Depreciation } & & -14.7& -14.7 \\ \hline \text { - EBIT } & & 42.3 & 42.3\\ \text { - Taxes (34\%) } & & -14.382 & -14.382\\ \hline \text { Unlevered net income } & &27.918 & 27.918 \\ \text { + Depreciation } & & 14.7 & 14.7 \\ \text { - Increases in net working capital } &&-5.3&-5.3 \\ \text { - Capital expenditures } & -147.0 \\ \text { + Continuation value }&& &12.5\\ \hline \text{= Free cash flow}& -147.0& 37.318 &49.818\\ \end{array}$$

a. For this base-case scenario, what is the NPV of the plant to manufacture lightweight trucks?

b. Based on input from the marketing department, Bauer is uncertain about its revenue forecast. In particular, management would like to examine the sensitivity of the NPV to the revenue assumptions. What is the NPV of this project if revenues are $8 \%$ higher than forecast? What is the NPV if revenues are $8 \%$ lower than forecast?

c. Rather than assuming that cash flows for this project are constant, management would like to explore the sensitivity of its analysis to possible growth in revenues and operating expenses. Specifically, management would like to assume that revenues, manufacturing expenses, and marketing expenses are as given in the table for year $1$ and grow by $3 \%$ per year every year starting in year $2$. Management also plans to assume that the initial capital expenditures (and therefore depreciation), additions to working capital, and continuation value remain as initially specified in the table. What is the NPV of this project under these alternative assumptions? How does the NPV change if the revenues and operating expenses grow by $6 \%$ per year rather than by $3 \%$ ?

d. To examine the sensitivity of this project to the discount rate, management would like to compute the NPV for different discount rates. Create a graph, with the discount rate on the $x$-axis and the NPV on the $y$-axis, for discount rates ranging from $5 \%$ to $30 \%$. For what ranges of discount rates does the project have a positive NPV?

Holt Enterprises recently paid a dividend, $D_{0}$, of $\$2.75$. It expects to have nonconstant growth of $18\%$ for $2$ years followed by a constant rate of $6\%$ thereafter. The firm’s required return is $12\%$. How far away is the horizon date?

Consider the three stocks in the following table. Pt represents the price at time t, and Qt represents shares outstanding at time t. Stock C splits two-for-one in the last period.

$$\begin{array}{|l|c|c|c|c|c|c|} \hline & \text{P0} & \text{Q0} & \text{P1} & \text{Q1} & \text{P2} &\text{Q2} \\ \hline \text{A} & 90 & 100 & 95 & 100 & 95 & 100 \\ \hline \text{B} & 50 & 200 & 45 & 200 & 45 & 200 \\ \hline \text{C} & 100 & 200 & 110 & 200 & 55 & 400 \\ \hline \end{array}$$

a. Calculate the rate of return on a price-weighted index of the three stocks for the first period ( t=0 to t=1).

b. What must happen to the divisor for the price-weighted index in year 2?

c. Calculate the rate of return of the price-weighted index for the second period ( t=1 to t=2).