INANCIAL LEVERAGE EFFECTS

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $10 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: $4.1 million with a 0.2 probability, $1.7 million with a 0.5 probability, and $0.5 million 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. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

Debt/Capital ratio is 10%, interest rate is 9%.

Debt/Capital ratio is 50%, interest rate is 11%.

Debt/Capital ratio is 60%, interest rate is 14%.

FINANCIAL LEVERAGE EFFECTS

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $11 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: $5.1 million with a 0.2 probability, $2.8 million with a 0.5 probability, and $0.5 million 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. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

Debt/Capital ratio is 10%, interest rate is 9%.

Debt/Capital ratio is 50%, interest rate is 11%.

Debt/Capital ratio is 60%, interest rate is 14%.

An oil company has some land that is reported to possibly contain oil. The company classifies such land into four categories by the total number of barrels that are expected to be obtained from the well, a 350,000 barrel well, 100,000 barrel well, 10,000 barrel well, and a dry well. The company is faced with deciding whether to drill for oil, to unconditionally lease the land, or to conditionally lease the land at a rate depending upon oil strike. The cost of drilling the well is $150,000 if it is a producing well and the cost of drilling is $100,000 if it is a dry well. For producing well, the profit per barrel of oil is $1.50, after deduction of processing and all other costs except drilling costs.

Under the unconditional lease agreement, the company receives $30,000 for the land whereas for the conditional lease agreement the company receives 50 cents for each barrel of oil extracted if it is a 350,000 or 100,000 barrel oil strike and nothing if otherwise.

Which alternative should be selected based on the following criteria?

     a) LaPlace

     b) Maximax

     c) Maximin

     d) Hurwicz with a = 0.3

     e) MinMax with regret

Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows.

(a)

Consider a random sample of size n = 2 (two customers), and let

X

be the sample mean number of packages shipped. Obtain the probability distribution of

X.

(b)

Refer to part (a) and calculate

P(X ≤ 2.5).

(c)

Again consider a random sample of size n = 2, but now focus on the statistic R = the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of R. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).]

(d)

If a random sample of size n = 4 is selected, what is

P(X ≤ 1.5)?

[Hint: You should not have to list all possible outcomes, only those for which

x ≤ 1.5.]

The production line at the Heinz ketchup factory is calibrated to fill bottles of ketchup with no more than 24 ounces of ketchup in each bottle. We certainly do not want ketchup to spill onto the assembly line equipment; that would create a mess.

In order to test how well our machinery is working, a sample of 70 bottles are randomly selected from a days production of filled ketchup bottles and the contents of each bottle are measured. The sample reveled a mean of 24.1 ounces per bottle, with a sample standard deviation of 0.3 ounces.

Use an α = .05.

A. Provide the appropriate hypothesis test criteria:

B. Using the data from the sample, answer the five fill-in-the-blank questions, and make the correct hypothesis test conclusion.

Based on these results, we should:

• Reject Ho

• Accept Ho

C. Should Heinz shut down the production line?

This question will be sent to your instructor for grading.

Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6,P(B) = 0.4,and P(A ∩ B) = 0.3,suppose that P(C) = 0.2,P(A ∩ C) = 0.12,P(B ∩ C) = 0.1, and P(A ∩ B ∩ C) = 0.08.

a)What is the probability that the selected student has at least one of the three types of cards?

b)What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card?

c)Calculate P(B | A)and P(A | B).

P(B | A)=

P(A | B)=

d)If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard?

e)Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards?

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $15 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 million with a 0.2 probability, $2.2 million with a 0.5 probability, and $0.4 million 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. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

RÔE = %

σ = %

CV =

Debt/Capital ratio is 10%, interest rate is 9%.

RÔE = %

σ = %

CV =

Debt/Capital ratio is 50%, interest rate is 11%.

RÔE = %

σ = %

CV =

Debt/Capital ratio is 60%, interest rate is 14%.

RÔE = %

σ = %

CV =

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $10 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, $2.9 million with a 0.5 probability, and $0.9 million 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. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

Debt/Capital ratio is 10%, interest rate is 9%.

Debt/Capital ratio is 50%, interest rate is 11%.

Debt/Capital ratio is 60%, interest rate is 14%.

Q4. A rigid strip footing is constructed on a layered soil deposit, as shown in the figure.

Before construction of the footing, laboratory tests on a saturated clay sample, taken at a depth of 6 m below the ground surface, gave the following results:

• Compression index: C_c = 0.3,
• Recompression index: C_r = 0.08  
• Over consolidation ratio: OCR = 1.5
• Water content: w = 25%
• Specific gravity: G_s = 2.65

Saturated unit weight of clay: g_sat = 19.5 kN/m³

1. Calculate the settlement of the footing due to deformation of the sand layer only. Sand properties are as follows:         

• Total unit weight: g_t = 18 kN/m³             
• Young’s modulus: E_s = 30 MPa                 
• Poisson’s ratio: n = 0.25

2. Based on the elastic theory (Boussinesq’s equation), calculate the change in vertical stress at point A long time after applying the surcharge load.
3. Using the theory of 1-D consolidation, calculate the total settlement of this rigid footing due to consolidation of the clay layer only, long time after applying the total load.

In class, you have seen how to calculate the maximum speed for a car to go around a flat curve (with friction), and for a banked curve (without friction). Here, you will consider the general case. (For each question part below, include a free-body diagram.) a) (3 points) Explain briefly why the car can go around the banked curve safely even without friction, and why that is not the case for the flat curve. b) (5 points) Now consider a curve that is banked so that a car can safely take it at a speed of 85 km/h, even if there were no friction. Assuming the radius of the curve is 68 m, calculate the angle at which it has been built. c) (6 points) For the banked curve, calculate the maximum speed that a car can have to safely go through it if the coefficient of static friction is 0.3. What will happen if the car is faster? d) (6 points) For the same curve, calculate the minimum speed the car must have to safely make it through. What will happen if the car is slower?