A firm which is unleveraged holds 1million shares priced at £80 each. The firm is looking to change its capital structure by borrowing £50 million in debt and repurchasing shares. The loan contract stipulates that the firm will be required to pay off £10 million of its debt every year. Calculate the value of the restructured firm if the tax rate is 40% and the cost of debt is 8%.

1. The target capital structure for a firm is 40% common stock, 10% preferred stock and 50% debt. If the cost of common equity is 18%, the cost of preferred stock is 10%, the before-tax cost of debt is 8%, and the firm’s tax rate is 35%. What is its weighted average cost of capital?

Indicate the detailed steps on how to use a FINANCIAL CALCULATOR to solve the problems.

Seven fair coins are flipped. The outcomes are assumed to be independent. Let X be the number of heads.

What is the probability that X < 3?

What is the probability that X ≥ 4?

What is the probability that 3 ≤ X < 7

How has the Middle East affected American politics, both domestic and foreign since 1968? Give at least seven (7) examples of influential Middle Eastern events to support your statement.

1. (25 points) The following is a simplified duopoly model of competition between two firms. Each firm is restricted to producing 25, 35, 50 or 100 units of output. The details of how the payoffs are derived are unimportant because payoffs are all given in the table below.

                                                                                  FIRM 2

1. (5 points) Firms simultaneously choose the quantity of outputs to produce, and then profits are realized. Find if there are any dominant strategies for the firms or not. In your response, make sure that you define what a dominant strategy is. Also describe the entire process that helped you in making that determination.

2. (5 points) Find the Nash equilibrium(s) in the game. Justify whether it is a Nash equilibrium or not. Describe in words.

3. (7.5 points) Now assume that FIRM 1 is the Stackelberg leader in this market. And FIRM 2 is the follower. Being the leader, FIRM 1 makes the first move in choosing the quantity of output, followed by FIRM 2. Draw the extensive form or the game tree for this sequential form game.

(7.5 points) Using the game tree, now determine the sub-game perfect Nash equilibrium(s). Describe the process that helps you in determining it

Let the random variable X represent a student’s score on an IQ test. Suppose that student IQ scores are Normally distributed with a mean of 100 and a standard deviation of 15.

Part A.Any student who scores at least 130 on an IQ test would be considered gifted. If a student has scored 130 on an IQ test, what percentile does this score represent? Part B.In a class of 50 students, how many would you expect to score at least 115 on an IQ test?

Part C.Suppose that 10 students are randomly selected from a large school. What is the chance that at least 3 of them will have an IQ score greater than 125 (use binomial PMF)

  Dillon Labs has asked its financial manager to measure the cost of each specific type of capital as well as the weighted average cost of capital. The weighted average cost is to be measured by using the following​ weights:

45%

​long-term debt,

15​%

preferred​ stock, and

40​%

common stock equity​ (retained earnings, new common​ stock, or​ both). The​ firm's tax rate is

23​%.

Debt The firm can sell for

​$1015

a

12-year,

​$1,000​-par-value

bond paying annual interest at a

7.00​%

coupon rate. A flotation cost of

44​%

of the par value is required.

Preferred stock  

8.00%

​(annual dividend) preferred stock having a par value of

​$100

can be sold for

​$88

An additional fee of

​$5

per share must be paid to the underwriters.

Common stock  The​ firm's common stock is currently selling for

​$60

per share. The stock has paid a dividend that has gradually increased for many​ years, rising from

​$2.75

ten years ago to the

​$4.70

dividend​ payment,

Upper D 0D0​,

that the company just recently made. If the company wants to issue new new common​ stock, it will sell them

​$2.00

below the current market price to attract​ investors, and the company will pay

​$4.00

per share in flotation costs.  

a.  Calculate the​ after-tax cost of debt.

b.  Calculate the cost of preferred stock.

c.  Calculate the cost of common stock​ (both retained earnings and new common​ stock).

d.  Calculate the WACC for Dillon Labs.

a.  The​ after-tax cost of debt using the​ bond's yield to maturity​ (YTM) is _____ ​%.

​(Round to two decimal​ places.)

The​ after-tax cost of debt using the approximation formula is ____%.

​(Round to two decimal​ places.)

b.  The cost of preferred stock is _____ ​%.

​(Round to two decimal​ places.)

c.  The cost of retained earnings is ____​%.

​(Round to two decimal​ places.)

The cost of new common stock is _____​%.

​(Round to two decimal​ places.)d.  

Using the cost of retained​ earnings, the​ firm's WACC is ____%.

​(Round to two decimal​ places.)

Using the cost of new common​ stock, the​ firm's WACC is

___ ​%.

​(Round to two decimal​ places.)

Let N1=40,X1=20, N2=40 AND X2=10.

At the 0.01 level of significance, is there evidence of a significant difference between the two population proportions.

Calculate the test statistic Zstat, based on the difference P1-P2.

A) The test statistic, Zstat is:

B) Calculate the P-value

C) Construct a 95​% confidence interval estimate of the difference between the two population proportions.

D) Construct a 99% confidence interval estimate of the difference between the two population proportions.

• Write a Java program that will add the digits of a person’s birth date to obtain a single digit to generate a numerology number.
• Write one separate method for each of the following tasks (it goes w/o saying that you will have a main() method along with these):
  • date validating
  • date crunching

First: Get a Date

Numerology has been used since ancient times to shed light on relationships, health, and global events. Each element in a birth date is believed to possess a special numerical significance. We are going to develop our own rudimentary numerology prediction program. The first thing to do is to ask the user to enter a birth date to process.

You will need to indicate to your user that they need to enter the month, day and year in that order separated by spaces and forward slashes, which look like this: /. An example would be 12 / 25 / 2112.  The spaces must be present between the numeric and character input.

Second: Validate the Date

The important and time-consuming portion of this program is validating your input from the user. This means that you need to check to make sure the month is between 1 and 12, the day is appropriate for the month, and the year is between 1500 and 3000, inclusive.

By “the day is appropriate for the month and year”, this means that if a date of January 32^nd is entered or a date of June 0^th is entered, you should recognize and report that. This also means that you should check to see that if the year is a leap year, you should allow February 29^th and if it's not a leap year, you should disallow February 29^{th .}

• Allow the user to input the entire date before you validate it.
• You should continuously re-prompt the user for a date until a valid date is entered (you should use a 'while' loop for this).
• If one part of the date fails (month, day, or year), re-prompt for the entire date again. Do not simply re-prompt for the offending part of the date. Output appropriate error messages for the incorrect dates. See the example runs for sample error messages.

Third: Crunch the Date

Then, you need to calculate a single digit from the birth date. For example, if your birth date is 3/19/1955 you add 3+1+9+1+9+5+5 to get 33. You would then break this apart and add 3+3 to get 6.

Once you have calculated the single-digit, PRINT it on the console (see the sample test runs).

• You will need to be careful because it is possible to have to “fold” the number more than just once, as in the above example. For example, if the birth date was 7/5/1942, you would add up the individual digits 7+5+1+9+4+2 to get 28, then you would need to add 2 + 8 to get 10. This is still a two-digit number, and needs to be added again – 1 + 0 – to get a single-digit result of 1.
• You can simplify the process by adding the month day and year together first (i.e., 7+5+1942, to get 1954) and then breaking down and adding that result (1+9+5+4), which results in 19, which needs to be broken down again to get 1+9 which results in 10, which then results in 1+0, or 1. You should never have to crunch a number more than 3 times and will usually only need to add the digits once.

Solution Suggestions

• It might actually be easier to work backward solving this program, like this, checking each step as you complete it:
  • Then add the code to take a date and crunch it down to a single digit. For simply testing this code, don’t worry about validating the date or input format yet; declare three variables (for example month, date, year), read in the date to process from the user, and then output the final single-digit number.
  • Finally, add code to validate the date that you read from the keyboard before crunching it. Validation will need to include tests for the month, day, and year as well as for using forward slashes between those pieces of information.
  • Make sure that your program continuously prompts the user for a date until a valid date is entered.
  • Make sure to allow the user to enter the entire date before validating it. In other words, don't just validate the month, then validate the day and then validate the year. Allow the entire date to be entered, then validate it and output an appropriate error message, repeating input if necessary.

Goals

• Use most of the concepts in Java that we have learned so far: if/else, while, methods.
  • arrays can be used but not required.
• Use only the data type int for numbers in this program; there’s no need to calculate floating-point numbers.
• Solve a moderately complex Java program using the techniques you’ve learned so far.

Points to Think About

• Validate to make sure that the year is between 1500 and 3000, inclusive.
• Validate to make sure that the month is between 1 and 12, inclusive.
• Validate to make sure that the day is appropriate for the month (at least >=1 and <= 28, 29, 30 or 31 depending on which month and year it is).
• Validate that the user uses forward slashes (/) between the month, day, and year.

MCQ

Which of the following constraint is not linear

   x + 2y ≤ 8

         5y≤ 11

   3xy + 2y≤ 9

   x + y ≤ 2

q2.     When the value of the Correlation coefficient r =0, then it has

Perfect positive correlation

No correlation

Positive correlation

Perfect negative correlation

q3

A furniture manufacturer produces two types of display cabinets Type A and Type B Each month x of type A and y of type B are produced. Profit on type A is 300SR and profit on type B is 150SR. The following constraints control monthly production :(i)              Not more than 50 display cabinets of type A and 40 display cabinets of type B can be made

(ii)            To show a profit at least 60 display cabinets in all must be made.

(iii)           The maximum number of display cabinets that can be produced is 80.

How many display cabinets of type A must be produced per month to maximize the profit:

80

50

30

40

q4

For the following Linear programming problemObjective to Maximize p= 50x + 20y

Subject to 20x + 40y ≤ 4000

                 100x + 50y ≤ 8000

                               x ≤ 60

                         x , y ≥ 0

Find which one is the optimal solution

( 60,40)

( 60,0 )

( 40,80 )

( 0, 100)

q5

  The following table shows the number of Motor registrations in a certain territory and the sales of Motor tyres by a firm in that territory,

Motor Registrations(x)

600

630

720

750

800

Number of Tyres sold(y)

1250

1100

1300

1350

1500

then the regression equation to estimate the sale of tyres when the motor registration is known is given by

  y = 1.4928x + 255.04

   y = 2.4444x + 355.09

   y = 3.4229x + 155.04

   y = 5.5674x + 786.09

q6

Most systems use a queue discipline known as

   Earliest due date

   Critical ratio

    Shortest processing time

   FIFO

q7

If the utilization factor for any M/M/1 model is 0.85 , then the percent idle time must be

0.25

0.15

0.45

None of the above

q8

Which of the following equalities is correct

SST = SSE + SSR

   SST = SSR – SSR

   SST = SST – SSE

None of the above