I want to to calculate the area between the x-axis and the function f(x) = sin(x) on the interval [0, pi]. The area we seek is enclosed in a rectangle bounded by the curves. x = 0, x = pi, y = 0, y = 1. Since we know the area of the rectangle is pi, we can generate random points inside the rectangle and keep track of how many of those points lie below the curve y = sin(x). A bit of algebra involving ratios, and you can estimate the area under the curve.

For the purposes of this task, we can assume that we know the value of pi, as provided by Matlab's built in library of constants. We assume that we do not know the true value of the integral (area), and so as stopping criteria, we will use percent change. I want the process to terminate when [A(k) - A(k-1)]/A(k-1) is less than 0.01.

You should try running the program with an error tolerance of 0.001 just to see how much longer it takes. You may have to terminate the process, as getting that level of precision might take a great many random numbers.

In the above notation, A(k) represents the approximated Area when 10^k random points are generated. Use k values of 0, 1, 2, 3, etc. Non-integer values of k will produce a non-integer value of 10^k, and I don't now if your code could interpret that correctly.

1. Jacqueline and Keith Sommers are considering the implications of refinancing their 30-year mortgage (interest rate = 7.25%) that they purchased 5 years ago at $300,000 (20% down payment and 80% mortgage loan monthly payment). Now after 5 years (60 monthly payments) the balance of loan has been reduced to $226,509.07.

Rates have declined considerably, and a major refinancing frenzy is underway.

They are trying to determine whether they should go in for a 15-year mortgage at 2.75% per year and whether they should ‘cash out’ the excess equity that has been built over the past 5 years.

Required:

a. What is Jacqueline and Keith’s monthly mortgage payment prior to the refinancing?

b. What percentage of the second payment was interest and what percentage applied to payment of the loan?

c. During the first 5 years, how much has the couple paid towards the mortgage. What proportion of this was applied toward interest?

d. Had the couple opted for the 15-year mortgage (15 year, 6.25%), how much higher would their monthly payment have been?

e. If the house is currently worth $355,000 and most lenders are willing to lend up to 90% of home value, how much excess equity can the Sommers cash out?

f. Under the original 15-year, 6.25% mortgage, how much interest would have been paid over the life of the loan? How does this compare with the 7.25%, 30-year mortgage? Please show all work.

Sterling, Inc. is a manufacturer of state-of-the-art computers. For the past ten years, Sterling has acquired all of its microchips from NoBugs Corporation, the only producer of chips meeting Sterling's high specifications. The relationship has been mutually profitable. Sterling could not have built its reputation as an industry leader without NoBugs's reliable and consistently high-quality products; Sterling's business has enabled NoBugs to grow rapidly while providing its investors with an attractive rate of return. Some months ago, several of Sterling's computers exploded shortly after installation. Upon investigation, Sterling discovered that tiny imperfections in NoBugs's microchips had aggravated a dormant design defect in the computers, causing the explosions. Analysis of the chips indicated that they were indeed below specifications and that the imperfections were caused by a slight miscalibration of NoBugs's encoding equipment. NoBugs recalibrated the equipment and promptly resumed production of perfect chips. Sterling's losses from the explosions - lost profits, out-of-pocket costs associated with compensating customers for the explosions, and injury to business reputation - are estimated to exceed $20 million. Sterling and NoBugs disagree on the amount of the loss for which NoBugs should be responsible. Sterling has a strong legal case for breach of contract against NoBugs. Sterling's CEO is considering a lawsuit. She asks you to prepare a report discussing litigation strategy and the advantages and disadvantages of litigation; and discussing pretrial planning should the company opt for litigation.

1. Maria goes to a shooting range. Based on her previous times at the shooting range, she believes she has a 53% chance of hitting the target. Suppose that as part of a training exercise, she has to take ten shots at a moving target.

1. What characteristics of this scenario indicate that you are working with Bernoulli trials?            (3 points)
2. What is the probability that she hits the 4^th target?    (1 point)
3. What is the probability that the first time she hits a target is not until her fourth shot?   (3 points)

Consider the question: What is the probability that she will hit 5 of the targets? Notice that this question is talking about any 5 of the targets and that there are many scenarios in which this could happen. Thus we should apply the binomial model to answer this question. There are two built-in commands for the binomial model in your graphing calculator, binompdf and binomcdf and they can be found by going to 2^nd DISTR and choose option A or B. Use one of these commands to answer the questions (d) through (h) below.

4. What is the probability that she will hit 5 targets?     (3 points)
5. What is the probability that she will hit at most 6 targets?     (3 points)
6. What is the probability that she will hit at least 4 targets?     (3 points)
7. What is the probability that she will hit between 4 and 7 targets (inclusive)?    (3 points)
8. What is the probability that she will hit at least one target?    (3 points)
9. What is the mean and standard deviation of the number of targets hit?    (4 points)

The library would like to compare the regression and exponential smoothing models to determine which is a better predictor, using the mean absolute error | (books borrowed) – (model’s estimate)|/n as a measure of prediction quality.

Select the best of the following four options for splitting the data:

A. 15% for training, 15% for validation, 70% for test
B. 15% for training, 70% for validation, 15% for test
C. 70% for training, 15% for validation, 15% for test
D. 55% for training, 15% for cross-validation, 15% for validation, 15% for test

The person who built these models discovered that although the regression model performed much better on the training set, the two models performed about the same on the validation set:

Mean absolute error (training set) Mean absolute error (validation set)

Regression model 110 140

Exponenetial Smoothing Model 140 150

Select all reasonable suggestions below:

A. To choose between the models, we should see which one does better on the training set.

B. The regression model is clearly better, because it does better on the training set and about the same on the validation set.

C. The regression model is probably fit too much to random patterns (i.e., it is overfit), because it performs much worse on the validation set than on the training set.

D. If there had been 20 models, the one that performed best on the validation set would probably not perform as well on the test set as it did on the validation set.

QUESTION 1 [Total = 15 marks]

James and Adrian are starting up their own small business, which involves the development and delivery of an online identity verification service, to which other businesses can sign up for a fee.

James has been working on developing the computer program and delivering the service with the support of friends for some time, with some success; having signed up a few businesses based in Brisbane and becoming a well-known figure in the local industry dealing with identity theft after invitations to speak on the topic at several workshops and conferences, trading under the name of IDSolutions. He has a registered business name and an ABN, but has not incorporated.

Adrian has experience in business and marketing and has proposed that they both invest $30,000 each into leasing some commercial space and engaging professional software developers to work with James, with a view to improving the computer program so as to expand its capacity to cope with a larger load as the business grows. Both James and Adrian are planning to give up other employment and work full time in the business. Apart from the computer equipment and premises leased, the assets of the business will likely consist of licence agreements with a number of businesses who have signed up for the service, James’ already- established program and the goodwill he has already built up (as well as any IP (intellectual property) they choose to register, such as trade marks).

Advise James and Adrian regarding the options they have in terms of the legal form their business can take, and any considerations they should take into account in making their choice.

The Stackpole Company retails two products, a standard and deluxe version of a luggage carrier.

The standard carrier sells for $28, has variable costs of $18, and direct fixed costs of $1,000,000. The deluxe model sells for $50, has variable costs of $30, and direct fixed costs of $1,000,000. The company has common fixed costs of $250,000. The anticipated sales mix for the company is 3:1 or 75/25. The actual level of sales units currently is 250,000 and your target income is $250,000. You expect sales to rise 10% in the coming year.

Directions:

You have been hired to build a CVP model to help the company understand the impact of business conditions on operating income. Your model should include breakeven in units with a pro forma income statement, units sales for a target income of $250,000 with a pro forma income statement, an income statement reflecting actual current sales, margin of safety in dollars and %, and degree of operating leverage. Your model should have the capability of computing B/E, target income, MOS, DOL, and predicting change in income based on a change in sales. Create a dashboard to show these variables.

Once you have built the model, use the model to determine changes to the dashboard variables. In a report to me, your CEO, show the original variables, the changed variables and explain why the change occurred.

1. Sales mix changes to 25/75
2. Common fixed costs increase by $100,000
3. Reduce VC of the standard carrier to $10 per unit

As a global manager, create a scenario for analysis using the three-sector model: Real Loanable Funds Market, Real Goods Market, and the Foreign Exchange Market for Question A. There is no “set” answer here. You are the manager doing the analysis and setting up the scenario. Use your own assumptions.

A. In the post-World War II period, the economies of Japan and Germany were rebuilt, and both economies were able to achieve economies of scale in the steel and automobile industries. In the mid-1990s, India and China built labor-intensive industries in the apparel industry, followed by other labor intensive industries expanded through an export-led growth policy on the part of China. Vietnam followed this type of policy beginning in 1986. The country has achieved stable growth, low inflation, and increasing prosperity. In the early 2000s, South Korea became a major producer of automobiles, and also expanded production in technology and related consumer goods for export. Currently, High Income economies (using the World Bank GNI per capita classification system) in North America, Europe, and the Far East (the Triad Area) engage extensively in trade in consumer goods. We find that the current level of global exports is about $19 trillion. The trade between nations of the Triad Area represents about $9.5 trillion. In the euro-zone, there is a division between stronger nations (Germany and France, for example) compared to other nations facing significant macroeconomic problems (Greece and Spain, for example).

Northwestern College is building a new science building. The initial costs are $10 million once every year for the next four years. The first cash outflow or expense is due one year from today and the last is due four years from today. The new science building will bring in an additional $3 million starting in Year 4 (i.e. four years from today). The additional revenue will grow at 1 percent per year for the next 20 years starting from Year 4. Assume the interest rate is 5 percent. (a) What is the correct interest rate to use for the initial costs (i.e. cash outflows)? Express your answer as a percentage rounded to two decimal places. (i.e. 6.538% would round to 6.54%) (3 points) (b) How many cash inflows are there in the NPV calculation? Express your answer as an integer. (2 points) (c) What is the present value of cash outflows of this project? Your answer should be expressed in the millions of dollars. DO NOT use a dollar sign, and keep three digits after the decimal point. (4 points) (d) What is the present value of cash inflows of this project? Your answer should be expressed in the millions of dollars. DO NOT use a dollar sign, and keep three digits after the decimal point. (4 points) (e) Should the new science building be built according to the NPV rule? Your answer should be either “Y” or “N” without the quotation mark. (2 points)

Sunny Valley Stables Inc. was established on April 1, 2017. The company provides stables, care for animals, and grounds for riding and showing horses. You have been hired as the new assistant financial controller. The following transactions for April 2017 are provided for your review.

1. Received contributions from five investors of $200,000 in cash ($40,000 each).
2. Built a barn for $142,000; paid half the amount in cash on April 1 and signed a three-year note payable for the balance.
3. Provided $15,260 in animal care services for customers, all on credit.
4. Rented stables to customers who cared for their own animals; received cash of $13,200.
5. Received from a customer $1,500 to board her horse in May, June, and July (record as Deferred Revenue).
6. Purchased hay and feed supplies on account for $3,210.
7. Paid $840 in cash for water utilities incurred in the month.
8. Paid $1,700 on accounts payable for previous purchases.
9. Received $1,000 from customers on accounts receivable.
10. Paid $4,000 in wages to employees who worked during the month.
11. At the end of the month, prepaid a two-year insurance policy for $3,600.
12. Received an electric utility bill for $1,200 for usage in April; bill will be paid next month.

Required:
1. & 2. Record in the T-accounts the effects of each transaction for Sunny Valley Stables in April, referencing each transaction in the accounts with the transaction letter. All accounts begin with zero balances. Show the unadjusted ending balances in the T-accounts.

3. Prepare an unadjusted trial balance as of April 30, 2017.