XM, Ltd. was a small engineering firm that built high-tech robotic devices for electronics manufacturers. One very complex device was partially completed at the end of 2018. Barb McLauren, head engineer, knew the experimental technology was a failure and XM would not be able to complete the $20,000,000 contract next year. However, the corporation was getting ready to be sold in January. She told the controller that the device was 80% complete at year-end and on track for successful completion the following spring; the controller accrued 80% of the contract revenue at December 31, 2018. McLauren sold the company in January 2019 and retired. By mid-year, it became apparent that XM would not be able to complete the project successfully and the new owner would never recoup his investment. Requirements

1. For complex, high-tech contracts, how does a company determine the percentage of completion and the amount of revenue to accrue?

2. What action do you think was taken by XM in 2019 with regard to the revenue that had been accrued the previous year?

Implement the Lorenz-63 model in MATLAB, and solve numerically (using MATLAB’s ode45 or other built-in solver) for any random, non-zero initial conditions to reproduce, qualitatively, Figures 3 and 4. Note that, as usual, you should label your axes and make the plots as “pretty” as possible.

The model equations are

dx/ dt = σ(y − x),

dy /dt= x(ρ−z)−y,

dz/dt = xy − βz.
Use parameter values σ = 10, ρ = 28, and β = 8/3.

MoTown Appliances sells built-in ranges for $ 1,400 each. The price includes a two-year warranty. During 2019, the company sells 1,650 ranges. On the basis of past experience, approximately 4% of units sold will require warranty replacement at an average cost of $ 450 per unit. The actual warranty costs paid by MoTown during 2019 for replacement was $ 25,000.

Instructions:

a) Prepare adjusting journal entries to record the estimated warranty expense and the warranty payments during 2019 at December 31, 2019.

b) Assuming the warranty liability account has an unadjusted credit balance of $ 900, what is the 2019 ending balance ( after adjustment )?

Built-Tight is preparing its master budget for the quarter ended September 30, 2017. Budgeted sales and cash payments for product costs for the quarter follow:

Sales are 25% cash and 75% on credit. All credit sales are collected in the month following the sale. The June 30 balance sheet includes balances of $15,000 in cash; $45,300 in accounts receivable; $4,800 in accounts payable; and a $5,300 balance in loans payable. A minimum cash balance of $15,000 is required. Loans are obtained at the end of any month when a cash shortage occurs. Interest is 1% per month based on the beginning-of-the-month loan balance and is paid at each month-end. If an excess balance of cash exists, loans are repaid at the end of the month. Operating expenses are paid in the month incurred and consist of sales commissions (10% of sales), office salaries ($4,300 per month), and rent ($6,800 per month).

Question 1

During the year to 31 December 2013, Acacia Mining Ltd built a new mining facility to take advantage of new laws regarding on-shore gas extraction. The construction of the facility cost K10 million, and to fund this, Acacia Mining Ltd took out a K10 million 6% loan on 1 January 2013, which will not be repaid until 2016. The 6% interest was paid on 31 December 2013. Construction work begun on 1st January 2013, and the work was completed on 30 November 2013. As not all funds were required immediately, Acacia Mining Ltd invested K3 million of the loan in 4% bonds from 1 January 2013 until 30 April 2013. Mining commenced on 1 December 2013 and is expected to continue for 10 years. As a condition of being allowed to construct the facility, Acacia Mining Ltd is required by law to dismantle it on 1 January 2024. Acacia Mining Ltd estimated that this would cost a further K3 million. As the equipment is extremely specialized, Acacia Mining Ltd invested significant resources in recruiting and training employees. Acacia Mining Ltd spent K600,000 on thus process in the year to 31 December 2013, believing it to be worthwhile as it anticipates that most employees will remain on the project for the entire 10 year duration. Acacia Mining Ltd has a cost of capital of 6%.

Required: Show, using extracts, the correct financial reporting treatment for the above items in financial statements for Acacia Mining Ltd for the year ended 31 December 2013.

3. R has a built-in character vector of US State names, state.name. Use this character vector and R's character functions to answer the following questions.Show R code

(a) List all the US State names that are more than one word. How many are there?

(b) What is the longest US State name(s) (including spaces) and how long is it?

(c) What is the longest single word US State name and how long is it?

(d) List all the US State names, where all of the upper and lower case “a"s are replaced with a capital “Z".

The “bottom-up” theory of galaxy formation postulates that galaxies are built up from smaller bodies, knots of gas that were a bit more dense than the surrounding gas that then collapsed under their own gravity and began to accrete additional material.

A. Calculate how many “building blocks” are required to form a galaxy with the mass of the Milky Way. Assume that each “block” has a mass of 1 million solar masses. Show your calculation.

B. If this galaxy formed over a time span of 5 billion years, how many years must have elapsed between mergers of these building blocks during its “construction phase”?

C. What evidence do astronomers know of that supports this theory for galaxy formation? Give at least four pieces of observational evidence and explain how they support the theory.

A plant is to be built to produce blasting devices for construction work, and the decision must be made as to the extent of automation in the plant. Additional automatic equipment increases the investment costs but lowers the probability of shipping a defective device to the field, which must then be shipped back to the factory and dismantled at cost of $10 per device. The operating costs are identical for the different levels of automation. It is estimated that the plant will operate 10 years. The interest rate is 20%, and the rate of production is 100,000 devices per year for all levels of automation. Prepare a table with a column for all possible levels of automation, a column for the expected number of defectives in 100,000 devices, a column for the expected annual cost of defectives, a column for the annual cost of investment and a column for the total expected annual cost. Using the table, find the level of automation that will minimize the expected total annual cost for the investment costs and the probabilities given below

Level of Automation, Probability of producing a defective, Cost of investment ($)
1 0.100 100,000
2 0.050 150,000
3 0.020 200,000
4 0.010 275,000
5 0.005 325,000
6 0.002 350,000
7 0.001 400,000

Load the USArrests sample dataset from the built-in datasets (data(USArrests)) into R using a dataframe (Note: Row names are states, not numerical values!). Use the kmeans package to perform a clustering of the data with increasing values of k from 2 to 10 - you will need to decide whether or not to center/scale the observations - justify your choice. Plot the within-cluster sum of squares for each value of k - what is the optimal number of clusters? Use the tidyverse and fviz cluster plotting method from factoextra to plot the optimal clustering.

Use program R. Provide code and plots.

3. Marz-Or-Bust ™ Corp. has built a spaceship to send astronauts to colonize Mars. For safety, they install 3 mutually independent computer systems for controlling the mission. Each has an 80% chance of successfully completing the long journey, but as long as at least two of them are working, the ship will reach Mars. Determine the probability of a completed mission. SHOW work/reasoning for full credit.