1. Alan owes Brian HK$5,000, which is due on 31 March. On 15 March, he sought Brian’s consent to accept a lesser sum of US$600 on 24 March (i.e., one week in advance of the due date) to discharge the whole debt. Brian agreed to this arrangement. Alan then made a bank loan of US$600 at an annual interest rate of 5% with a view to paying Brian. Today is 24 March, Brian has now changed his mind. He insists to revert to the previous position of full payment HK$5,000 to be paid on 31 March. Advise Alan if his part payment is able to discharge the whole debt in such case. [ Discuss the doctrine of promissory estoppel.]

2       Milky entered into a contract for the hire of 6 rooms in New Castle Hotel in    Kowloon West. The purpose of the contract was to watch the fireworks gala in the Victoria Harbour on the 1st July (Reunification Day) through the windows of the rooms. Milky planned to invite her close friends and their families to stay in the 6 rooms to enjoy the fireworks. Just two hours before start of the fireworks, the Hong Kong Police Force received a serious threat from some terrorist organizations that they would launch large scale attack to the crowds who gathered to watch the fireworks. The Hong Kong Government immediate ordered the cancellation of the fireworks and gave an order that this kind of gala will not be launched at least for five years. Milky, having already paid a deposit, refused to pay the balance of the room charges. The hotel took legal action to recover the balance.

Required:

Analyse the chance of success by the hotel and explain in detail the legal principles that you base on for analysis.

3      Devil Computers Ltd (DCL) produces hard disks for installing in computers. The Hong Kong Land Bank (HKLB) would like to purchase new computers for its new computer room situate at the fourth floor of its headquarters in Homantin. HKLB asked DCL for their hard disks which could survive in good conditions for at least 3 years. DCL sold some of their “long life” hard disks to HKLB.

         In fact, the “long life” hard disks only survived for 6 months and the staff of HKLB complained about the performance and quality of the hard disks.

Required:

Advise whether HKLB could claim damages and repudiate the contract of sale with DCL under the provisions of the Sale of Goods Ordinance. Detail explanation of that specific provision is necessary.     

The Sai Kung Inn is a small family-run hotel in the New Territories. As a family-owned business, it relies mainly on traveler recommendations and on visitors to local Sai Kung residents. In particular, it ranks in the top 10% of TripAdvisor’s accommodations in Sai Kung. The Sai Kung Inn has 12 guest rooms, and to keep the operation running efficiently it employs two full-time reception staff, and three morning housekeeping staff.

Winnie is the hotel manager and the daughter of the property owner. She is considering to adopt a balanced scorecard approach for performance evaluation. She has identified a number of potential performance measures:

1. 1) Number of items on hotel restaurant menu

2. 2) Revenue

3. 3) Percentage of reception staff completing hospitality and customer satisfaction course

4. 4) Customer satisfaction with dining options

5. 5) Average percentage occupancy

6. 6) Number of restaurant staff completing cooking training courses

7. 7) Percentage of cleaning staff completing housekeeping and hygiene courses

8. 8) Average TripAdvisor rating

9. 9) Number of guest complaints about room cleanliness

10. 10) Average number of minutes taken to process guests’ check-in

11. 11) Total profits

12. 12) Frequency and quality of room cleaning

Required:

1. (a) Using the 12 performance measures suggested above, draw a balanced scorecard diagram for The Sai Kung Inn with the four main categories of the balanced scorecard, classifying each of the performance measures into one of the four categories. Draw arrows between individual performance measures to show causal links and indicate with a “+” or “–” whether the performance measure should increase or decrease.

2. (b) Winnie believes that The Sai Kung Inn’s occupancy rate is lower than her competitors because The Sai Kung Inn charges slightly higher prices and does not attract guests who prefer cheaper accommodation. Winnie believes that in order to improve the financial performance of The Sai Kung Inn, the company should focus on improving customer satisfaction to justify higher prices, instead of reducing costs to compete on price. She would like to improve the rank on TripAdvisor to be the top-rated accommodation in Sai Kung, by focusing on operational and staff improvements. Help Winnie develop two new performance measures to build into her balanced scorecard. For each performance measure you suggest, identify which category it would fit into, how to measure it, and how it relates to the organization goal.

Microeconomics has traditionally been built on the foundation of rational choice.   However, since the 70’s insights from blending psychology and economics have been changing the landscape.   Some have argued this new line of thinking, most often associated with behavioral economics, has laid waste to the micro model of choice.  

To what extent does the rational choice model have a future?   Can it absorb the new insights from behavioral? Do you think we will have two competing models of choice going forward?  

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.

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.

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.