Quantitative Methods for Business SAIBT

Assignment 1 (1 2017)

Due 1 pm Monday 10 April 2017

• The assignments are to be submitted by 1:00pm on the due date on line. A hard copy is to be handed in during class.

• An assignment submitted late, without an extension being granted, will attract a penalty of 5% (5 marks) per each working day or part thereof beyond the due day and time. Please refer to the Course Information Booklet for the course policy regarding extensions.

• Please remember to fill out and attach a cover sheet. A copy of the cover sheet can be downloaded from the Course web page.

• Please make sure that the pages of your submission are in the correct order and that they are stapled securely in the top left-hand corner only. Please make sure that each page shows your name and the page number.

• Please – no plastic sleeves or any type of folder!

• Please copy and paste any EXCEL printouts into your assignment

• All graphs and tables must include your USER ID in the title

• Show all your work!

The assignment will be in two parts.

• The first part will contain a summary of your answers to the five questions. Each summary will be one or two paragraphs. (20 marks)

• Your calculations will be included in an appendix. Your answers in the appendix will follow the format as set out in this question sheet. (80 marks)

The report will have a maximum of 4 marks for each question

Question 1 (Total of 8 marks)

A store advertises a filing cabinet for a reduced price of $299 after a $50 trade-in on any old cabinet.

(a) (2 marks) What percentage discount does the old cabinet represent?

(b) (4 marks) If the store offers a further discount of 15% off the reduced price for cash, what price (to the nearest dollar) would the cabinet be now after a trade-in?

(c) (2 marks) A customer with a trade-in offers the store a $260 cash price for the cabinet. Is that a better deal (for the customer) than the store is offering?

Question 2 (Total of 12 marks)

On Mary’s 16th birthday, her parents invest on her behalf an amount of $5,000 into an account that pays interest at 3.8% compounded semi-annually.

(a) (5 marks) How much will the account be worth on Mary’s 21st birthday?

(b) (7 marks) Would Mary be better off if the account paid interest at 3.6% compounded quarterly? Explain.

Question 3 (Total of 12 marks)

Luxury Rides Taxi Service must replace cars every 5 years at a cost of $450,000. The company is considering depositing $4,000 at the end of each month at 8% per year compounded monthly. Confirm your answer using EXCEL. Will they meet the target with this strategy? Explain. If your answer is no, what size deposits should they be making instead?

Question 4 (Total of 24 marks)

Kate and Miles are shopping for a new home. They can afford a downpayment of $50,000 and monthly payments of at most $2,500.

(a) (7 marks) Sterling Bank has offered to finance a loan at 8.75% per year compounded monthly for 30 years. What is the most expensive house (to the nearest dollar) they can afford to buy?

(b) (6 marks) Kate and Miles ultimately make a downpayment of $50,000 on a $300,000 home and finance the balance through Creative Financing Inc. at 8.25% per year compounded monthly for 25 years. What monthly payments should Kate and Miles make to pay off the house?

(c) (8 marks) Referring to part (b), use EXCEL to set up an Amortisation Schedule for the first 12 months of the loan. Attach the printout or copy your EXCEL amortisation into your assignment submission.

EXCEL Instructions: Please refer to the amortisation example in Week 3 lecture notes and Topic 3 in the EXCEL Booklet.

(d) (3 marks) Referring to the Amortisation Schedule from part (c), how much interest in total will Kate and Miles pay over the first year of their loan? How much equity (downpayment plus repaid principal) in the house will they have at the end of the first year?

Question 5 (Total of 24 marks)

Hit-and-Miss Airlines are considering providing a new daily service between two cities. The aircraft has a maximum capacity of 200 passengers and each flight incurs a fixed cost of $27,000 regardless of the number of passangers. In addition, a cost is also incurred of $75 per passanger to cover such things as catering, booking, baggage handling.

(a) (12 marks) The company is thinking of charging $225 per ticket. How many passengers will the airline need on each flight to break even? Find the break-even point algebraically and illustrate it using an EXCEL graph. Attach the printout or copy your EXCEL graph into your assignment submission. Based on your analysis, will Hit-and-Miss realize a profit or a loss if 160 seats are sold for a particular flight? Explain briefly.

(b) EXCEL Instructions: Create a column called Number of Passengers and in that column enter values from 0 to 200 in increments of 20. Then create two more columns, one for Total Cost and another for Total Revenue. Enter appropriate formulae in EXCEL to obtain the total cost and total revenue corresponding to each value in the Number of Passengers column. Highlight the resulting three sets of numbers and go to the Chart Wizard to obtain the graph. Make sure that your graph has been labelled appropriately (i.e. title, axis labels, legend). Please refer to Topic 3 in the EXCEL Booklet for further instructions on entering formulae and graphing in EXCEL.

(c) (6 marks) Hit-and-Miss Airlines know from previous experience that they are unlikely to sell more than 80 percent of seats on any one flight. Assuming they sell exactly this many, what price per seat should they charge to break even?

(d) (6 marks) The company also has the option of accepting a cargo contract. Under this contract, the airline will receive $5,000 per flight for transporting cargo but, because of the extra weight, it will have to reduce its maximum number of passengers to 190. Find the new break-even ticket price for a full flight.

GRAND TOTAL 100 MARKS

Assignment 1 (1 2017)

Due 1 pm Monday 10 April 2017

• The assignments are to be submitted by 1:00pm on the due date on line. A hard copy is to be handed in during class.

• An assignment submitted late, without an extension being granted, will attract a penalty of 5% (5 marks) per each working day or part thereof beyond the due day and time. Please refer to the Course Information Booklet for the course policy regarding extensions.

• Please remember to fill out and attach a cover sheet. A copy of the cover sheet can be downloaded from the Course web page.

• Please make sure that the pages of your submission are in the correct order and that they are stapled securely in the top left-hand corner only. Please make sure that each page shows your name and the page number.

• Please – no plastic sleeves or any type of folder!

• Please copy and paste any EXCEL printouts into your assignment

• All graphs and tables must include your USER ID in the title

• Show all your work!

The assignment will be in two parts.

• The first part will contain a summary of your answers to the five questions. Each summary will be one or two paragraphs. (20 marks)

• Your calculations will be included in an appendix. Your answers in the appendix will follow the format as set out in this question sheet. (80 marks)

The report will have a maximum of 4 marks for each question

Question 1 (Total of 8 marks)

A store advertises a filing cabinet for a reduced price of $299 after a $50 trade-in on any old cabinet.

(a) (2 marks) What percentage discount does the old cabinet represent?

(b) (4 marks) If the store offers a further discount of 15% off the reduced price for cash, what price (to the nearest dollar) would the cabinet be now after a trade-in?

(c) (2 marks) A customer with a trade-in offers the store a $260 cash price for the cabinet. Is that a better deal (for the customer) than the store is offering?

Question 2 (Total of 12 marks)

On Mary’s 16th birthday, her parents invest on her behalf an amount of $5,000 into an account that pays interest at 3.8% compounded semi-annually.

(a) (5 marks) How much will the account be worth on Mary’s 21st birthday?

(b) (7 marks) Would Mary be better off if the account paid interest at 3.6% compounded quarterly? Explain.

Question 3 (Total of 12 marks)

Luxury Rides Taxi Service must replace cars every 5 years at a cost of $450,000. The company is considering depositing $4,000 at the end of each month at 8% per year compounded monthly. Confirm your answer using EXCEL. Will they meet the target with this strategy? Explain. If your answer is no, what size deposits should they be making instead?

Question 4 (Total of 24 marks)

Kate and Miles are shopping for a new home. They can afford a downpayment of $50,000 and monthly payments of at most $2,500.

(a) (7 marks) Sterling Bank has offered to finance a loan at 8.75% per year compounded monthly for 30 years. What is the most expensive house (to the nearest dollar) they can afford to buy?

(b) (6 marks) Kate and Miles ultimately make a downpayment of $50,000 on a $300,000 home and finance the balance through Creative Financing Inc. at 8.25% per year compounded monthly for 25 years. What monthly payments should Kate and Miles make to pay off the house?

(c) (8 marks) Referring to part (b), use EXCEL to set up an Amortisation Schedule for the first 12 months of the loan. Attach the printout or copy your EXCEL amortisation into your assignment submission.

EXCEL Instructions: Please refer to the amortisation example in Week 3 lecture notes and Topic 3 in the EXCEL Booklet.

(d) (3 marks) Referring to the Amortisation Schedule from part (c), how much interest in total will Kate and Miles pay over the first year of their loan? How much equity (downpayment plus repaid principal) in the house will they have at the end of the first year?

Question 5 (Total of 24 marks)

Hit-and-Miss Airlines are considering providing a new daily service between two cities. The aircraft has a maximum capacity of 200 passengers and each flight incurs a fixed cost of $27,000 regardless of the number of passangers. In addition, a cost is also incurred of $75 per passanger to cover such things as catering, booking, baggage handling.

(a) (12 marks) The company is thinking of charging $225 per ticket. How many passengers will the airline need on each flight to break even? Find the break-even point algebraically and illustrate it using an EXCEL graph. Attach the printout or copy your EXCEL graph into your assignment submission. Based on your analysis, will Hit-and-Miss realize a profit or a loss if 160 seats are sold for a particular flight? Explain briefly.

(b) EXCEL Instructions: Create a column called Number of Passengers and in that column enter values from 0 to 200 in increments of 20. Then create two more columns, one for Total Cost and another for Total Revenue. Enter appropriate formulae in EXCEL to obtain the total cost and total revenue corresponding to each value in the Number of Passengers column. Highlight the resulting three sets of numbers and go to the Chart Wizard to obtain the graph. Make sure that your graph has been labelled appropriately (i.e. title, axis labels, legend). Please refer to Topic 3 in the EXCEL Booklet for further instructions on entering formulae and graphing in EXCEL.

(c) (6 marks) Hit-and-Miss Airlines know from previous experience that they are unlikely to sell more than 80 percent of seats on any one flight. Assuming they sell exactly this many, what price per seat should they charge to break even?

(d) (6 marks) The company also has the option of accepting a cargo contract. Under this contract, the airline will receive $5,000 per flight for transporting cargo but, because of the extra weight, it will have to reduce its maximum number of passengers to 190. Find the new break-even ticket price for a full flight.

GRAND TOTAL 100 MARKS

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