Question 1 (Total of 20 marks)
(a) (8 marks) A store discounts its televisions by 20%. If customers pay cash, they are given a further 5% off the already discounted price. If the cash price is $375, what was the original list price (to the nearest dollar)?
(b) (8 marks) Joe and Diane are partners in a clothing business and agree to share the profits in the following manner: Diane receives the first $45,000 or 40% of the profit, whichever is larger, and Joe receives $25,000 or 20% of the profit, whichever is smaller, while any remaining money is placed in the bank. If the profit is $120,000, how much will each partner receive? How much will be placed in the bank?
(c) (4 marks) During a sale, 584 items are sold in 25 minutes. Express the sales as the number of items sold per hour.
Question 2 (Total of 18 marks)
You have just inherited a house from your rich uncle, Mr. E. Scrooge, who recently passed away. A real estate agent has told you that you can rent the house to students for $800 a month for 5 years starting immediately, with rent payments due at the start of each month. At the end of 5 years the house will be demolished and the land sold for $350,000.
(a) (8 marks) If the interest rate is expected to be 7% per year compounded monthly for the next 5 years, find the present value of the rent you would receive over the next 5 years.
(b) (6 marks) What is the present value of the $350,000 you will receive from the sale of the land in 5 years? Use the interest rate from part (a).
(c) (4 marks) What is the maximum price you could expect to receive for your house and land if you sold it today to someone who was a housing investor? Explain briefly.
PLEASE TURN OVER
Question 3 (Total of 14 marks)
The SuperSecure Insurance Company provides the following superannuation scheme for men and women who own their own businesses. If $250 is invested at the end of each month for 10 years, at the end of 10 years the company will give the investor the amount deposited, a bonus of $2,000, plus the interest earned. The interest rate is 6% compounded monthly.
(a) (8 marks) Find the amount a business owner would receive at the end of 10 years.
(b) (6 marks) What regular payments R would need to be made at the end of each month to receive the amount found in part (a) if SuperSecure did not pay the $2,000 bonus?
Question 4 (Total of 24 marks)
The Early-Bird Real Estate Investment Corporation has purchased an office block for $3,000,000. They agree to pay this back in 6 equal quarterly instalments, with the first payment due at the beginning of the next quarter. The interest rate is 6% per annum compounded quarterly.
(a) (6 marks) What is the size of the required quarterly payments?
(b) (12 marks) Use EXCEL to set up an Amortisation Schedule showing for each quarter: the amount owing at the start of each quarter, the payment made, the interest portion and the principal portion of the payment, and the new balance at the end of the quarter. Attach the printout or copy your EXCEL amortisation schedule into your assignment submission.
EXCEL Instructions: Please refer to Topic 3 in the EXCEL Booklet for instructions on entering formulae in EXCEL.
(c) (6 marks) Suppose that instead of the payment size found in part (a), the corporation makes quarterly payments of $350,000. How many payments will now be required to pay off the office block? Use your amortisation schedule from part (b). If the final payment due is less than $350,000, what is its amount?
Question 5 (Total of 24 marks)
A company makes and sells 200 units of a product every week. The fixed costs for buildings, machines and employees are $14,000 a week, while raw material and other variable costs are $50 per unit.
(a) (12 marks) If the selling price is $140 per unit, what is the break-even number of units? 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. On your graph, identify the region corresponding to profits and the region corresponding to losses.
EXCEL Instructions: Create a column called Number of Units and in that column enter values from 0 to 400 in increments of 50. 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 Units column. Highlight the resulting three sets of numbers and go to SCATTERPLOT 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.
(b) (4 marks) Based on your graph from part (a), is there a profit or a loss if 200 units are sold in a week at a price of $140 per unit? Explain briefly. Calculate the weekly profit or loss amount.
(c) (8 marks) How many units should the company produce per week to make a profit if the selling price is lowered to $120 per unit? Is the rise in sales to 450 units per week sufficient for the company to make a profit? Explain briefly. Calculate the weekly profit/loss amount.