Eynesbury: Quantitative Methods for Business Assignment Questions -
Question 1 - A store advertises a HD plasma television screen for a reduced price of $2999 after a $50 trade-in on any old working television.
(a) What percentage discount does the old television represent?
(b) If the store offers a further discount of 15% off the reduced price for cash, what price (to the nearest dollar) would the plasma television be now after a trade-in?
(c) A customer with a trade-in offers the store a $2600 cash price for the plasma television. Is that a better deal (for the customer) than the store is offering?
Question 2 - Provide written responses to the following:
(a) Provide a clear explanation of what is meant by the phrase 'the time value of money'. As part of your explanation supply examples to clarify your comments.
(b) The process of compounding and discounting in finance are related. Explain this relationship.
(c) 'In order to compare two or more interest rates, they must be expressed on a suitable common scale.' Explain the meaning of this quotation and give some numerical examples to illustrate your response.
(d) What is meant by the term 'Redundant Constraints'? Provide an example in support of your discussion.
Question 3 - Luxury Rides Taxi Service must replace cars every 5 years at a cost of $450,000. The company is considering depositing $6,000 at the end of each month at 8% per year compounded monthly.
(a) Will they meet the target with this strategy? Explain. Show any necessary calculations to support your answer.
(b) If your answer is no, what size deposit should they make now to make up the shortfall?
Question 4 - Kate and Miles are shopping for a new home. They can afford a down-payment of $50,000 and monthly payments of at most $2,500.
(a) 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) Kate and Miles ultimately make a down-payment of $50,000 on a $300,000 home and finance the balance through Creative Financing Inc. at 8.25% per year compounded monthly for 25 years. What monthly payments should Kate and Miles make to pay off the house?
(c) Referring to part (b), use EXCEL to set up an Amortisation Schedule for the first 12 months of the loan. Attach the printout or copy your EXCEL amortisation into your assignment submission.
Instructions: Use the following headings for your amortisation schedule.
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Period
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Opening Balance
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Interest
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Payment
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Closing Balance
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(d) Referring to the Amortisation Schedule from part (c), how much interest in total will Kate and Miles pay over the first year of their loan? How much equity (down payment plus repaid principal) in the house will they have at the end of the first year?
Question 5 - Jameson's hotel group prepares published accounts on a quarterly basis. The senior management is reviewing the performance of one of the hotels in the group and making plans for 2018/19. They have in front of them the results for 2017/18 (based on actual results for the first two quarters and forecasts to the end of the year).
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Quarter
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Sales
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Profit/(loss)
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$
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$
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1
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400,000
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(280,000)
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2
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1,200,000
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360,000
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3
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1,600,000
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680,000
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4
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800,000
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40,000
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The total estimated number of visitors (guest nights) for 2017/18 is 50,000. The results follow a regular pattern, with no unexpected cost fluctuations beyond the seasonal trading pattern. Management intend to add to their plans for 2018/19 an anticipated increase in unit variable costs of 10% and a profit target for the hotel of $1 million.
Required:
(a) Determine the total variable and total fixed costs of the hotel for 2017/18, by using both a PV chart and by calculation.
(b) i. If there is no increase in visitors for 2018/19, what will be the required revenue rate per hotel visitor to meet the profit target?
ii. If the required revenue rate per visitor is not raised above the 2018/19 level, how many visitors are required to meet the profit target?
(c) Outline and briefly discuss the assumptions underlying the accountants' typical PV or break-even analysis and assess whether they limit its usefulness.
Question 6 - A garden store prepares various grades of wood chips for mulch for sale in various tonnages for delivery to large garden construction sites around town. The grades are (a) fine, (b) standard and (c) course. The process requires red gum, machine time, labour time, and storage space.
The garden store owner has identified that the store can generate $90 profit per storage bin for fine, $90 for standard but only $60 for course chips.
Each load of chips require inputs in the following quantities: Fine: 5 tonnes of material, 2 machine hours, 2 hours of labour and 1 storage bin Standard: 6 tonnes of material, 4 machine hours, 4 hours of labour and 1 storage bin Course: 3 tonnes of material, 5 machine hours, 3 hours of labour and 1 storage bin
Unfortunately, like every business, the garden store has limits in its production capacity. It is able to handle 600 tonnes of red gum at any one time, the machine can only operate for 600 hours before major maintenance must occur, it only has sufficient staff to provide 480 hours of labour time and it has 150 storage bins.
Required:
(a) What is the marginal value of a tonne of red gum? Over what range is this price value appropriate?
(b) What is the maximum price the store would be justified in paying for additional red gum?
(c) What is the marginal value of labour? Over what range is this value in effect?
(d) The manager obtained additional machine time through better scheduling. How much additional machine time can be effectively used for this operation? Why?
(e) If the manager can obtain either additional red gum or additional storage space, which one should the manager choose and how much (assuming additional quantities cost the same as usual)?
(f) If a change in the course chip operation increased the profit on course chips from $60 per bin to $70 per bin, would the optimal quantities change? Would the value of the objective function change? If so, what would the new value(s) be?
(g) If profits on course chips increased to $70 per bin and profits on fine chips decreased by $6.00, would the optimal quantities change? Would the value of the objective function change? If so, what would the new value(s) be?