Reference no: EM132352565
Quantitative Methods Assignment
QUESTION 1
Kim and Lee wish to buy a house and have it paid off in ten years. They have realized that at different stages of their life cycle they will have different capacities to make loan repayments. Their plans and budgets are captured in the tables below:
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Assignment Groups Alpha or Gamma
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Interest rate of loan that they have access to:
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J12 = 4.92% p.a.
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Both working during first three years with no children.
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Max repayment of $3000 per month for months 1 to 36
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Five years of reduced income whilst raising a pre-school child.
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Max repayment of $1800 per month for months 37 to 96
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Two years of further reduced income after second child is born.
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Max Repayment of $1500 per month for months 97 to 120
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Assignment Groups Beta or Delta
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Interest rate of loan that they have access to:
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J26 = 4.68% p.a.
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Frequent International Holidays for two years.
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Max repayment of $800 per fortnight for fortnights 1 to 52
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Regular domestic travel for four years.
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Max repayment of $1200 per fortnight for fortnights 53 to 156
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Settled down homebodies.
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Max Repayment of $1500 per fortnight for fortnights 157 to 260
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a) Assuming they make the maximum payments that they have budgeted for, illustrate the cash flows associated with the loan as a fully labelled time line diagram. (Assume the first repayment occurs one period after they take out the loan.)
b) By breaking this cash flow into three simple annuities, determine the maximum amount that Kim and Lee can borrow if they are to pay off the loan in ten years.
c) Assuming that Kim and Lee borrow the maximum amount that they can afford to pay back in ten years, construct an amortisation table showing the last three payments.
QUESTION 2
Door2DoorCo are a large courier company who have just received a shipment of X new vans. They wish to lock in a tyre supply contract to keep these vans well shod over the Y months that they intend to keep the vans. The vans come with low quality tyres that will need to be replaced in 2 months.
Two suppliers, ThriftyTread and WiserWheels have expressed interest at supplying tyres at a fixed price for the duration. The offers are summarised below:
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Assignment Allocation
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Alpha or Beta
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Gamma or Delta
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Number of Vans, X
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120
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100
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Corporate Discount Rate
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J1 = 12.68% p.a.
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J1 = 14.03% p.a.
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Initial Tyre Life
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2 months.
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2 months
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Keep vans for (Y)
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50 months
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38 months
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ThriftyTread
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$100.00
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$100.00
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Four months
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Four months
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2, 6, 10, ..., 46, 50 months
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2, 6, 10, ..., 34, 38 months
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WiserWheels
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$148.00
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$77.50
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Six months
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Three months
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2, 8, 14, ...,44, 50 months
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2, 5, 8, ..., 35, 38 months
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a) For each of the two potential suppliers, illustrate Door2DoorCO's tyre expenditure for the new vans as a fully labelled timeline diagram. (Remember that there are X new vans, and assume each van has 4 tyres.)
b) Determine the value in period 2 dollars of the expenditure stream if Door2DoorCo decide to go with ThriftyTreads. [Hint, you will firstly need to find the j3 rate equivalent to the corporate discount rate, you will then need to find the PV of the expenditure stream in period 2 dollars]
c) Thus determine the present value of the expenditure stream if Door2DoorCo decide to go with ThriftyTreads. [NB this is a bit tricky and is aimed at stronger students]
d) Determine the value in period 2 dollars of the expenditure stream if Door2DoorCo decide to go with WiserWheels.
e) Thus determine the present value of the expenditure stream if Door2DoorCo decide to go with WiserWheels [NB this is a bit tricky and is aimed at stronger students]
f) Comparing your answers for part (b) with part (d), OR part (c) with part (e), explain which tyre supplier Door2DoorCo should choose.
g) Suggest three legitimate business considerations which a manager may take into account that might influence or even change the recommendation from part (f). NB "These tyres are prettier", "This company will bribe me with a kickback", or "My wife works for that company" are NOT legitimate business reasons. (Write around 20~30 words explaining/justifying each consideration.)