(Question 1)

Geoffrey is the owner of a small grocery store, and is considering buying a car to help him transport his wares. He has found a suitable used car online that he was able to negotiate to a price of $34,000. After doing a bit more research, he has found the following additional expenses involved in the purchase:

• Insurance and registration will cost $440 per year, payable at the start of each year
• Based on mileage estimates, petrol will cost $250 per fortnight, payableat the end of each fortnight
• Servicing will cost $310 per year, payable at the end of each year (as the car was recently serviced by the previous owner

Assume that these are the only expenses involved with the purchase and operation of the car.

Geoffrey believes that the car can be used for 5 years before it will no longer be reliable, at which point he expects to sell it for a quarter of its current purchase price. He also has a business account at the bank that lets him borrow or invest money at 4.5% per annum effective.

(a) Calculate the present value of the running costs (i.e. the insurance and registration, the petrol, and the servicing).

(b) Calculate the present value of the sale price.

(c) What is the total cost of buying and running the car in today's dollars? Your answer should also take into account the eventual sale price.

(d) What is the equivalent monthly repayment over the next 5 years, where payments are made at the end of each month?

INPUTS CALCULATIONS Periodic cost of service a) Borrow/invest rate Periodicity of service Periodicity of service Start or end of period? Nominal periodic rate Effective periodic rate Number of periods PV of future liabilities b) Number of periods Periodic cost of service "Loan" amount today Start or end of period? Effective periodic rate for "loan" EAR for "loan"INPUTS CALCULATIONS Cost of car Insurance/Registration a ) Insurance/registration Periodic cost Periodic interest rate Frequency Number of payments Start or end of period? PV Insurance Petrol Petrol Periodic cost Periodic interest rate Frequency Number of payments Start or end of period? PV Petrol Servicing Servicing Periodic cost Periodic interest rate Frequency Number of payments Start or end of period? PV Servicing Life of car (years) Total Interest rate (EAR) b) Sale price in the future PV Sale price c) Total cost d) Payment frequency Periodic interest rate Number of payments Periodic repaymentINPUTS CALCULATIONS Single payment a ) Periodicity of repayment Term of agreement (years) Number of repayments Geoffrey's interest rate (EAR) Periodic interest rate PV of loan Level repayment size b ) Number of years passed Level repayment size Loan outstanding c) Total payments made Loan outstanding Interest paid d) Overal benefit amount Periodicity of benefit Number of benefit 'payments' Cost today Effective periodic rate Nominal annual rate