Question

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 $37,000. After doing a bit more research, he has found the following additional expenses involved in the purchase: Insurance and registration will cost $470 per year, payable at the start of each year Based on mileage estimates, petrol will cost $220 per fortnight, payableat the end of each fortnight Servicing will cost $350 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 4.6% 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?

Answer 1

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

Present value of insurance and registration costs.

Insurance cost present value
years	amount	discounting factor	present value
1	470	1	470
2	470	0.956022945	449.33
3	470	0.913979	429.57
4	470	0.873785727	410.6793
5	470	0.835359204	392.6188
		Total cost	2152.20

  Present value of petrol costs.

Petrol cost
years	amount	discounting factor	present value
1	220	0.977517107	215.0538
	220	0.955539694	210.2187
2	220	0.934056403	205.4924
	220	0.913056107	200.8723
3	220	0.892527963	196.3562
	220	0.872461352	191.9415
4	220	0.852845896	187.6261
	220	0.833671453	183.4077
5	220	0.814928106	179.2842
	220	0.796606165	175.2534
		Total cost	1945.506

present value of servicing costs( since the car was recently serviced by the previous owner so we are not incurring any expenses in year 1 )

Servicing cost
years	amount	discounting factor	present value
1	NIL	-	-
2	350	0.913979	319.8927
3	350	0.873785727	305.825
4	350	0.835359204	292.3757
5	350	0.798622566	279.5179
		Total cost	1197.61

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

=$ 37000 X 0.7986225 = $ 29,549.032

(c) The total cost of buying and running the car in today's dollars.

so the total cost will be = present value of ( purchasing price of car + insurance and registration + petrol costs + servicing costs ) - selling price of car =

$ 37000 + $ 2152.20 + $ 1945.506 + $ 1197.61 - $ 29,549.032 = $ 12746.29.

(d) Equivalent monthly repayment over the next 5 years.

monthly repayment = $ 42295.322 / 60 = $ 704.92 ( OR ) $ 12746.29 / 60 = $ 212.43