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 $440 per year, payable at the start of each year
• Based on mileage estimates, petrol will cost $270 per fortnight, payable at the end of each fortnight
• Servicing will cost $360 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 3.0% 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. PV of running costs
PV of insurance & registration costs
PV of annuity-due of $ 440/ beg. of yr. at 3% p.a. for n=5
440*4.71710	-2075.52
(P/A due ,i=3%,n=5)
PV of petrol costs
PV of ordinary annuity of $270 at end of FN at 3% p.a. --ie.3%/12/2=0.125% for n=5*12 mths.*2 fortnights=120
270*111.36912=	-30069.66
(P/A,i=0.125%,n=120)
PV of servicing costs
PV of ordinary annuity $ 360/at end of yr. at 3% p.a. for n=5
360*4.57971=	-1648.69
(P/A ,i=3%,n=5)
Total PV of running costs	-33793.88	Ans.a.
b.PV of sales price
PV of sales price= 25%*Purchase price
ie. 37000*25%=9250*0.86261=	7979.13	Ans.b.
c.Net total cost of buying & running the car in PV $=
Initial purchase price	-37000
PV of insurance & registration costs	-2075.52
PV of petrol costs	-30069.66
PV of servicing costs	-1648.69
Less: PV of salvage	7979.13
Total cost of buying & running	-62814.75	Ans.c
d. Equivalent monthly repayment over the next 5 yrs.
Net total cost/Annuity factor on monthly basis
62814.75/55.65236=	1128.70
P/A,i=3%/12= 0.25%(monthly), n= 5 yrs.*12 mths.=60
ie.	1128.70	(Ans. d)