Question

ECON5028 PPAIC 1) You are faced with a choice of buying a diesel engined car or its petrol equivalent. The Diesel version costs £17,000 and the petrol equivalent £15,500. The diesel car has a fuel consumption of 40 miles per gallon and the petrol version 30 miles per gallon. A litre of diesel costs £1.40 and a litre of petrol £1.35. Assume there are 4.5 litres per gallon. The mileage driven is forecast as being 12,000 miles per year and the car is expected to last 10 years. Assume no residual value. a) Construct the relevant cash flow diagrams and assuming all other costs are the same, which would be the better ie. cheaper purchase on the basis of a DCF calculation using a 5% discount rate? b) What discount rate would make the purchaser indifferent (ie equalise total costs) of the choice? c) What annual mileage would make the purchaser indifferent between the two options at the 5% discount rate? d) What yearly % change in fuel prices would make the purchaser indifferent between the two options at a 5% discount rate assuming the fuel price of the more expensive choice had remained constant? (75%)

Answer 1

We have calculated the cost of expenses to buy a diesel car and the petrol car. Please find below the calculations: For cost of diesel/petrol each year the calculations are as follows:

Diesel: Car will run for 12,000 miles each year, So the car will require 300 gallons of diesel per year (12000/40) as it averages 40 miles per gallons. Each gallons has 4.5 liters of diesel, which is 1350 liters of diesel. The total cost is 1350 * 1.40 = 1890

Petrol: Car will run for 12,000 miles each year, So the car will require 400 gallons of petrol per year (12000/30) as it averages 30 miles per gallons. Each gallons has 4.5 liters of petrol, which is 1800 liters of petrol. The total cost is 1800 * 1.35 = 2430

Diesel Car cash flow

Diesel car
Particulars
Cash Outflow to buy the car	17000
Petrol Expenses at Year 1	1890
Petrol Expenses at Year 2	1890
Petrol Expenses at Year 3	1890
Petrol Expenses at Year 4	1890
Petrol Expenses at Year 5	1890
Petrol Expenses at Year 6	1890
Petrol Expenses at Year 7	1890
Petrol Expenses at Year 8	1890
Petrol Expenses at Year 9	1890
Petrol Expenses at Year 10	1890
Cost of capital	5.00%
Present value of cash flows	14,594.08
Total Outflow = Cost of car + Cost of Petrol	31,594.08

Petrol Car:

Petrol Car
Particulars
Cash Outflow to buy the car	15500
Petrol Expenses at Year 1	2430
Petrol Expenses at Year 2	2430
Petrol Expenses at Year 3	2430
Petrol Expenses at Year 4	2430
Petrol Expenses at Year 5	2430
Petrol Expenses at Year 6	2430
Petrol Expenses at Year 7	2430
Petrol Expenses at Year 8	2430
Petrol Expenses at Year 9	2430
Petrol Expenses at Year 10	2430
Cost of capital	5.00%
Present value of cash flows	18,763.82
Total Outflow = Cost of car + Cost of Petrol	34,263.82

The cheaper purchase would be the diesel car.

b) to calculate this we need to find the IRR of the difference of the cash flows of the two projects:

First we will find the IRR of the difference of the values of cash flow of the two cars:

Cash Outflow to buy the car	1500
Petrol Expenses at Year 1	-540
Petrol Expenses at Year 2	-540
Petrol Expenses at Year 3	-540
Petrol Expenses at Year 4	-540
Petrol Expenses at Year 5	-540
Petrol Expenses at Year 6	-540
Petrol Expenses at Year 7	-540
Petrol Expenses at Year 8	-540
Petrol Expenses at Year 9	-540
Petrol Expenses at Year 10	-540
IRR	34%

So at 34% discount rate the cost of the two cars will be almost equal, please find the calculation:

Diesel car			Petrol Car
Particulars			Particulars
Cash Outflow to buy the car	17000		Cash Outflow to buy the car	15500
Petrol Expenses at Year 1	1890		Petrol Expenses at Year 1	2430
Petrol Expenses at Year 2	1890		Petrol Expenses at Year 2	2430
Petrol Expenses at Year 3	1890		Petrol Expenses at Year 3	2430
Petrol Expenses at Year 4	1890		Petrol Expenses at Year 4	2430
Petrol Expenses at Year 5	1890		Petrol Expenses at Year 5	2430
Petrol Expenses at Year 6	1890		Petrol Expenses at Year 6	2430
Petrol Expenses at Year 7	1890		Petrol Expenses at Year 7	2430
Petrol Expenses at Year 8	1890		Petrol Expenses at Year 8	2430
Petrol Expenses at Year 9	1890		Petrol Expenses at Year 9	2430
Petrol Expenses at Year 10	1890		Petrol Expenses at Year 10	2430
Cost of capital	34.00%		Cost of capital	34.00%
Present value of cash flows	₹ 5,261.02		Present value of cash flows	₹ 6,764.16
Total Outflow = Cost of car + Cost of Petrol	₹ 22,261.02		Total Outflow = Cost of car + Cost of Petrol	₹ 22,264.16

c) This can be calculated using various combinations of the mileage, the calculation done below is based on the mileage of 6000 miles per year the cost difference is almost similar and has a small difference of 584 pounds over the period of 10 years

Diesel car			Petrol Car
Particulars			Particulars
Cash Outflow to buy the car	17000		Cash Outflow to buy the car	15500
Petrol Expenses at Year 1	945		Petrol Expenses at Year 1	1215
Petrol Expenses at Year 2	945		Petrol Expenses at Year 2	1215
Petrol Expenses at Year 3	945		Petrol Expenses at Year 3	1215
Petrol Expenses at Year 4	945		Petrol Expenses at Year 4	1215
Petrol Expenses at Year 5	945		Petrol Expenses at Year 5	1215
Petrol Expenses at Year 6	945		Petrol Expenses at Year 6	1215
Petrol Expenses at Year 7	945		Petrol Expenses at Year 7	1215
Petrol Expenses at Year 8	945		Petrol Expenses at Year 8	1215
Petrol Expenses at Year 9	945		Petrol Expenses at Year 9	1215
Petrol Expenses at Year 10	945		Petrol Expenses at Year 10	1215
Cost of capital	5.00%		Cost of capital	5.00%
Present value of cash flows	₹ 7,297.04		Present value of cash flows	₹ 9,381.91
Total Outflow = Cost of car + Cost of Petrol	₹ 24,297.04		Total Outflow = Cost of car + Cost of Petrol	₹ 24,881.91

d) For this calculation the fuel price of diesel car would increase I have assumed to be an increase of 4.5% the reason for selecting the rate is as we are discounting the cash flows by 5%, so I calculated the increase the rate of diesel close to discount rate as the petrol rate is constant. We have got the following calculation: The cost is almost in the same range

Diesel car			Petrol Car
Particulars			Particulars
Cash Outflow to buy the car	17000		Cash Outflow to buy the car	15500
Petrol Expenses at Year 1	1890		Petrol Expenses at Year 1	2430
Petrol Expenses at Year 2	1975		Petrol Expenses at Year 2	2430
Petrol Expenses at Year 3	2064		Petrol Expenses at Year 3	2430
Petrol Expenses at Year 4	2157		Petrol Expenses at Year 4	2430
Petrol Expenses at Year 5	2254		Petrol Expenses at Year 5	2430
Petrol Expenses at Year 6	2355		Petrol Expenses at Year 6	2430
Petrol Expenses at Year 7	2461		Petrol Expenses at Year 7	2430
Petrol Expenses at Year 8	2572		Petrol Expenses at Year 8	2430
Petrol Expenses at Year 9	2687		Petrol Expenses at Year 9	2430
Petrol Expenses at Year 10	2808		Petrol Expenses at Year 10	2430
Cost of capital	5.00%		Cost of capital	5.00%
Present value of cash flows	₹ 17,618.07		Present value of cash flows	₹ 18,763.82
Total Outflow = Cost of car + Cost of Petrol	₹ 34,618.07		Total Outflow = Cost of car + Cost of Petrol	₹ 34,263.82