Question

A consulting engineering firm’s CFO wants to purchase either Ford Explorers or Toyota 4Runners for company principals. The two models under consideration cost $30,900 for the Ford and $36,400 for the Toyota. When considering life-cycle costs, the AOC of the Explorer is expected to be $600 per year more than that of the 4Runner. The trade-in values after 3 years are estimated to be 50% of the first cost for the Explorer and 60% for the 4Runner. (a) What is the incremental ROR between the two vehicles? (b) Provided the firm’s MARR is 18% per year, which vehicle should it buy? using spreadsheet

Answer 1

Given Data:

Let x be the Annual Operating Cost for Toyota 4Runners:

	Ford Explorers	Toyota 4Runners
Cost of Vehicle	30900	36400
Annual Operating Charges	600 + x	x
Trade In (Salvage Value after 3 years)	15450	21840

Salvage value is calculated by 50% of Ford Explorers & 60% of Toyota 4Runners (given)

Cost Structure Year-Wise: (Negative sign means money outfolw and positive sign is money inflow)

Cost (Year Wise)	Ford Explorers	Toyota 4Runners
Year 0	-30900	-36400
Year 1	-(600 + x)	-x
Year 2	-(600 + x)	-x
Year 3	-(600 + x)	-x
Year 3	15450	21840

Incremental Cost: (Cost of Ford Explorers - Cost of Toyota 4Runners)

Cost (Year Wise)	Incremental Cost
Year 0	5500
Year 1	-600
Year 2	-600
Year 3	-6990

For Year 3, annual aperating cost and salvage value is added.

Positive sign denotes savings and negative sign denotes cost.

a) In spreadsheet, we can use the function IRR with array of incremental values and a random guess.

We get, the IRR = 15.5450%

b)

Let's find the PW of incremental cost using MARR = 18%

Year	C= Incremental Cost	k = (1+ MARR)^Year	j= 1/k	S = C*j
0	5500	1	1	5500
1	-600	1.18	0.847458	-508.475
2	-600	1.3924	0.718184	-430.911
3	-6990	1.643032	0.608631	-4254.33
			SUM	306.285

SUM is the present value of incremental cost.

Since the present value is positive, means the investment is economic i.e. it is better to invest in Ford Explorers over Toyota 4Runners.