Question

A recent college grad is trying to decide whether he should keep his presently owned car or purchase a new one. A new car will cost $26,000 and have annual operation and maintenance costs of $1200 per year with an $8000 salvage value in 5 years, which is its economic service life. The presently owned car has a resale value now of $5000; 1 year from now it will be $3000, 2 years from now $2500, and 3 years from now $2200. Its operating cost is expected to be $1900 during the first year, with costs increasing by $200 per year. The presently owned car will definitely not be kept longer than 3 more years. Should the presently owned car be sold now? Use annual worth calculations at i=10% per year

Some solution hints given :

AEC for challenger= 26000 (A/P, 10%, 5) + 1200 – 8000 (P/F, 10%, 5) = 6478.35 To find the economic service life for defender, calculate AEC for
n=1: 5000(A/P, 10%, 1) – 3000 + 1900 = 4400

n=2: 5000(A/P, 10%, 2) – 2500 (A/F, 10%, 2) + 1900 + 200 (A/G, 10%, 2) = 3685.74
n=3: 5000(A/P, 10%, 3) – 2200 (A/F, 10%, 3) + 1900 + 200 (A/G, 10%, 3) = 3433.2
AEC is minimized for the defender when n=3. The economic service life for defender is 3 years. Since 3433.2 < 6478.35, the defender must be kept. The current car should not be sold now.

The above solution provides that the current car should not be sold now. It must be kept for at least 3 years. What should be done after year 3? That is, should it be sold at the end of year 3? Or, should it be kept for one more year until the end of year 4? Conduct marginal analysis to answer this question based on the additional information given below.

• Market value of the current car at the end of year 4: $2000

• Operating cost for the current car during year 4: $6000

Answer 1

Option 1		Sell Now
		Particulars	0	1	2	3	4	5
		Purchase new car	26000
		AMC		1200	1200	1200	1200	1200
		Salvage Value						-8000
		Resale of Old Car	-5000
		Net Cash Outflow	21000	1200	1200	1200	1200	-6800
		PVF @ 10%	1	0.909091	0.826446	0.751315	0.683013	0.620921
		PV of Cash Outflow	21000	1090.909	991.7355	901.5778	819.6161	-4222.26
		Total PV	20581.57
	Divide by	PVAF( 10%,5)	3.790787
		Annualised Cost	5429.367
Option 2		Sell After 1 year
		Particulars	0	1	2	3	4	5	6
		Purchase new car		26000
		AMC		1900	1200	1200	1200	1200	1200
		Salvage Value							-8000
		Resale of Old Car		-3000
		Net Cash Outflow		24900	1200	1200	1200	1200	-6800
		PVF @ 10%	1	0.909091	0.826446	0.751315	0.683013	0.620921	0.564474
		PV of Cash Outflow		22636.36	991.7355	901.5778	819.6161	745.1056	-3838.42
		Total PV	22255.98
	Divide by	PVAF( 10%,6)	4.355261
		Annualised Cost	5110.136
Option 3		Sell After 2 year
		Particulars	0	1	2	3	4	5	6	7
		Purchase new car			26000
		AMC		1900	2100	1200	1200	1200	1200	1200
		Salvage Value								-8000
		Resale of Old Car			-2500
		Net Cash Outflow		1900	25600	1200	1200	1200	1200	-6800
		PVF @ 10%	1	0.909091	0.826446	0.751315	0.683013	0.620921	0.564474	0.513158
		PV of Cash Outflow		1727.273	21157.02	901.5778	819.6161	745.1056	677.3687	-3489.48
		Total PV	22538.49
	Divide by	PVAF( 10%,7)	4.868419
		Annualised Cost	4629.53
Option 4		Sell After 3 year
		Particulars	0	1	2	3	4	5	6	7	8
		Purchase new car				26000
		AMC		1900	2100	2300	1200	1200	1200	1200	1200
		Salvage Value									-8000
		Resale of Old Car				-2200
		Net Cash Outflow		1900	2100	26100	1200	1200	1200	1200	-6800
		PVF @ 10%	1	0.909091	0.826446	0.751315	0.683013	0.620921	0.564474	0.513158	0.466507
		PV of Cash Outflow		1727.273	1735.537	19609.32	819.6161	745.1056	677.3687	615.7897	-3172.25
		Total PV	22757.76
	Divide by	PVAF( 10%,8)	5.334926
		Annualised Cost	4265.805
		CONCLUSION
		Since, Annualised cost is least in option 4, he should sell car after 3 years.