Question

ou are trying to pick the least-expensive car for your new delivery service. You have two choices: the Scion xA, which will cost $20,500 to purchase and which will have OCF of –$2,500 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $29,000 to purchase and which will have OCF of –$1,300 annually throughout that vehicle’s expected 4-year life. Both cars will be worthless at the end of their life. You intend to replace whichever type of car you choose with the same thing when its life runs out, again and again out into the foreseeable future.     

If the business has a cost of capital of 11 percent, calculate the EAC. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

     

Scion's EAC	$
Toyota's EAC	$

Answer 1

	Calculation of EAC(Effective Annualised Cost)
	Annuity Factor of $1 @11% for 3 Years			=(1/1.11^3)+(1/1.11^2)+(1/1.11)		$           2.44
	Annuity Factor of $1 @11% for 4 Years			=(1/1.11^4)+(1/1.11^3)+(1/1.11^2)+(1/1.11)		$           3.10
		For Scion xA
	Year	Amount	PVF@11%	Present Value
	0	$ -20,500.00	1	$         -20,500.00
	1	$ -2,500.00	0.90	$           -2,252.25
	2	$ -2,500.00	0.81	$           -2,029.06
	3	$ -2,500.00	0.73	$           -1,827.98
		TOTAL		$         -26,609.29
		Effective Annualised Cost(EAC)		=PresentValue/Annuity Factor
		Effective Annualised Cost(EAC)		=-26609.29/2.44
				$         -10,888.87
		For Toyota Prius
	Year	Amount	PVF@11%	Present Value
	0	$ -29,000.00	1	$ -29,000.00
	1	$ -1,300.00	0.90	$           -1,171.17
	2	$ -1,300.00	0.81	$           -1,055.11
	3	$ -1,300.00	0.73	$ -950.55
	4	$ -1,300.00	0.66	$ -856.35
		TOTAL		$         -33,033.18
		Effective Annualised Cost(EAC)		=-33033.18/3.10
				$         -10,647.46
		EAC
		For Scion xA		$         -10,888.87
		For Toyota Prius		$         -10,647.46
		Since Toyota Prius has lower EAC, hence the company should opt for this.