Question

A firm is considering replacing the existing industrial air conditioning unit. They will pick one of two units. The first, the AC360, costs $26,456.00 to install, $5,136.00 to operate per year for 7 years at which time it will be sold for $6,888.00. The second, RayCool 8, costs $41,798.00 to install, $2,013.00 to operate per year for 5 years at which time it will be sold for $8,968.00. The firm’s cost of capital is 6.80%. What is the equivalent annual cost of the RayCool8? Assume that there are no taxes .

Answer 1

Equivalent annual cost of the RayCool8	=	Annual value of initial cost	+	Annual operating cost	-	Annual value of selling price
	=	$ 10,139.61	+	$ 2,013.00	-	$ 1,565.69
	=	$ 10,586.92
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.0680)^-5)/0.0680		i	=	6.80%
	=	4.12224808		n	=	5
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.0680)^5)-1)/0.0680		i	=	6.80%
	=	5.72783354		n	=	5
Equivalent annual value of initial cost	=	Initial cost	/	Present value of annuity of 1
	=	$ 41,798.00	/	4.1222481
	=	$ 10,139.61
Equivalent annual value of selling value	=	Selling value	/	Future value of annuity of 1
	=	$   8,968.00	/	5.7278335
	=	$   1,565.69