Question

You need a new oven for your bakery. Your current oven is worn out so you are trying to decide which one of two ovens to buy as a replacement. Whichever oven you purchase will be replaced after its useful life. Oven A costs $25,000 and costs $3,000 a year to operate over an 8-year life. Oven B costs $20,000 and costs $4,500 a year to operate over a 6-year life. Given this information, which one of the following statements is correct if the applicable discount rate is 10 percent? A) The equivalent annual cost of oven A is -$7,481. B) The equivalent annual cost of oven B is -$8,209. C) Oven A lowers the annual cost by $1,406 as compared to oven B. D) Oven B lowers the annual cost by $1,598 as compared to oven A.

why choose c here

Answer 1

C) Oven A lowers the annual cost by $1,406 as compared to oven B.

Working:

Equiavlent annual cost			=	(Initial cost/cumulative discount factor)+Annual cost
a.
Equivalent annual cost of Oven A				=	(-25000/5.3349)+(-)3000
				=	$       -7,686
Working:
Cumulative discount factor				=	(1-(1+i)^-n)/i		Where,
				=	(1-(1+0.10)^-8)/0.10		i	10%
				=	5.3349		n	8
b.
Equivalent annual cost of Oven B				=	(-20000/4.3553)+(-)4500
				=	$       -9,092
Working:
Cumulative discount factor				=	(1-(1+i)^-n)/i		Where,
				=	(1-(1+0.10)^-6)/0.10		i	10%
				=	4.3553		n	6
c.
Change in Equivalent annual cost				=	$       -9,092	-	$   -7,686
				=	$       -1,406
So, Oven A lowers the annual cost by $1,406 as compared to oven B