Question

PLEASE ANSWER WITHOUT EXCEL

A hotel is looking to replace its outdated alarm system to comply with safety standards. It has two options: System A costs $35,000 and lasts nine years. System B costs $22,000 and lasts six years. Maintenance throughout the year will cost $2,000 for System A and $3000 for System B, recognized at the end of each year. The hotel’s cost of capital is 10%. Which alarm system should the hotel choose? (Please Show work and explain answer)

Answer 1

Answer:

Given

System A

Initial cost I=$35000

Annual Maintenance M=$2000

N=9

r=10%

Annual Equivalent cost = Annual equivalent for initial cost for 9 years + Annual Maintenance

Annual Equivalent cost =I*r/(1-(1+r)^-N)+M=35000*10%/(1-(1+10%)^-9)+2000

Annual Equivalent cost =$8077.42 Eq 1

System B

Initial cost I=$22000

Annual Maintenance M=$3000

N=6

r=10%

Annual Equivalent cost = Annual equivalent for initial cost for 6 years + Annual Maintenance

Annual Equivalent cost =I*r/(1-(1+r)^-N)+M=22000*10%/(1-(1+10%)^-6)+3000

Annual Equivalent cost =$8051.36 Eq 2

So from equation 1 and 2 we find that system B has less annual equivalent cost than System A so we will choose system B.