Question

Two incinerators are being considered by a waste management company. Design A has an initial cost of $2,500,000, has annual operating and maintenance costs of $800,000, and requires overhauls every 5 years at a cost of $1,250,000. Design B is more sophisticated, including computer controls; it has an initial cost of $5,750,000, has annual operating and maintenance costs of $600,000, and requires overhauls every 10 years at a cost of $3,000,000. Using a 5 percent/year interest rate, determine the capitalized cost for each design and recommend which should be chosen.

Answer 1

Answer: please refer to the explanation section

Explanation:

Design A

Initial cost $2500 000

operating and maintenance cost = $800 000

Overhauls = $1250000 in 5 years

R = 5%

PV= overhaul cost/(1+r)^n + maintenance cost(1 -(1+r)^-5)/r

PV = 1250000/(1 + 0.05)^5  + 800000(1 - (1 + 0.05)^-5)/0.05

PV = 979407.71 + 3463581.34 = 4442989.05

costs to be capitalized = present value of overhaul costs = 979407. 71

Design A will be valued at = 2500000 +  979407. 71 = 347907.71

Total cost of Choosing Design A = 979407.71 + 3463581.34 + 2500000

Total cost of Choosing Design A = 6942989.05

Design B

initial cost = $5750000

Operating and Maintenance = $600000

Overhauls = $3000000 in 10 years

PV= overhaul cost/(1+r)^n + maintenance cost(1 -(1+r)^-5)/r

PV = 3000000/(1 + 0.05)^10  + 600000(1 - (1 + 0.05)^-10)/0.05

PV = 1841739.76 + 4633040.96 = 6474780.72

Cost to be capitalized = overhaul cost = 1841739.76

Design B will be value at = 1841739.76 + 5750000 = 7591739.76

Total cost of costs Design B = 1841739.76 + 5750000 + 4633040.96

Total cost of costs Design B = 12224780.72

Design B involves more costs than Design A. Present value for total cost for choosing Design B is Higher than the present value for Total costs of choosing Design A

Choose Design A