Question

Salt Line Co needs a specific equipment for their desalination project and it has received two quotes.

Under first quote the initial manufacturing costs are $100,000, which will be followed by servicing costs of $3,000 a year at the end of each of the next three years. At the end of third year Salt Line will have to replace the equipment.

Under second quote, the initial manufacturing costs are $90,000, which will be followed by servicing costs of $8,000 a year at the end of Year 1, $9,000 at the end of Year 2, and $10,000 at the end of each of Years 3 and 4. At the end of fourth year Salt Line will have to replace the equipment.

The discount rate is 9%. Ignore depreciation and taxes. Calculate the annual equivalent cost (AEC) of each and explain which quote Salt Line should accept.

Answer 1

NPV of costs of first quote = 100,000 + 3,000*PVAF(9%, 3 years)

= 100,000 + 3,000*2.53129

= $107,593.88

annual equivalent cost = NPV/PVAF(9%, 3 years)

= 107,593.88/2.53129

= $42,505.55

NPV of costs of Second quote = 90,000 + 8,000*PVF(9%, 1 year) + 9,000*PVF(9%, 2years) + 10,000*PVF(9%, 3 years) + 10,000*PVF(9%, 4 years)

= 90,000 + 8,000*0.9174 + 9,000*0.8417 + 10,000*0.7722 + 10,000*0.7084

= $119,720.5

annual equivalent cost = NPV/PVAF(9%, 4 years)

= 119,720.5/3.23972

= $36,953.97

Since AEC of second quote is lower, Salt Line should accept second quote