a) You are trying to choose between purchasing one of two machines for a factory

Question

a) You are trying to choose between purchasing one of two machines for a factory. Machine A costs $15,396.00 to purchase and has a 3.00 year life. Machine B costs $19,419.00 to purchase but has a 5.00 year life. Regardless of which machine you purchase, it will have to be replaced at the end of its operating life. Which machine should you choose and what is the cost TODAY of running the machine for the next 28.00 years? Assume a discount rate of 14.00 percent.

b) A lawn service company uses a low-end mower for their yards. The mower costs $2,000.00 initially, and then has an annual cost of $300.00 for gasoline and servicing. The company uses the mower for three years and then replaces with an identical model. The company has a 12.00% desired return on their investments. What is the NPV of one mower for the firm over 3 years?(express as a negative)

Explanation / Answer

a) Initial cost of machine A = $15,396.00

Life of Machine A = 3 years

Equivalent annual cost (or EAC) is the cost per year of owning, operating, and maintaining an asset over its lifetime.

Equivalent annual cost of Machine A = Initial Cost / cdf(14% 3years) = 15,396 / 2.3216 = $6632

Initial cost of machine B = $19,419

Life of Machine B = 5 years

Equivalent annual cost of Machine B = Initial Cost / cdf(14% 5years) = $19,419 / 3.4331= $5,656

Since equivalent annual cost of Machine B is lower, it is preferable to use machine B over machine A

Which machine should you choose and what is the cost TODAY of running the machine for the next 28.00 years?

Since we need to calculate cost of running machine today for next 28 year, it is prefereble to use Machine B for 25 years since it is more economical to use machine B. However we must use machine A for last 3 years since machine B has life of 5 years and we have to incurr entire cost of $19,419 for using it for 3 years. Thus it is better to use Machine A for last 3 years as it costs only $15,396.

COST TODAY = P/V of using machine B for 25 years + P/V of using machine A for last 3 years

=EACB x cdf(14%,25 years) + Cost of Machine A x df(14%,25 years)

{why df 25 years for Machine A? because cost is to be incurred after 25 years}

=$5,656 x 6.8729 + $15,396 x 0.0378

=$38,873 + $582

$39,455

a) Initial cost = -$2,000

annual cost = -$300

NPV of one mower = 2000 + 300 x cdf(12%,3years) = 2000 + 300 x 2.4018 = -$2,721

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