Question

Consider a factory that must have an air cleaner that is mandated by law. There are two choices:

• The “Cadillac cleaner” costs $4,000 today, has annual (after-tax) operating costs of $100, and

lasts 10 years.

• The “Cheapskate cleaner” costs $1,000 today, has annual (after-tax) operating costs of $500,

and lasts 5 years.

• the after-tax salvage value of “Cadillac Cleaner” is $500, and the after-tax salvage value of

“Cheapskate Cleaner” is also $500.

Assuming a 10% discount rate, which cleaner should we choose? Please show the timeline of cashflows for each machine and also show the equations used in the computation.

Answer 1

As the expected lives of the 2 options are considerably different, we need to use special methods to compare these options. Two such methods are the replacement chain adjustment & the equivalent annual annuity method. The solution given below uses the replacement chain adjustment in which the cash flows show replacement of cleaner 2 in the 5th year. The cashflows for Cleaner 1 (Cadillac) do not require any adjustment (being the longer life of the 2)

The relevant cash flows & NPV calculations will be as shown below (Formulas shown in next screenshot)

Formulas used:

The timeline for Cadillac cleaner will look like:

The timeline for cheapskate cleaner will look like:

As the NPV of Cheapstake cleaner is higher than the Cadillac cleaner, it implies that Cheapskate cleaner is a more cost effective option between these 2 so it should be used.