A janitorial services firm is considering two brands of industrial vacuum cleaners to equip their staff. Option A will cost $1,500, require servicing of $200 per year, and it will last five years. Option B will cost $1,000, require servicing of $100 per year, and it will last three years. If the cost of capital is 8%, which is the better option, given that the firm has an ongoing requirement for vacuum cleaners?

The correct answer is Option (B).

Explanation:

According to the scenario, the given data are as follows:

For option (A)

Cost = $1,500

Cost of capital = 8%

Servicing cost = $200

Life period = 5 years

So, we can calculate equivalent annual annuity by using following method:

Equivalent annual annuity =  [$1,500 + ($200 x PVIFA8%,5)] ÷ PVIFA8%,5

By putting the value, we get ( refer to the PVIFA table)

= [$1,500 + ( $200 × 3.9927)] ÷ 3.9927

= $575.68

For option (B)

Cost = $1,000

Cost of capital = 8%

Servicing cost = $100

Life period = 3 years

So, we can calculate equivalent annual annuity by using following method:

Equivalent annual annuity =  [$1,000 + ($100 x PVIFA8%,3)] ÷ PVIFA8%,3

By putting the value, we get ( refer to the PVIFA table)

= [$1,000 + ( $100 × 2.5771)] ÷ 2.5771

= $488.03

So, option B is the better option because it has less equivalent annual annuity than option A.

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