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You are considering two home security companies for your new house. The first company offers free installation and equipment, but will charge you $401.00 per year forever. The second company charges $783.00 for installation, but will charge you $204.00 per year forever. Assume that payments are at the END of the year. Your personal interest rate is 5.00% per year, and you want to evaluate each proposal. What is the present value (PV) of the free installation?

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Answer:

The second option is the cheapest.

Explanation:

Giving the following information:

The first company offers free installation and equipment, but will charge you $401.00 per year forever. The second company charges $783.00 for installation, but will charge you $204.00 per year forever. Assume that payments are at the END of the year. Your personal interest rate is 5.00% per year

To calculate the present value, we need to use the formula for a perpetual annuity:

PV= Cf/i

Cf= cash flow

i= interest rate

Option 1:

PV= 401/0.05= $8,020

Option 2:

PV= 204/0.05 + 783/1.05= $4,825.71

The second option is the cheapest.

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